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PLATINUM: Semi-Supervised Model Agnostic Meta-Learning using Submodular Mutual Information
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Few-shot classification (FSC) requires training models using a few (typically one to five) data points per class. Meta-learning has proven to be able to learn a parametrized model for FSC by training on various other classification tasks. In this work, we propose PLATINUM (semi-suPervised modeL Agnostic meTa learnIng usiNg sUbmodular Mutual information ), a novel semi-supervised model agnostic meta learning framework that uses the submodular mutual in- formation (SMI) functions to boost the perfor- mance of FSC. PLATINUM leverages unlabeled data in the inner and outer loop using SMI func- tions during meta-training and obtains richer meta- learned parameterizations. We study the per- formance of PLATINUM in two scenarios - 1) where the unlabeled data points belong to the same set of classes as the labeled set of a cer- tain episode, and 2) where there exist out-of- distribution classes that do not belong to the la- beled set. We evaluate our method on various settings on the miniImageNet, tieredImageNet and CIFAR-FS datasets. Our experiments show that PLATINUM outperforms MAML and semi- supervised approaches like pseduo-labeling for semi-supervised FSC, especially for small ratio of labeled to unlabeled samples.
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Changbin Li, Suraj Kothawade, Feng Chen, Rishabh Iyer
| null | null | 2,022 |
icml
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Deconfounded Value Decomposition for Multi-Agent Reinforcement Learning
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Value decomposition (VD) methods have been widely used in cooperative multi-agent reinforcement learning (MARL), where credit assignment plays an important role in guiding the agents’ decentralized execution. In this paper, we investigate VD from a novel perspective of causal inference. We first show that the environment in existing VD methods is an unobserved confounder as the common cause factor of the global state and the joint value function, which leads to the confounding bias on learning credit assignment. We then present our approach, deconfounded value decomposition (DVD), which cuts off the backdoor confounding path from the global state to the joint value function. The cut is implemented by introducing the trajectory graph, which depends only on the local trajectories, as a proxy confounder. DVD is general enough to be applied to various VD methods, and extensive experiments show that DVD can consistently achieve significant performance gains over different state-of-the-art VD methods on StarCraft II and MACO benchmarks.
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Jiahui Li, Kun Kuang, Baoxiang Wang, Furui Liu, Long Chen, Changjie Fan, Fei Wu, Jun Xiao
| null | null | 2,022 |
icml
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C-MinHash: Improving Minwise Hashing with Circulant Permutation
| null |
Minwise hashing (MinHash) is an important and practical algorithm for generating random hashes to approximate the Jaccard (resemblance) similarity in massive binary (0/1) data. The basic theory of MinHash requires applying hundreds or even thousands of independent random permutations to each data vector in the dataset, in order to obtain reliable results for (e.g.,) building large-scale learning models or approximate near neighbor search. In this paper, we propose Circulant MinHash (C-MinHash) and provide the surprising theoretical results that using only two independent random permutations in a circulant manner leads to uniformly smaller Jaccard estimation variance than that of the classical MinHash with K independent permutations. Experiments are conducted to show the effectiveness of the proposed method. We also propose a more convenient C-MinHash variant which reduces two permutations to just one, with extensive numerical results to validate that it achieves essentially the same estimation accuracy as using two permutations.
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Xiaoyun Li, Ping Li
| null | null | 2,022 |
icml
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BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation
| null |
Vision-Language Pre-training (VLP) has advanced the performance for many vision-language tasks. However, most existing pre-trained models only excel in either understanding-based tasks or generation-based tasks. Furthermore, performance improvement has been largely achieved by scaling up the dataset with noisy image-text pairs collected from the web, which is a suboptimal source of supervision. In this paper, we propose BLIP, a new VLP framework which transfers flexibly to both vision-language understanding and generation tasks. BLIP effectively utilizes the noisy web data by bootstrapping the captions, where a captioner generates synthetic captions and a filter removes the noisy ones. We achieve state-of-the-art results on a wide range of vision-language tasks, such as image-text retrieval (+2.7% in average recall@1), image captioning (+2.8% in CIDEr), and VQA (+1.6% in VQA score). BLIP also demonstrates strong generalization ability when directly transferred to video-language tasks in a zero-shot manner. Code and models are available at https://github.com/salesforce/BLIP.
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Junnan Li, Dongxu Li, Caiming Xiong, Steven Hoi
| null | null | 2,022 |
icml
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Achieving Fairness at No Utility Cost via Data Reweighing with Influence
| null |
With the fast development of algorithmic governance, fairness has become a compulsory property for machine learning models to suppress unintentional discrimination. In this paper, we focus on the pre-processing aspect for achieving fairness, and propose a data reweighing approach that only adjusts the weight for samples in the training phase. Different from most previous reweighing methods which usually assign a uniform weight for each (sub)group, we granularly model the influence of each training sample with regard to fairness-related quantity and predictive utility, and compute individual weights based on influence under the constraints from both fairness and utility. Experimental results reveal that previous methods achieve fairness at a non-negligible cost of utility, while as a significant advantage, our approach can empirically release the tradeoff and obtain cost-free fairness for equal opportunity. We demonstrate the cost-free fairness through vanilla classifiers and standard training processes, compared to baseline methods on multiple real-world tabular datasets. Code available at https://github.com/brandeis-machine-learning/influence-fairness.
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Peizhao Li, Hongfu Liu
| null | null | 2,022 |
icml
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MetAug: Contrastive Learning via Meta Feature Augmentation
| null |
What matters for contrastive learning? We argue that contrastive learning heavily relies on informative features, or “hard” (positive or negative) features. Early works include more informative features by applying complex data augmentations and large batch size or memory bank, and recent works design elaborate sampling approaches to explore informative features. The key challenge toward exploring such features is that the source multi-view data is generated by applying random data augmentations, making it infeasible to always add useful information in the augmented data. Consequently, the informativeness of features learned from such augmented data is limited. In response, we propose to directly augment the features in latent space, thereby learning discriminative representations without a large amount of input data. We perform a meta learning technique to build the augmentation generator that updates its network parameters by considering the performance of the encoder. However, insufficient input data may lead the encoder to learn collapsed features and therefore malfunction the augmentation generator. A new margin-injected regularization is further added in the objective function to avoid the encoder learning a degenerate mapping. To contrast all features in one gradient back-propagation step, we adopt the proposed optimization-driven unified contrastive loss instead of the conventional contrastive loss. Empirically, our method achieves state-of-the-art results on several benchmark datasets.
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Jiangmeng Li, Wenwen Qiang, Changwen Zheng, Bing Su, Hui Xiong
| null | null | 2,022 |
icml
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High Probability Guarantees for Nonconvex Stochastic Gradient Descent with Heavy Tails
| null |
Stochastic gradient descent (SGD) is the workhorse in modern machine learning and data-driven optimization. Despite its popularity, existing theoretical guarantees for SGD are mainly derived in expectation and for convex learning problems. High probability guarantees of nonconvex SGD are scarce, and typically rely on “light-tail” noise assumptions and study the optimization and generalization performance separately. In this paper, we develop high probability bounds for nonconvex SGD with a joint perspective of optimization and generalization performance. Instead of the light tail assumption, we consider the gradient noise following a heavy-tailed sub-Weibull distribution, a novel class generalizing the sub-Gaussian and sub-Exponential families to potentially heavier-tailed distributions. Under these complicated settings, we first present high probability bounds with best-known rates in general nonconvex learning, then move to nonconvex learning with a gradient dominance curvature condition, for which we improve the learning guarantees to fast rates. We further obtain sharper learning guarantees by considering a mild Bernstein-type noise condition. Our analysis also reveals the effect of trade-offs between the optimization and generalization performance under different conditions. In the last, we show that gradient clipping can be employed to remove the bounded gradient-type assumptions. Additionally, in this case, the stepsize of SGD is completely oblivious to the knowledge of smoothness.
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Shaojie Li, Yong Liu
| null | null | 2,022 |
icml
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CerDEQ: Certifiable Deep Equilibrium Model
| null |
Recently, certifiable robust training methods via bound propagation have been proposed for training neural networks with certifiable robustness guarantees. However, no neural architectures with regular convolution and linear layers perform better in the certifiable training than the plain CNNs, since the output bounds for the deep explicit models increase quickly as their depth increases. And such a phenomenon significantly hinders certifiable training. Meanwhile, the Deep Equilibrium Model (DEQ) is more representative and robust due to their equivalent infinite depth and controllable global Lipschitz. But no work has been proposed to explore whether DEQ can show advantages in certified training. In this work, we aim to tackle the problem of DEQ’s certified training. To obtain the output bound based on the bound propagation scheme in the implicit model, we first involve the adjoint DEQ for bound approximation. Furthermore, we also use the weight orthogonalization method and other tricks specified for DEQ to stabilize the certifiable training. With our approach, we can obtain the certifiable DEQ called CerDEQ. Our CerDEQ can achieve state-of-the-art performance compared with models using regular convolution and linear layers on $\ell_\infty$ tasks with $\epsilon=8/255$: $64.72%$ certified error for CIFAR-$10$ and $94.45%$ certified error for Tiny ImageNet.
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Mingjie Li, Yisen Wang, Zhouchen Lin
| null | null | 2,022 |
icml
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PMIC: Improving Multi-Agent Reinforcement Learning with Progressive Mutual Information Collaboration
| null |
Learning to collaborate is critical in Multi-Agent Reinforcement Learning (MARL). Previous works promote collaboration by maximizing the correlation of agents’ behaviors, which is typically characterized by Mutual Information (MI) in different forms. However, we reveal sub-optimal collaborative behaviors also emerge with strong correlations, and simply maximizing the MI can, surprisingly, hinder the learning towards better collaboration. To address this issue, we propose a novel MARL framework, called Progressive Mutual Information Collaboration (PMIC), for more effective MI-driven collaboration. PMIC uses a new collaboration criterion measured by the MI between global states and joint actions. Based on this criterion, the key idea of PMIC is maximizing the MI associated with superior collaborative behaviors and minimizing the MI associated with inferior ones. The two MI objectives play complementary roles by facilitating better collaborations while avoiding falling into sub-optimal ones. Experiments on a wide range of MARL benchmarks show the superior performance of PMIC compared with other algorithms.
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Pengyi Li, Hongyao Tang, Tianpei Yang, Xiaotian Hao, Tong Sang, Yan Zheng, Jianye Hao, Matthew E. Taylor, Wenyuan Tao, Zhen Wang
| null | null | 2,022 |
icml
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Restarted Nonconvex Accelerated Gradient Descent: No More Polylogarithmic Factor in the $O(ε^-7/4)$ Complexity
| null |
This paper studies the accelerated gradient descent for general nonconvex problems under the gradient Lipschitz and Hessian Lipschitz assumptions. We establish that a simple restarted accelerated gradient descent (AGD) finds an $\epsilon$-approximate first-order stationary point in $O(\epsilon^{-7/4})$ gradient computations with simple proofs. Our complexity does not hide any polylogarithmic factors, and thus it improves over the state-of-the-art one by the $O(\log\frac{1}{\epsilon})$ factor. Our simple algorithm only consists of Nesterov’s classical AGD and a restart mechanism, and it does not need the negative curvature exploitation or the optimization of regularized surrogate functions. Technically, our simple proof does not invoke the analysis for the strongly convex AGD, which is crucial to remove the $O(\log\frac{1}{\epsilon})$ factor.
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Huan Li, Zhouchen Lin
| null | null | 2,022 |
icml
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Difference Advantage Estimation for Multi-Agent Policy Gradients
| null |
Multi-agent policy gradient methods in centralized training with decentralized execution recently witnessed many progresses. During centralized training, multi-agent credit assignment is crucial, which can substantially promote learning performance. However, explicit multi-agent credit assignment in multi-agent policy gradient methods still receives less attention. In this paper, we investigate multi-agent credit assignment induced by reward shaping and provide a theoretical understanding in terms of its credit assignment and policy bias. Based on this, we propose an exponentially weighted advantage estimator, which is analogous to GAE, to enable multi-agent credit assignment while allowing the tradeoff with policy bias. Empirical results show that our approach can successfully perform effective multi-agent credit assignment, and thus substantially outperforms other advantage estimators.
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Yueheng Li, Guangming Xie, Zongqing Lu
| null | null | 2,022 |
icml
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Let Invariant Rationale Discovery Inspire Graph Contrastive Learning
| null |
Leading graph contrastive learning (GCL) methods perform graph augmentations in two fashions: (1) randomly corrupting the anchor graph, which could cause the loss of semantic information, or (2) using domain knowledge to maintain salient features, which undermines the generalization to other domains. Taking an invariance look at GCL, we argue that a high-performing augmentation should preserve the salient semantics of anchor graphs regarding instance-discrimination. To this end, we relate GCL with invariant rationale discovery, and propose a new framework, Rationale-aware Graph Contrastive Learning (RGCL). Specifically, without supervision signals, RGCL uses a rationale generator to reveal salient features about graph instance-discrimination as the rationale, and then creates rationale-aware views for contrastive learning. This rationale-aware pre-training scheme endows the backbone model with the powerful representation ability, further facilitating the fine-tuning on downstream tasks. On MNIST-Superpixel and MUTAG datasets, visual inspections on the discovered rationales showcase that the rationale generator successfully captures the salient features (\ie distinguishing semantic nodes in graphs). On biochemical molecule and social network benchmark datasets, the state-of-the-art performance of RGCL demonstrates the effectiveness of rationale-aware views for contrastive learning. Our codes are available at https://github.com/lsh0520/RGCL.
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Sihang Li, Xiang Wang, An Zhang, Yingxin Wu, Xiangnan He, Tat-Seng Chua
| null | null | 2,022 |
icml
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Private Adaptive Optimization with Side information
| null |
Adaptive optimization methods have become the default solvers for many machine learning tasks. Unfortunately, the benefits of adaptivity may degrade when training with differential privacy, as the noise added to ensure privacy reduces the effectiveness of the adaptive preconditioner. To this end, we propose AdaDPS, a general framework that uses non-sensitive side information to precondition the gradients, allowing the effective use of adaptive methods in private settings. We formally show AdaDPS reduces the amount of noise needed to achieve similar privacy guarantees, thereby improving optimization performance. Empirically, we leverage simple and readily available side information to explore the performance of AdaDPS in practice, comparing to strong baselines in both centralized and federated settings. Our results show that AdaDPS improves accuracy by 7.7% (absolute) on average—yielding state-of-the-art privacy-utility trade-offs on large-scale text and image benchmarks.
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Tian Li, Manzil Zaheer, Sashank Reddi, Virginia Smith
| null | null | 2,022 |
icml
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Generalization Guarantee of Training Graph Convolutional Networks with Graph Topology Sampling
| null |
Graph convolutional networks (GCNs) have recently achieved great empirical success in learning graph-structured data. To address its scalability issue due to the recursive embedding of neighboring features, graph topology sampling has been proposed to reduce the memory and computational cost of training GCNs, and it has achieved comparable test performance to those without topology sampling in many empirical studies. To the best of our knowledge, this paper provides the first theoretical justification of graph topology sampling in training (up to) three-layer GCNs for semi-supervised node classification. We formally characterize some sufficient conditions on graph topology sampling such that GCN training leads to diminishing generalization error. Moreover, our method tackles the non-convex interaction of weights across layers, which is under-explored in the existing theoretical analyses of GCNs. This paper characterizes the impact of graph structures and topology sampling on the generalization performance and sample complexity explicitly, and the theoretical findings are also justified through numerical experiments.
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Hongkang Li, Meng Wang, Sijia Liu, Pin-Yu Chen, Jinjun Xiong
| null | null | 2,022 |
icml
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Permutation Search of Tensor Network Structures via Local Sampling
| null |
Recent works put much effort into tensor network structure search (TN-SS), aiming to select suitable tensor network (TN) structures, involving the TN-ranks, formats, and so on, for the decomposition or learning tasks. In this paper, we consider a practical variant of TN-SS, dubbed TN permutation search (TN-PS), in which we search for good mappings from tensor modes onto TN vertices (core tensors) for compact TN representations. We conduct a theoretical investigation of TN-PS and propose a practically-efficient algorithm to resolve the problem. Theoretically, we prove the counting and metric properties of search spaces of TN-PS, analyzing for the first time the impact of TN structures on these unique properties. Numerically, we propose a novel meta-heuristic algorithm, in which the searching is done by randomly sampling in a neighborhood established in our theory, and then recurrently updating the neighborhood until convergence. Numerical results demonstrate that the new algorithm can reduce the required model size of TNs in extensive benchmarks, implying the improvement in the expressive power of TNs. Furthermore, the computational cost for the new algorithm is significantly less than that in (Li and Sun, 2020).
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Chao Li, Junhua Zeng, Zerui Tao, Qibin Zhao
| null | null | 2,022 |
icml
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Hessian-Free High-Resolution Nesterov Acceleration For Sampling
| null |
Nesterov’s Accelerated Gradient (NAG) for optimization has better performance than its continuous time limit (noiseless kinetic Langevin) when a finite step-size is employed (Shi et al., 2021). This work explores the sampling counterpart of this phenonemon and proposes a diffusion process, whose discretizations can yield accelerated gradient-based MCMC methods. More precisely, we reformulate the optimizer of NAG for strongly convex functions (NAG-SC) as a Hessian-Free High-Resolution ODE, change its high-resolution coefficient to a hyperparameter, inject appropriate noise, and discretize the resulting diffusion process. The acceleration effect of the new hyperparameter is quantified and it is not an artificial one created by time-rescaling. Instead, acceleration beyond underdamped Langevin in $W_2$ distance is quantitatively established for log-strongly-concave-and-smooth targets, at both the continuous dynamics level and the discrete algorithm level. Empirical experiments in both log-strongly-concave and multi-modal cases also numerically demonstrate this acceleration.
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Ruilin Li, Hongyuan Zha, Molei Tao
| null | null | 2,022 |
icml
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HousE: Knowledge Graph Embedding with Householder Parameterization
| null |
The effectiveness of knowledge graph embedding (KGE) largely depends on the ability to model intrinsic relation patterns and mapping properties. However, existing approaches can only capture some of them with insufficient modeling capacity. In this work, we propose a more powerful KGE framework named HousE, which involves a novel parameterization based on two kinds of Householder transformations: (1) Householder rotations to achieve superior capacity of modeling relation patterns; (2) Householder projections to handle sophisticated relation mapping properties. Theoretically, HousE is capable of modeling crucial relation patterns and mapping properties simultaneously. Besides, HousE is a generalization of existing rotation-based models while extending the rotations to high-dimensional spaces. Empirically, HousE achieves new state-of-the-art performance on five benchmark datasets. Our code is available at https://github.com/anrep/HousE.
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Rui Li, Jianan Zhao, Chaozhuo Li, Di He, Yiqi Wang, Yuming Liu, Hao Sun, Senzhang Wang, Weiwei Deng, Yanming Shen, Xing Xie, Qi Zhang
| null | null | 2,022 |
icml
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Finding Global Homophily in Graph Neural Networks When Meeting Heterophily
| null |
We investigate graph neural networks on graphs with heterophily. Some existing methods amplify a node’s neighborhood with multi-hop neighbors to include more nodes with homophily. However, it is a significant challenge to set personalized neighborhood sizes for different nodes. Further, for other homophilous nodes excluded in the neighborhood, they are ignored for information aggregation. To address these problems, we propose two models GloGNN and GloGNN++, which generate a node’s embedding by aggregating information from global nodes in the graph. In each layer, both models learn a coefficient matrix to capture the correlations between nodes, based on which neighborhood aggregation is performed. The coefficient matrix allows signed values and is derived from an optimization problem that has a closed-form solution. We further accelerate neighborhood aggregation and derive a linear time complexity. We theoretically explain the models’ effectiveness by proving that both the coefficient matrix and the generated node embedding matrix have the desired grouping effect. We conduct extensive experiments to compare our models against 11 other competitors on 15 benchmark datasets in a wide range of domains, scales and graph heterophilies. Experimental results show that our methods achieve superior performance and are also very efficient.
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Xiang Li, Renyu Zhu, Yao Cheng, Caihua Shan, Siqiang Luo, Dongsheng Li, Weining Qian
| null | null | 2,022 |
icml
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Fat–Tailed Variational Inference with Anisotropic Tail Adaptive Flows
| null |
While fat-tailed densities commonly arise as posterior and marginal distributions in robust models and scale mixtures, they present a problematic scenario when Gaussian-based variational inference fails to accurately capture tail decay. We first improve previous theory on tails of Lipschitz flows by quantifying how they affect the rate of tail decay and expanding the theory to non-Lipschitz polynomial flows. Next, we develop an alternative theory for multivariate tail parameters which is sensitive to tail-anisotropy. In doing so, we unveil a fundamental problem which plagues many existing flow-based methods: they can only model tail-isotropic distributions (i.e., distributions having the same tail parameter in every direction). To mitigate this and enable modeling of tail-anisotropic targets, we propose anisotropic tail-adaptive flows (ATAF). Experimental results confirm ATAF on both synthetic and real-world targets is competitive with prior work while also exhibiting appropriate tail-anisotropy.
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Feynman Liang, Michael Mahoney, Liam Hodgkinson
| null | null | 2,022 |
icml
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Double Sampling Randomized Smoothing
| null |
Neural networks (NNs) are known to be vulnerable against adversarial perturbations, and thus there is a line of work aiming to provide robustness certification for NNs, such as randomized smoothing, which samples smoothing noises from a certain distribution to certify the robustness for a smoothed classifier. However, as previous work shows, the certified robust radius in randomized smoothing suffers from scaling to large datasets ("curse of dimensionality"). To overcome this hurdle, we propose a Double Sampling Randomized Smoothing (DSRS) framework, which exploits the sampled probability from an additional smoothing distribution to tighten the robustness certification of the previous smoothed classifier. Theoretically, under mild assumptions, we prove that DSRS can certify $\Theta(\sqrt d)$ robust radius under $\ell_2$ norm where $d$ is the input dimension, which implies that DSRS may be able to break the curse of dimensionality of randomized smoothing. We instantiate DSRS for a generalized family of Gaussian smoothing and propose an efficient and sound computing method based on customized dual optimization considering sampling error. Extensive experiments on MNIST, CIFAR-10, and ImageNet verify our theory and show that DSRS certifies larger robust radii than existing baselines consistently under different settings. Code is available at https://github.com/llylly/DSRS.
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Linyi Li, Jiawei Zhang, Tao Xie, Bo Li
| null | null | 2,022 |
icml
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Reducing Variance in Temporal-Difference Value Estimation via Ensemble of Deep Networks
| null |
In temporal-difference reinforcement learning algorithms, variance in value estimation can cause instability and overestimation of the maximal target value. Many algorithms have been proposed to reduce overestimation, including several recent ensemble methods, however none have shown success in sample-efficient learning through addressing estimation variance as the root cause of overestimation. In this paper, we propose MeanQ, a simple ensemble method that estimates target values as ensemble means. Despite its simplicity, MeanQ shows remarkable sample efficiency in experiments on the Atari Learning Environment benchmark. Importantly, we find that an ensemble of size 5 sufficiently reduces estimation variance to obviate the lagging target network, eliminating it as a source of bias and further gaining sample efficiency. We justify intuitively and empirically the design choices in MeanQ, including the necessity of independent experience sampling. On a set of 26 benchmark Atari environments, MeanQ outperforms all tested baselines, including the best available baseline, SUNRISE, at 100K interaction steps in 16/26 environments, and by 68% on average. MeanQ also outperforms Rainbow DQN at 500K steps in 21/26 environments, and by 49% on average, and achieves average human-level performance using 200K ($\pm$100K) interaction steps. Our implementation is available at https://github.com/indylab/MeanQ.
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Litian Liang, Yaosheng Xu, Stephen Mcaleer, Dailin Hu, Alexander Ihler, Pieter Abbeel, Roy Fox
| null | null | 2,022 |
icml
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TSPipe: Learn from Teacher Faster with Pipelines
| null |
The teacher-student (TS) framework, training a (student) network by utilizing an auxiliary superior (teacher) network, has been adopted as a popular training paradigm in many machine learning schemes, since the seminal work—Knowledge distillation (KD) for model compression and transfer learning. Many recent self-supervised learning (SSL) schemes also adopt the TS framework, where teacher networks are maintained as the moving average of student networks, called the momentum networks. This paper presents TSPipe, a pipelined approach to accelerate the training process of any TS frameworks including KD and SSL. Under the observation that the teacher network does not need a backward pass, our main idea is to schedule the computation of the teacher and student network separately, and fully utilize the GPU during training by interleaving the computations of the two networks and relaxing their dependencies. In case the teacher network requires a momentum update, we use delayed parameter updates only on the teacher network to attain high model accuracy. Compared to existing pipeline parallelism schemes, which sacrifice either training throughput or model accuracy, TSPipe provides better performance trade-offs, achieving up to 12.15x higher throughput.
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Hwijoon Lim, Yechan Kim, Sukmin Yun, Jinwoo Shin, Dongsu Han
| null | null | 2,022 |
icml
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Exploring and Exploiting Hubness Priors for High-Quality GAN Latent Sampling
| null |
Despite the extensive studies on Generative Adversarial Networks (GANs), how to reliably sample high-quality images from their latent spaces remains an under-explored topic. In this paper, we propose a novel GAN latent sampling method by exploring and exploiting the hubness priors of GAN latent distributions. Our key insight is that the high dimensionality of the GAN latent space will inevitably lead to the emergence of hub latents that usually have much larger sampling densities than other latents in the latent space. As a result, these hub latents are better trained and thus contribute more to the synthesis of high-quality images. Unlike the a posterior "cherry-picking", our method is highly efficient as it is an a priori method that identifies high-quality latents before the synthesis of images. Furthermore, we show that the well-known but purely empirical truncation trick is a naive approximation to the central clustering effect of hub latents, which not only uncovers the rationale of the truncation trick, but also indicates the superiority and fundamentality of our method. Extensive experimental results demonstrate the effectiveness of the proposed method. Our code is available at: https://github.com/Byronliang8/HubnessGANSampling.
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Yuanbang Liang, Jing Wu, Yu-Kun Lai, Yipeng Qin
| null | null | 2,022 |
icml
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Flow-Guided Sparse Transformer for Video Deblurring
| null |
Exploiting similar and sharper scene patches in spatio-temporal neighborhoods is critical for video deblurring. However, CNN-based methods show limitations in capturing long-range dependencies and modeling non-local self-similarity. In this paper, we propose a novel framework, Flow-Guided Sparse Transformer (FGST), for video deblurring. In FGST, we customize a self-attention module, Flow-Guided Sparse Window-based Multi-head Self-Attention (FGSW-MSA). For each $query$ element on the blurry reference frame, FGSW-MSA enjoys the guidance of the estimated optical flow to globally sample spatially sparse yet highly related $key$ elements corresponding to the same scene patch in neighboring frames. Besides, we present a Recurrent Embedding (RE) mechanism to transfer information from past frames and strengthen long-range temporal dependencies. Comprehensive experiments demonstrate that our proposed FGST outperforms state-of-the-art (SOTA) methods on both DVD and GOPRO datasets and yields visually pleasant results in real video deblurring. https://github.com/linjing7/VR-Baseline
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Jing Lin, Yuanhao Cai, Xiaowan Hu, Haoqian Wang, Youliang Yan, Xueyi Zou, Henghui Ding, Yulun Zhang, Radu Timofte, Luc Van Gool
| null | null | 2,022 |
icml
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Unsupervised Flow-Aligned Sequence-to-Sequence Learning for Video Restoration
| null |
How to properly model the inter-frame relation within the video sequence is an important but unsolved challenge for video restoration (VR). In this work, we propose an unsupervised flow-aligned sequence-to-sequence model (S2SVR) to address this problem. On the one hand, the sequence-to-sequence model, which has proven capable of sequence modeling in the field of natural language processing, is explored for the first time in VR. Optimized serialization modeling shows potential in capturing long-range dependencies among frames. On the other hand, we equip the sequence-to-sequence model with an unsupervised optical flow estimator to maximize its potential. The flow estimator is trained with our proposed unsupervised distillation loss, which can alleviate the data discrepancy and inaccurate degraded optical flow issues of previous flow-based methods. With reliable optical flow, we can establish accurate correspondence among multiple frames, narrowing the domain difference between 1D language and 2D misaligned frames and improving the potential of the sequence-to-sequence model. S2SVR shows superior performance in multiple VR tasks, including video deblurring, video super-resolution, and compressed video quality enhancement. https://github.com/linjing7/VR-Baseline
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Jing Lin, Xiaowan Hu, Yuanhao Cai, Haoqian Wang, Youliang Yan, Xueyi Zou, Yulun Zhang, Luc Van Gool
| null | null | 2,022 |
icml
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Learning Augmented Binary Search Trees
| null |
A treap is a classic randomized binary search tree data structure that is easy to implement and supports O(log n) expected time access. However, classic treaps do not take advantage of the input distribution or patterns in the input. Given recent advances in algorithms with predictions, we propose pairing treaps with machine advice to form a learning-augmented treap. We are the first to propose a learning-augmented data structure that supports binary search tree operations such as range-query and successor functionalities. With the assumption that we have access to advice from a frequency estimation oracle, we assign learned priorities to the nodes to better improve the treap’s structure. We theoretically analyze the learning-augmented treap’s performance under various input distributions and show that under those circumstances, our learning-augmented treap has stronger guarantees than classic treaps and other classic tree-based data structures. Further, we experimentally evaluate our learned treap on synthetic datasets and demonstrate a performance advantage over other search tree data structures. We also present experiments on real world datasets with known frequency estimation oracles and show improvements as well.
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Honghao Lin, Tian Luo, David Woodruff
| null | null | 2,022 |
icml
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Decentralized Online Convex Optimization in Networked Systems
| null |
We study the problem of networked online convex optimization, where each agent individually decides on an action at every time step and agents cooperatively seek to minimize the total global cost over a finite horizon. The global cost is made up of three types of local costs: convex node costs, temporal interaction costs, and spatial interaction costs. In deciding their individual action at each time, an agent has access to predictions of local cost functions for the next $k$ time steps in an $r$-hop neighborhood. Our work proposes a novel online algorithm, Localized Predictive Control (LPC), which generalizes predictive control to multi-agent systems. We show that LPC achieves a competitive ratio of $1 + \tilde{O}(\rho_T^k) + \tilde{O}(\rho_S^r)$ in an adversarial setting, where $\rho_T$ and $\rho_S$ are constants in $(0, 1)$ that increase with the relative strength of temporal and spatial interaction costs, respectively. This is the first competitive ratio bound on decentralized predictive control for networked online convex optimization. Further, we show that the dependence on $k$ and $r$ in our results is near optimal by lower bounding the competitive ratio of any decentralized online algorithm.
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Yiheng Lin, Judy Gan, Guannan Qu, Yash Kanoria, Adam Wierman
| null | null | 2,022 |
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Learning Multiscale Transformer Models for Sequence Generation
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Multiscale feature hierarchies have been witnessed the success in the computer vision area. This further motivates researchers to design multiscale Transformer for natural language processing, mostly based on the self-attention mechanism. For example, restricting the receptive field across heads or extracting local fine-grained features via convolutions. However, most of existing works directly modeled local features but ignored the word-boundary information. This results in redundant and ambiguous attention distributions, which lacks of interpretability. In this work, we define those scales in different linguistic units, including sub-words, words and phrases. We built a multiscale Transformer model by establishing relationships among scales based on word-boundary information and phrase-level prior knowledge. The proposed \textbf{U}niversal \textbf{M}ulti\textbf{S}cale \textbf{T}ransformer, namely \textsc{Umst}, was evaluated on two sequence generation tasks. Notably, it yielded consistent performance gains over the strong baseline on several test sets without sacrificing the efficiency.
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Bei Li, Tong Zheng, Yi Jing, Chengbo Jiao, Tong Xiao, Jingbo Zhu
| null | null | 2,022 |
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Online Nonsubmodular Minimization with Delayed Costs: From Full Information to Bandit Feedback
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Motivated by applications to online learning in sparse estimation and Bayesian optimization, we consider the problem of online unconstrained nonsubmodular minimization with delayed costs in both full information and bandit feedback settings. In contrast to previous works on online unconstrained submodular minimization, we focus on a class of nonsubmodular functions with special structure, and prove regret guarantees for several variants of the online and approximate online bandit gradient descent algorithms in static and delayed scenarios. We derive bounds for the agent’s regret in the full information and bandit feedback setting, even if the delay between choosing a decision and receiving the incurred cost is unbounded. Key to our approach is the notion of $(\alpha, \beta)$-regret and the extension of the generic convex relaxation model from \citet{El-2020-Optimal}, the analysis of which is of independent interest. We conduct and showcase several simulation studies to demonstrate the efficacy of our algorithms.
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Tianyi Lin, Aldo Pacchiano, Yaodong Yu, Michael Jordan
| null | null | 2,022 |
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Constrained Gradient Descent: A Powerful and Principled Evasion Attack Against Neural Networks
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We propose new, more efficient targeted white-box attacks against deep neural networks. Our attacks better align with the attacker’s goal: (1) tricking a model to assign higher probability to the target class than to any other class, while (2) staying within an $\epsilon$-distance of the attacked input. First, we demonstrate a loss function that explicitly encodes (1) and show that Auto-PGD finds more attacks with it. Second, we propose a new attack method, Constrained Gradient Descent (CGD), using a refinement of our loss function that captures both (1) and (2). CGD seeks to satisfy both attacker objectives—misclassification and bounded $\ell_{p}$-norm—in a principled manner, as part of the optimization, instead of via ad hoc post-processing techniques (e.g., projection or clipping). We show that CGD is more successful on CIFAR10 (0.9–4.2%) and ImageNet (8.6–13.6%) than state-of-the-art attacks while consuming less time (11.4–18.8%). Statistical tests confirm that our attack outperforms others against leading defenses on different datasets and values of $\epsilon$.
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Weiran Lin, Keane Lucas, Lujo Bauer, Michael K. Reiter, Mahmood Sharif
| null | null | 2,022 |
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Measuring the Effect of Training Data on Deep Learning Predictions via Randomized Experiments
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We develop a new, principled algorithm for estimating the contribution of training data points to the behavior of a deep learning model, such as a specific prediction it makes. Our algorithm estimates the AME, a quantity that measures the expected (average) marginal effect of adding a data point to a subset of the training data, sampled from a given distribution. When subsets are sampled from the uniform distribution, the AME reduces to the well-known Shapley value. Our approach is inspired by causal inference and randomized experiments: we sample different subsets of the training data to train multiple submodels, and evaluate each submodel’s behavior. We then use a LASSO regression to jointly estimate the AME of each data point, based on the subset compositions. Under sparsity assumptions ($k \ll N$ datapoints have large AME), our estimator requires only $O(k\log N)$ randomized submodel trainings, improving upon the best prior Shapley value estimators.
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Jinkun Lin, Anqi Zhang, Mathias Lécuyer, Jinyang Li, Aurojit Panda, Siddhartha Sen
| null | null | 2,022 |
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Delayed Reinforcement Learning by Imitation
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When the agent’s observations or interactions are delayed, classic reinforcement learning tools usually fail. In this paper, we propose a simple yet new and efficient solution to this problem. We assume that, in the undelayed environment, an efficient policy is known or can be easily learnt, but the task may suffer from delays in practice and we thus want to take them into account. We present a novel algorithm, Delayed Imitation with Dataset Aggregation (DIDA), which builds upon imitation learning methods to learn how to act in a delayed environment from undelayed demonstrations. We provide a theoretical analysis of the approach that will guide the practical design of DIDA. These results are also of general interest in the delayed reinforcement learning literature by providing bounds on the performance between delayed and undelayed tasks, under smoothness conditions. We show empirically that DIDA obtains high performances with a remarkable sample efficiency on a variety of tasks, including robotic locomotion, classic control, and trading.
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Pierre Liotet, Davide Maran, Lorenzo Bisi, Marcello Restelli
| null | null | 2,022 |
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Interactively Learning Preference Constraints in Linear Bandits
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We study sequential decision-making with known rewards and unknown constraints, motivated by situations where the constraints represent expensive-to-evaluate human preferences, such as safe and comfortable driving behavior. We formalize the challenge of interactively learning about these constraints as a novel linear bandit problem which we call constrained linear best-arm identification. To solve this problem, we propose the Adaptive Constraint Learning (ACOL) algorithm. We provide an instance-dependent lower bound for constrained linear best-arm identification and show that ACOL’s sample complexity matches the lower bound in the worst-case. In the average case, ACOL’s sample complexity bound is still significantly tighter than bounds of simpler approaches. In synthetic experiments, ACOL performs on par with an oracle solution and outperforms a range of baselines. As an application, we consider learning constraints to represent human preferences in a driving simulation. ACOL is significantly more sample efficient than alternatives for this application. Further, we find that learning preferences as constraints is more robust to changes in the driving scenario than encoding the preferences directly in the reward function.
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David Lindner, Sebastian Tschiatschek, Katja Hofmann, Andreas Krause
| null | null | 2,022 |
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StreamingQA: A Benchmark for Adaptation to New Knowledge over Time in Question Answering Models
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Knowledge and language understanding of models evaluated through question answering (QA) has been usually studied on static snapshots of knowledge, like Wikipedia. However, our world is dynamic, evolves over time, and our models’ knowledge becomes outdated. To study how semi-parametric QA models and their underlying parametric language models (LMs) adapt to evolving knowledge, we construct a new large-scale dataset, StreamingQA, with human written and generated questions asked on a given date, to be answered from 14 years of time-stamped news articles. We evaluate our models quarterly as they read new articles not seen in pre-training. We show that parametric models can be updated without full retraining, while avoiding catastrophic forgetting. For semi-parametric models, adding new articles into the search space allows for rapid adaptation, however, models with an outdated underlying LM under-perform those with a retrained LM. For questions about higher-frequency named entities, parametric updates are particularly beneficial. In our dynamic world, the StreamingQA dataset enables a more realistic evaluation of QA models, and our experiments highlight several promising directions for future research.
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Adam Liska, Tomas Kocisky, Elena Gribovskaya, Tayfun Terzi, Eren Sezener, Devang Agrawal, Cyprien De Masson D’Autume, Tim Scholtes, Manzil Zaheer, Susannah Young, Ellen Gilsenan-Mcmahon, Sophia Austin, Phil Blunsom, Angeliki Lazaridou
| null | null | 2,022 |
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CITRIS: Causal Identifiability from Temporal Intervened Sequences
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Understanding the latent causal factors of a dynamical system from visual observations is considered a crucial step towards agents reasoning in complex environments. In this paper, we propose CITRIS, a variational autoencoder framework that learns causal representations from temporal sequences of images in which underlying causal factors have possibly been intervened upon. In contrast to the recent literature, CITRIS exploits temporality and observing intervention targets to identify scalar and multidimensional causal factors, such as 3D rotation angles. Furthermore, by introducing a normalizing flow, CITRIS can be easily extended to leverage and disentangle representations obtained by already pretrained autoencoders. Extending previous results on scalar causal factors, we prove identifiability in a more general setting, in which only some components of a causal factor are affected by interventions. In experiments on 3D rendered image sequences, CITRIS outperforms previous methods on recovering the underlying causal variables. Moreover, using pretrained autoencoders, CITRIS can even generalize to unseen instantiations of causal factors, opening future research areas in sim-to-real generalization for causal representation learning.
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Phillip Lippe, Sara Magliacane, Sindy Löwe, Yuki M Asano, Taco Cohen, Stratis Gavves
| null | null | 2,022 |
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Distributionally Robust $Q$-Learning
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Reinforcement learning (RL) has demonstrated remarkable achievements in simulated environments. However, carrying this success to real environments requires the important attribute of robustness, which the existing RL algorithms often lack as they assume that the future deployment environment is the same as the training environment (i.e. simulator) in which the policy is learned. This assumption often does not hold due to the discrepancy between the simulator and the real environment and, as a result, and hence renders the learned policy fragile when deployed. In this paper, we propose a novel distributionally robust $Q$-learning algorithm that learns the best policy in the worst distributional perturbation of the environment. Our algorithm first transforms the infinite-dimensional learning problem (since the environment MDP perturbation lies in an infinite-dimensional space) into a finite-dimensional dual problem and subsequently uses a multi-level Monte-Carlo scheme to approximate the dual value using samples from the simulator. Despite the complexity, we show that the resulting distributionally robust $Q$-learning algorithm asymptotically converges to optimal worst-case policy, thus making it robust to future environment changes. Simulation results further demonstrate its strong empirical robustness.
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Zijian Liu, Qinxun Bai, Jose Blanchet, Perry Dong, Wei Xu, Zhengqing Zhou, Zhengyuan Zhou
| null | null | 2,022 |
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Constrained Variational Policy Optimization for Safe Reinforcement Learning
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Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying them to safety-critical applications. Previous primal-dual style approaches suffer from instability issues and lack optimality guarantees. This paper overcomes the issues from the perspective of probabilistic inference. We introduce a novel Expectation-Maximization approach to naturally incorporate constraints during the policy learning: 1) a provable optimal non-parametric variational distribution could be computed in closed form after a convex optimization (E-step); 2) the policy parameter is improved within the trust region based on the optimal variational distribution (M-step). The proposed algorithm decomposes the safe RL problem into a convex optimization phase and a supervised learning phase, which yields a more stable training performance. A wide range of experiments on continuous robotic tasks shows that the proposed method achieves significantly better constraint satisfaction performance and better sample efficiency than baselines. The code is available at https://github.com/liuzuxin/cvpo-safe-rl.
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Zuxin Liu, Zhepeng Cen, Vladislav Isenbaev, Wei Liu, Steven Wu, Bo Li, Ding Zhao
| null | null | 2,022 |
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Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint
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Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation theories suggest that with sufficiently many parameters, neural networks can well approximate certain classes of functions in terms of the function value. The neural network themselves, however, can be highly nonsmooth. To bridge this gap, we take convolutional residual networks (ConvResNets) as an example, and prove that large ConvResNets can not only approximate a target function in terms of function value, but also exhibit sufficient first-order smoothness. Moreover, we extend our theory to approximating functions supported on a low-dimensional manifold. Our theory partially justifies the benefits of using deep and wide networks in practice. Numerical experiments on adversarial robust image classification are provided to support our theory.
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Hao Liu, Minshuo Chen, Siawpeng Er, Wenjing Liao, Tong Zhang, Tuo Zhao
| null | null | 2,022 |
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Boosting Graph Structure Learning with Dummy Nodes
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With the development of graph kernels and graph representation learning, many superior methods have been proposed to handle scalability and oversmoothing issues on graph structure learning. However, most of those strategies are designed based on practical experience rather than theoretical analysis. In this paper, we use a particular dummy node connecting to all existing vertices without affecting original vertex and edge properties. We further prove that such the dummy node can help build an efficient monomorphic edge-to-vertex transform and an epimorphic inverse to recover the original graph back. It also indicates that adding dummy nodes can preserve local and global structures for better graph representation learning. We extend graph kernels and graph neural networks with dummy nodes and conduct experiments on graph classification and subgraph isomorphism matching tasks. Empirical results demonstrate that taking graphs with dummy nodes as input significantly boosts graph structure learning, and using their edge-to-vertex graphs can also achieve similar results. We also discuss the gain of expressive power from the dummy in neural networks.
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Xin Liu, Jiayang Cheng, Yangqiu Song, Xin Jiang
| null | null | 2,022 |
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Equivalence Analysis between Counterfactual Regret Minimization and Online Mirror Descent
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Follow-the-Regularized-Leader (FTRL) and Online Mirror Descent (OMD) are regret minimization algorithms for Online Convex Optimization (OCO), they are mathematically elegant but less practical in solving Extensive-Form Games (EFGs). Counterfactual Regret Minimization (CFR) is a technique for approximating Nash equilibria in EFGs. CFR and its variants have a fast convergence rate in practice, but their theoretical results are not satisfactory. In recent years, researchers have been trying to link CFRs with OCO algorithms, which may provide new theoretical results and inspire new algorithms. However, existing analysis is restricted to local decision points. In this paper, we show that CFRs with Regret Matching and Regret Matching+ are equivalent to special cases of FTRL and OMD, respectively. According to these equivalences, a new FTRL and a new OMD algorithm, which can be considered as extensions of vanilla CFR and CFR+, are derived. The experimental results show that the two variants converge faster than conventional FTRL and OMD, even faster than vanilla CFR and CFR+ in some EFGs.
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Weiming Liu, Huacong Jiang, Bin Li, Houqiang Li
| null | null | 2,022 |
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Gating Dropout: Communication-efficient Regularization for Sparsely Activated Transformers
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Sparsely activated transformers, such as Mixture of Experts (MoE), have received great interest due to their outrageous scaling capability which enables dramatical increases in model size without significant increases in computational cost. To achieve this, MoE models replace the feedforward sub-layer with Mixture-of-Experts sub-layer in transformers and use a gating network to route each token to its assigned experts. Since the common practice for efficient training of such models requires distributing experts and tokens across different machines, this routing strategy often incurs huge cross-machine communication cost because tokens and their assigned experts likely reside in different machines. In this paper, we propose Gating Dropout, which allows tokens to ignore the gating network and stay at their local machines, thus reducing the cross-machine communication. Similar to traditional dropout, we also show that Gating Dropout has a regularization effect during training, resulting in improved generalization performance. We validate the effectiveness of Gating Dropout on multilingual machine translation tasks. Our results demonstrate that Gating Dropout improves a state-of-the-art MoE model with faster wall-clock time convergence rates and better BLEU scores for a variety of model sizes and datasets.
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Rui Liu, Young Jin Kim, Alexandre Muzio, Hany Hassan
| null | null | 2,022 |
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Simplex Neural Population Learning: Any-Mixture Bayes-Optimality in Symmetric Zero-sum Games
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Learning to play optimally against any mixture over a diverse set of strategies is of important practical interests in competitive games. In this paper, we propose simplex-NeuPL that satisfies two desiderata simultaneously: i) learning a population of strategically diverse basis policies, represented by a single conditional network; ii) using the same network, learn best-responses to any mixture over the simplex of basis policies. We show that the resulting conditional policies incorporate prior information about their opponents effectively, enabling near optimal returns against arbitrary mixture policies in a game with tractable best-responses. We verify that such policies behave Bayes-optimally under uncertainty and offer insights in using this flexibility at test time. Finally, we offer evidence that learning best-responses to any mixture policies is an effective auxiliary task for strategic exploration, which, by itself, can lead to more performant populations.
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Siqi Liu, Marc Lanctot, Luke Marris, Nicolas Heess
| null | null | 2,022 |
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Rethinking Attention-Model Explainability through Faithfulness Violation Test
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Attention mechanisms are dominating the explainability of deep models. They produce probability distributions over the input, which are widely deemed as feature-importance indicators. However, in this paper, we find one critical limitation in attention explanations: weakness in identifying the polarity of feature impact. This would be somehow misleading – features with higher attention weights may not faithfully contribute to model predictions; instead, they can impose suppression effects. With this finding, we reflect on the explainability of current attention-based techniques, such as Attention $\bigodot$ Gradient and LRP-based attention explanations. We first propose an actionable diagnostic methodology (henceforth faithfulness violation test) to measure the consistency between explanation weights and the impact polarity. Through the extensive experiments, we then show that most tested explanation methods are unexpectedly hindered by the faithfulness violation issue, especially the raw attention. Empirical analyses on the factors affecting violation issues further provide useful observations for adopting explanation methods in attention models.
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Yibing Liu, Haoliang Li, Yangyang Guo, Chenqi Kong, Jing Li, Shiqi Wang
| null | null | 2,022 |
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Welfare Maximization in Competitive Equilibrium: Reinforcement Learning for Markov Exchange Economy
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We study a bilevel economic system, which we refer to as a Markov exchange economy (MEE), from the point of view of multi-agent reinforcement learning (MARL). An MEE involves a central planner and a group of self-interested agents. The goal of the agents is to form a Competitive Equilibrium (CE), where each agent myopically maximizes her own utility at each step. The goal of the central planner is to steer the system so as to maximize social welfare, which is defined as the sum of the utilities of all agents. Working in a setting in which the utility function and the system dynamics are both unknown, we propose to find the socially optimal policy and the CE from data via both online and offline variants of MARL. Concretely, we first devise a novel suboptimality metric specifically tailored to MEE, such that minimizing such a metric certifies globally optimal policies for both the planner and the agents. Second, in the online setting, we propose an algorithm, dubbed as \texttt{MOLM}, which combines the optimism principle for exploration with subgame CE seeking. Our algorithm can readily incorporate general function approximation tools for handling large state spaces and achieves a sublinear regret. Finally, we adapt the algorithm to an offline setting based on the pessimism principle and establish an upper bound on the suboptimality.
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Zhihan Liu, Miao Lu, Zhaoran Wang, Michael Jordan, Zhuoran Yang
| null | null | 2,022 |
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Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training
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Recently, Optimization-Derived Learning (ODL) has attracted attention from learning and vision areas, which designs learning models from the perspective of optimization. However, previous ODL approaches regard the training and hyper-training procedures as two separated stages, meaning that the hyper-training variables have to be fixed during the training process, and thus it is also impossible to simultaneously obtain the convergence of training and hyper-training variables. In this work, we design a Generalized Krasnoselskii-Mann (GKM) scheme based on fixed-point iterations as our fundamental ODL module, which unifies existing ODL methods as special cases. Under the GKM scheme, a Bilevel Meta Optimization (BMO) algorithmic framework is constructed to solve the optimal training and hyper-training variables together. We rigorously prove the essential joint convergence of the fixed-point iteration for training and the process of optimizing hyper-parameters for hyper-training, both on the approximation quality, and on the stationary analysis. Experiments demonstrate the efficiency of BMO with competitive performance on sparse coding and real-world applications such as image deconvolution and rain streak removal.
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Risheng Liu, Xuan Liu, Shangzhi Zeng, Jin Zhang, Yixuan Zhang
| null | null | 2,022 |
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Deep Neural Network Fusion via Graph Matching with Applications to Model Ensemble and Federated Learning
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Model fusion without accessing training data in machine learning has attracted increasing interest due to the practical resource-saving and data privacy issues. During the training process, the neural weights of each model can be randomly permuted, and we have to align the channels of each layer before fusing them. Regrading the channels as nodes and weights as edges, aligning the channels to maximize weight similarity is a challenging NP-hard assignment problem. Due to its quadratic assignment nature, we formulate the model fusion problem as a graph matching task, considering the second-order similarity of model weights instead of previous work merely formulating model fusion as a linear assignment problem. For the rising problem scale and multi-model consistency issues, we propose an efficient graduated assignment-based model fusion method, dubbed GAMF, which iteratively updates the matchings in a consistency-maintaining manner. We apply GAMF to tackle the compact model ensemble task and federated learning task on MNIST, CIFAR-10, CIFAR-100, and Tiny-Imagenet. The performance shows the efficacy of our GAMF compared to state-of-the-art baselines.
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Chang Liu, Chenfei Lou, Runzhong Wang, Alan Yuhan Xi, Li Shen, Junchi Yan
| null | null | 2,022 |
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Adaptive Accelerated (Extra-)Gradient Methods with Variance Reduction
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In this paper, we study the finite-sum convex optimization problem focusing on the general convex case. Recently, the study of variance reduced (VR) methods and their accelerated variants has made exciting progress. However, the step size used in the existing VR algorithms typically depends on the smoothness parameter, which is often unknown and requires tuning in practice. To address this problem, we propose two novel adaptive VR algorithms: Adaptive Variance Reduced Accelerated Extra-Gradient (AdaVRAE) and Adaptive Variance Reduced Accelerated Gradient (AdaVRAG). Our algorithms do not require knowledge of the smoothness parameter. AdaVRAE uses $\mathcal{O}\left(n\log\log n+\sqrt{\frac{n\beta}{\epsilon}}\right)$ and AdaVRAG uses $\mathcal{O}\left(n\log\log n+\sqrt{\frac{n\beta\log\beta}{\epsilon}}\right)$ gradient evaluations to attain an $\mathcal{O}(\epsilon)$-suboptimal solution, where $n$ is the number of functions in the finite sum and $\beta$ is the smoothness parameter. This result matches the best-known convergence rate of non-adaptive VR methods and it improves upon the convergence of the state of the art adaptive VR method, AdaSVRG. We demonstrate the superior performance of our algorithms compared with previous methods in experiments on real-world datasets.
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Zijian Liu, Ta Duy Nguyen, Alina Ene, Huy Nguyen
| null | null | 2,022 |
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Communication-efficient Distributed Learning for Large Batch Optimization
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Many communication-efficient methods have been proposed for distributed learning, whereby gradient compression is used to reduce the communication cost. However, given recent advances in large batch optimization (e.g., large batch SGD and its variant LARS with layerwise adaptive learning rates), the compute power of each machine is being fully utilized. This means, in modern distributed learning, the per-machine computation cost is no longer negligible compared to the communication cost. In this paper, we propose new gradient compression methods for large batch optimization, JointSpar and its variant JointSpar-LARS with layerwise adaptive learning rates, that jointly reduce both the computation and the communication cost. To achieve this, we take advantage of the redundancy in the gradient computation, unlike the existing methods compute all coordinates of the gradient vector, even if some coordinates are later dropped for communication efficiency. JointSpar and its variant further reduce the training time by avoiding the wasted computation on dropped coordinates. While computationally more efficient, we prove that JointSpar and its variant also maintain the same convergence rates as their respective baseline methods. Extensive experiments show that, by reducing the time per iteration, our methods converge faster than state-of-the-art compression methods in terms of wall-clock time.
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Rui Liu, Barzan Mozafari
| null | null | 2,022 |
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Generating 3D Molecules for Target Protein Binding
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A fundamental problem in drug discovery is to design molecules that bind to specific proteins. To tackle this problem using machine learning methods, here we propose a novel and effective framework, known as GraphBP, to generate 3D molecules that bind to given proteins by placing atoms of specific types and locations to the given binding site one by one. In particular, at each step, we first employ a 3D graph neural network to obtain geometry-aware and chemically informative representations from the intermediate contextual information. Such context includes the given binding site and atoms placed in the previous steps. Second, to preserve the desirable equivariance property, we select a local reference atom according to the designed auxiliary classifiers and then construct a local spherical coordinate system. Finally, to place a new atom, we generate its atom type and relative location w.r.t. the constructed local coordinate system via a flow model. We also consider generating the variables of interest sequentially to capture the underlying dependencies among them. Experiments demonstrate that our GraphBP is effective to generate 3D molecules with binding ability to target protein binding sites. Our implementation is available at https://github.com/divelab/GraphBP.
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Meng Liu, Youzhi Luo, Kanji Uchino, Koji Maruhashi, Shuiwang Ji
| null | null | 2,022 |
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Kill a Bird with Two Stones: Closing the Convergence Gaps in Non-Strongly Convex Optimization by Directly Accelerated SVRG with Double Compensation and Snapshots
| null |
Recently, some accelerated stochastic variance reduction algorithms such as Katyusha and ASVRG-ADMM achieve faster convergence than non-accelerated methods such as SVRG and SVRG-ADMM. However, there are still some gaps between the oracle complexities and their lower bounds. To fill in these gaps, this paper proposes a novel Directly Accelerated stochastic Variance reductIon (DAVIS) algorithm with two Snapshots for non-strongly convex (non-SC) unconstrained problems. Our theoretical results show that DAVIS achieves the optimal convergence rate O(1/(nS^2)) and optimal gradient complexity O(n+\sqrt{nL/\epsilon}), which is identical to its lower bound. To the best of our knowledge, this is the first directly accelerated algorithm that attains the optimal lower bound and improves the convergence rate from O(1/S^2) to O(1/(nS^2)). Moreover, we extend DAVIS and theoretical results to non-SC problems with a structured regularizer, and prove that the proposed algorithm with double-snapshots also attains the optimal convergence rate O(1/(nS)) and optimal oracle complexity O(n+L/\epsilon) for such problems, and it is at least a factor n/S faster than existing accelerated stochastic algorithms, where n\gg S in general.
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Yuanyuan Liu, Fanhua Shang, Weixin An, Hongying Liu, Zhouchen Lin
| null | null | 2,022 |
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REvolveR: Continuous Evolutionary Models for Robot-to-robot Policy Transfer
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A popular paradigm in robotic learning is to train a policy from scratch for every new robot. This is not only inefficient but also often impractical for complex robots. In this work, we consider the problem of transferring a policy across two different robots with significantly different parameters such as kinematics and morphology. Existing approaches that train a new policy by matching the action or state transition distribution, including imitation learning methods, fail due to optimal action and/or state distribution being mismatched in different robots. In this paper, we propose a novel method named REvolveR of using continuous evolutionary models for robotic policy transfer implemented in a physics simulator. We interpolate between the source robot and the target robot by finding a continuous evolutionary change of robot parameters. An expert policy on the source robot is transferred through training on a sequence of intermediate robots that gradually evolve into the target robot. Experiments on a physics simulator show that the proposed continuous evolutionary model can effectively transfer the policy across robots and achieve superior sample efficiency on new robots. The proposed method is especially advantageous in sparse reward settings where exploration can be significantly reduced.
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Xingyu Liu, Deepak Pathak, Kris Kitani
| null | null | 2,022 |
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Asking for Knowledge (AFK): Training RL Agents to Query External Knowledge Using Language
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To solve difficult tasks, humans ask questions to acquire knowledge from external sources. In contrast, classical reinforcement learning agents lack such an ability and often resort to exploratory behavior. This is exacerbated as few present-day environments support querying for knowledge. In order to study how agents can be taught to query external knowledge via language, we first introduce two new environments: the grid-world-based Q-BabyAI and the text-based Q-TextWorld. In addition to physical interactions, an agent can query an external knowledge source specialized for these environments to gather information. Second, we propose the ‘Asking for Knowledge’ (AFK) agent, which learns to generate language commands to query for meaningful knowledge that helps solve the tasks. AFK leverages a non-parametric memory, a pointer mechanism and an episodic exploration bonus to tackle (1) irrelevant information, (2) a large query language space, (3) delayed reward for making meaningful queries. Extensive experiments demonstrate that the AFK agent outperforms recent baselines on the challenging Q-BabyAI and Q-TextWorld environments.
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Iou-Jen Liu, Xingdi Yuan, Marc-Alexandre Côté, Pierre-Yves Oudeyer, Alexander Schwing
| null | null | 2,022 |
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Learning Markov Games with Adversarial Opponents: Efficient Algorithms and Fundamental Limits
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An ideal strategy in zero-sum games should not only grant the player an average reward no less than the value of Nash equilibrium, but also exploit the (adaptive) opponents when they are suboptimal. While most existing works in Markov games focus exclusively on the former objective, it remains open whether we can achieve both objectives simultaneously. To address this problem, this work studies no-regret learning in Markov games with adversarial opponents when competing against the best fixed policy in hindsight. Along this direction, we present a new complete set of positive and negative results: When the policies of the opponents are revealed at the end of each episode, we propose new efficient algorithms achieving $\sqrt{K}$ regret bounds when either (1) the baseline policy class is small or (2) the opponent’s policy class is small. This is complemented with an exponential lower bound when neither conditions are true. When the policies of the opponents are not revealed, we prove a statistical hardness result even in the most favorable scenario when both above conditions are true. Our hardness result is much stronger than the existing hardness results which either only involve computational hardness, or require further restrictions on the algorithms.
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Qinghua Liu, Yuanhao Wang, Chi Jin
| null | null | 2,022 |
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Learning from Demonstration: Provably Efficient Adversarial Policy Imitation with Linear Function Approximation
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In generative adversarial imitation learning (GAIL), the agent aims to learn a policy from an expert demonstration so that its performance cannot be discriminated from the expert policy on a certain predefined reward set. In this paper, we study GAIL in both online and offline settings with linear function approximation, where both the transition and reward function are linear in the feature maps. Besides the expert demonstration, in the online setting the agent can interact with the environment, while in the offline setting the agent only accesses an additional dataset collected by a prior. For online GAIL, we propose an optimistic generative adversarial policy imitation algorithm (OGAPI) and prove that OGAPI achieves $\widetilde{\mathcal{O}}(\sqrt{H^4d^3K}+\sqrt{H^3d^2K^2/N_1})$ regret. Here $N_1$ represents the number of trajectories of the expert demonstration, $d$ is the feature dimension, and $K$ is the number of episodes. For offline GAIL, we propose a pessimistic generative adversarial policy imitation algorithm (PGAPI). We also obtain the optimality gap of PGAPI, achieving the minimax lower bound in the utilization of the additional dataset. Assuming sufficient coverage on the additional dataset, we show that PGAPI achieves $\widetilde{\mathcal{O}}(\sqrt{H^4d^2/K}+\sqrt{H^4d^3/N_2}+\sqrt{H^3d^2/N_1})$ optimality gap. Here $N_2$ represents the number of trajectories of the additional dataset with sufficient coverage.
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Zhihan Liu, Yufeng Zhang, Zuyue Fu, Zhuoran Yang, Zhaoran Wang
| null | null | 2,022 |
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Plan Your Target and Learn Your Skills: Transferable State-Only Imitation Learning via Decoupled Policy Optimization
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Recent progress in state-only imitation learning extends the scope of applicability of imitation learning to real-world settings by relieving the need for observing expert actions. However, existing solutions only learn to extract a state-to-action mapping policy from the data, without considering how the expert plans to the target. This hinders the ability to leverage demonstrations and limits the flexibility of the policy. In this paper, we introduce Decoupled Policy Optimization (DePO), which explicitly decouples the policy as a high-level state planner and an inverse dynamics model. With embedded decoupled policy gradient and generative adversarial training, DePO enables knowledge transfer to different action spaces or state transition dynamics, and can generalize the planner to out-of-demonstration state regions. Our in-depth experimental analysis shows the effectiveness of DePO on learning a generalized target state planner while achieving the best imitation performance. We demonstrate the appealing usage of DePO for transferring across different tasks by pre-training, and the potential for co-training agents with various skills.
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Minghuan Liu, Zhengbang Zhu, Yuzheng Zhuang, Weinan Zhang, Jianye Hao, Yong Yu, Jun Wang
| null | null | 2,022 |
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GACT: Activation Compressed Training for Generic Network Architectures
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Training large neural network (NN) models requires extensive memory resources, and Activation Compression Training (ACT) is a promising approach to reduce training memory footprint. This paper presents GACT, an ACT framework to support a broad range of machine learning tasks for generic NN architectures with limited domain knowledge. By analyzing a linearized version of ACT’s approximate gradient, we prove the convergence of GACT without prior knowledge on operator type or model architecture. To make training stable, we propose an algorithm that decides the compression ratio for each tensor by estimating its impact on the gradient at run time. We implement GACT as a PyTorch library that readily applies to any NN architecture. GACT reduces the activation memory for convolutional NNs, transformers, and graph NNs by up to 8.1x, enabling training with a 4.2x to 24.7x larger batch size, with negligible accuracy loss.
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Xiaoxuan Liu, Lianmin Zheng, Dequan Wang, Yukuo Cen, Weize Chen, Xu Han, Jianfei Chen, Zhiyuan Liu, Jie Tang, Joey Gonzalez, Michael Mahoney, Alvin Cheung
| null | null | 2,022 |
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Robust Training under Label Noise by Over-parameterization
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Recently, over-parameterized deep networks, with increasingly more network parameters than training samples, have dominated the performances of modern machine learning. However, when the training data is corrupted, it has been well-known that over-parameterized networks tend to overfit and do not generalize. In this work, we propose a principled approach for robust training of over-parameterized deep networks in classification tasks where a proportion of training labels are corrupted. The main idea is yet very simple: label noise is sparse and incoherent with the network learned from clean data, so we model the noise and learn to separate it from the data. Specifically, we model the label noise via another sparse over-parameterization term, and exploit implicit algorithmic regularizations to recover and separate the underlying corruptions. Remarkably, when trained using such a simple method in practice, we demonstrate state-of-the-art test accuracy against label noise on a variety of real datasets. Furthermore, our experimental results are corroborated by theory on simplified linear models, showing that exact separation between sparse noise and low-rank data can be achieved under incoherent conditions. The work opens many interesting directions for improving over-parameterized models by using sparse over-parameterization and implicit regularization. Code is available at https://github.com/shengliu66/SOP.
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Sheng Liu, Zhihui Zhu, Qing Qu, Chong You
| null | null | 2,022 |
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On the Impossibility of Learning to Cooperate with Adaptive Partner Strategies in Repeated Games
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Learning to cooperate with other agents is challenging when those agents also possess the ability to adapt to our own behavior. Practical and theoretical approaches to learning in cooperative settings typically assume that other agents’ behaviors are stationary, or else make very specific assumptions about other agents’ learning processes. The goal of this work is to understand whether we can reliably learn to cooperate with other agents without such restrictive assumptions, which are unlikely to hold in real-world applications. Our main contribution is a set of impossibility results, which show that no learning algorithm can reliably learn to cooperate with all possible adaptive partners in a repeated matrix game, even if that partner is guaranteed to cooperate with some stationary strategy. Motivated by these results, we then discuss potential alternative assumptions which capture the idea that an adaptive partner will only adapt rationally to our behavior.
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Robert Loftin, Frans A Oliehoek
| null | null | 2,022 |
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AutoIP: A United Framework to Integrate Physics into Gaussian Processes
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Physical modeling is critical for many modern science and engineering applications. From a data science or machine learning perspective, where more domain-agnostic, data-driven models are pervasive, physical knowledge {—} often expressed as differential equations {—} is valuable in that it is complementary to data, and it can potentially help overcome issues such as data sparsity, noise, and inaccuracy. In this work, we propose a simple, yet powerful and general framework {—} AutoIP, for Automatically Incorporating Physics {—} that can integrate all kinds of differential equations into Gaussian Processes (GPs) to enhance prediction accuracy and uncertainty quantification. These equations can be linear or nonlinear, spatial, temporal, or spatio-temporal, complete or incomplete with unknown source terms, and so on. Based on kernel differentiation, we construct a GP prior to sample the values of the target function, equation related derivatives, and latent source functions, which are all jointly from a multivariate Gaussian distribution. The sampled values are fed to two likelihoods: one to fit the observations, and the other to conform to the equation. We use the whitening method to evade the strong dependency between the sampled function values and kernel parameters, and we develop a stochastic variational learning algorithm. AutoIP shows improvement upon vanilla GPs in both simulation and several real-world applications, even using rough, incomplete equations.
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Da Long, Zheng Wang, Aditi Krishnapriyan, Robert Kirby, Shandian Zhe, Michael Mahoney
| null | null | 2,022 |
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Bayesian Model Selection, the Marginal Likelihood, and Generalization
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How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive approach to this foundational question, automatically encoding Occam’s razor. Although it has been observed that the marginal likelihood can overfit and is sensitive to prior assumptions, its limitations for hyperparameter learning and discrete model comparison have not been thoroughly investigated. We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing. We then highlight the conceptual and practical issues in using the marginal likelihood as a proxy for generalization. Namely, we show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search, and can lead to both underfitting and overfitting in hyperparameter learning. We provide a partial remedy through a conditional marginal likelihood, which we show is more aligned with generalization, and practically valuable for large-scale hyperparameter learning, such as in deep kernel learning.
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Sanae Lotfi, Pavel Izmailov, Gregory Benton, Micah Goldblum, Andrew Gordon Wilson
| null | null | 2,022 |
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Fluctuations, Bias, Variance & Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension
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From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is therefore key to understanding robust generalisation. In this manuscript we develop a quantitative and rigorous theory for the study of fluctuations in an ensemble of generalised linear models trained on different, but correlated, features in high-dimensions. In particular, we provide a complete description of the asymptotic joint distribution of the empirical risk minimiser for generic convex loss and regularisation in the high-dimensional limit. Our result encompasses a rich set of classification and regression tasks, such as the lazy regime of overparametrised neural networks, or equivalently the random features approximation of kernels. While allowing to study directly the mitigating effect of ensembling (or bagging) on the bias-variance decomposition of the test error, our analysis also helps disentangle the contribution of statistical fluctuations, and the singular role played by the interpolation threshold that are at the roots of the “double-descent” phenomenon.
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Bruno Loureiro, Cedric Gerbelot, Maria Refinetti, Gabriele Sicuro, Florent Krzakala
| null | null | 2,022 |
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A Single-Loop Gradient Descent and Perturbed Ascent Algorithm for Nonconvex Functional Constrained Optimization
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Nonconvex constrained optimization problems can be used to model a number of machine learning problems, such as multi-class Neyman-Pearson classification and constrained Markov decision processes. However, such kinds of problems are challenging because both the objective and constraints are possibly nonconvex, so it is difficult to balance the reduction of the loss value and reduction of constraint violation. Although there are a few methods that solve this class of problems, all of them are double-loop or triple-loop algorithms, and they require oracles to solve some subproblems up to certain accuracy by tuning multiple hyperparameters at each iteration. In this paper, we propose a novel gradient descent and perturbed ascent (GDPA) algorithm to solve a class of smooth nonconvex inequality constrained problems. The GDPA is a primal-dual algorithm, which only exploits the first-order information of both the objective and constraint functions to update the primal and dual variables in an alternating way. The key feature of the proposed algorithm is that it is a single-loop algorithm, where only two step-sizes need to be tuned. We show that under a mild regularity condition GDPA is able to find Karush-Kuhn-Tucker (KKT) points of nonconvex functional constrained problems with convergence rate guarantees. To the best of our knowledge, it is the first single-loop algorithm that can solve the general nonconvex smooth problems with nonconvex inequality constraints. Numerical results also showcase the superiority of GDPA compared with the best-known algorithms (in terms of both stationarity measure and feasibility of the obtained solutions).
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Songtao Lu
| null | null | 2,022 |
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Additive Gaussian Processes Revisited
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Gaussian Process (GP) models are a class of flexible non-parametric models that have rich representational power. By using a Gaussian process with additive structure, complex responses can be modelled whilst retaining interpretability. Previous work showed that additive Gaussian process models require high-dimensional interaction terms. We propose the orthogonal additive kernel (OAK), which imposes an orthogonality constraint on the additive functions, enabling an identifiable, low-dimensional representation of the functional relationship. We connect the OAK kernel to functional ANOVA decomposition, and show improved convergence rates for sparse computation methods. With only a small number of additive low-dimensional terms, we demonstrate the OAK model achieves similar or better predictive performance compared to black-box models, while retaining interpretability.
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Xiaoyu Lu, Alexis Boukouvalas, James Hensman
| null | null | 2,022 |
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A Statistical Manifold Framework for Point Cloud Data
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Many problems in machine learning involve data sets in which each data point is a point cloud in $\mathbb{R}^D$. A growing number of applications require a means of measuring not only distances between point clouds, but also angles, volumes, derivatives, and other more advanced concepts. To formulate and quantify these concepts in a coordinate-invariant way, we develop a Riemannian geometric framework for point cloud data. By interpreting each point in a point cloud as a sample drawn from some given underlying probability density, the space of point cloud data can be given the structure of a statistical manifold – each point on this manifold represents a point cloud – with the Fisher information metric acting as a natural Riemannian metric. Two autoencoder applications of our framework are presented: (i) smoothly deforming one 3D object into another via interpolation between the two corresponding point clouds; (ii) learning an optimal set of latent space coordinates for point cloud data that best preserves angles and distances, and thus produces a more discriminative representation space. Experiments with large-scale standard benchmark point cloud data show greatly improved classification accuracy vis-á-vis existing methods. Code is available at https://github.com/seungyeon-k/SMF-public.
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Yonghyeon Lee, Seungyeon Kim, Jinwon Choi, Frank Park
| null | null | 2,022 |
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Confidence Score for Source-Free Unsupervised Domain Adaptation
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Source-free unsupervised domain adaptation (SFUDA) aims to obtain high performance in the unlabeled target domain using the pre-trained source model, not the source data. Existing SFUDA methods assign the same importance to all target samples, which is vulnerable to incorrect pseudo-labels. To differentiate between sample importance, in this study, we propose a novel sample-wise confidence score, the Joint Model-Data Structure (JMDS) score for SFUDA. Unlike existing confidence scores that use only one of the source or target domain knowledge, the JMDS score uses both knowledge. We then propose a Confidence score Weighting Adaptation using the JMDS (CoWA-JMDS) framework for SFUDA. CoWA-JMDS consists of the JMDS scores as sample weights and weight Mixup that is our proposed variant of Mixup. Weight Mixup promotes the model make more use of the target domain knowledge. The experimental results show that the JMDS score outperforms the existing confidence scores. Moreover, CoWA-JMDS achieves state-of-the-art performance on various SFUDA scenarios: closed, open, and partial-set scenarios.
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Jonghyun Lee, Dahuin Jung, Junho Yim, Sungroh Yoon
| null | null | 2,022 |
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A Random Matrix Analysis of Data Stream Clustering: Coping With Limited Memory Resources
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This article introduces a random matrix framework for the analysis of clustering on high-dimensional data streams, a particularly relevant setting for a more sober processing of large amounts of data with limited memory and energy resources. Assuming data $\mathbf{x}_1, \mathbf{x}_2, \ldots$ arrives as a continuous flow and a small number $L$ of them can be kept in the learning pipeline, one has only access to the diagonal elements of the Gram kernel matrix: $\left[ \mathbf{K}_L \right]_{i, j} = \frac{1}{p} \mathbf{x}_i^\top \mathbf{x}_j \mathbf{1}_{\left\lvert i - j \right\rvert < L}$. Under a large-dimensional data regime, we derive the limiting spectral distribution of the banded kernel matrix $\mathbf{K}_L$ and study its isolated eigenvalues and eigenvectors, which behave in an unfamiliar way. We detail how these results can be used to perform efficient online kernel spectral clustering and provide theoretical performance guarantees. Our findings are empirically confirmed on image clustering tasks. Leveraging on optimality results of spectral methods for clustering, this work offers insights on efficient online clustering techniques for high-dimensional data.
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Hugo Lebeau, Romain Couillet, Florent Chatelain
| null | null | 2,022 |
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Differentially Private Maximal Information Coefficients
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The Maximal Information Coefficient (MIC) is a powerful statistic to identify dependencies between variables. However, it may be applied to sensitive data, and publishing it could leak private information. As a solution, we present algorithms to approximate MIC in a way that provides differential privacy. We show that the natural application of the classic Laplace mechanism yields insufficient accuracy. We therefore introduce the MICr statistic, which is a new MIC approximation that is more compatible with differential privacy. We prove MICr is a consistent estimator for MIC, and we provide two differentially private versions of it. We perform experiments on a variety of real and synthetic datasets. The results show that the private MICr statistics significantly outperform direct application of the Laplace mechanism. Moreover, experiments on real-world datasets show accuracy that is usable when the sample size is at least moderately large.
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John Lazarsfeld, Aaron Johnson, Emmanuel Adeniran
| null | null | 2,022 |
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Convergence of Policy Gradient for Entropy Regularized MDPs with Neural Network Approximation in the Mean-Field Regime
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We study the global convergence of policy gradient for infinite-horizon, continuous state and action space, and entropy-regularized Markov decision processes (MDPs). We consider a softmax policy with (one-hidden layer) neural network approximation in a mean-field regime. Additional entropic regularization in the associated mean-field probability measure is added, and the corresponding gradient flow is studied in the 2-Wasserstein metric. We show that the objective function is increasing along the gradient flow. Further, we prove that if the regularization in terms of the mean-field measure is sufficient, the gradient flow converges exponentially fast to the unique stationary solution, which is the unique maximizer of the regularized MDP objective. Lastly, we study the sensitivity of the value function along the gradient flow with respect to regularization parameters and the initial condition. Our results rely on the careful analysis of the non-linear Fokker–Planck–Kolmogorov equation and extend the pioneering work of \cite{mei2020global} and \cite{agarwal2020optimality}, which quantify the global convergence rate of policy gradient for entropy-regularized MDPs in the tabular setting.
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James-Michael Leahy, Bekzhan Kerimkulov, David Siska, Lukasz Szpruch
| null | null | 2,022 |
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Neurocoder: General-Purpose Computation Using Stored Neural Programs
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Artificial Neural Networks are functionally equivalent to special-purpose computers. Their inter-neuronal connection weights represent the learnt Neural Program that instructs the networks on how to compute the data. However, without storing Neural Programs, they are restricted to only one, overwriting learnt programs when trained on new data. Here we design Neurocoder, a new class of general-purpose neural networks in which the neural network “codes” itself in a data-responsive way by composing relevant programs from a set of shareable, modular programs stored in external memory. This time, a Neural Program is efficiently treated as data in memory. Integrating Neurocoder into current neural architectures, we demonstrate new capacity to learn modular programs, reuse simple programs to build complex ones, handle pattern shifts and remember old programs as new ones are learnt, and show substantial performance improvement in solving object recognition, playing video games and continual learning tasks.
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Hung Le, Svetha Venkatesh
| null | null | 2,022 |
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Maslow’s Hammer in Catastrophic Forgetting: Node Re-Use vs. Node Activation
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Continual learning—learning new tasks in sequence while maintaining performance on old tasks—remains particularly challenging for artificial neural networks. Surprisingly, the amount of forgetting does not increase with the dissimilarity between the learned tasks, but appears to be worst in an intermediate similarity regime. In this paper we theoretically analyse both a synthetic teacher-student framework and a real data setup to provide an explanation of this phenomenon that we name Maslow’s Hammer hypothesis. Our analysis reveals the presence of a trade-off between node activation and node re-use that results in worst forgetting in the intermediate regime. Using this understanding we reinterpret popular algorithmic interventions for catastrophic interference in terms of this trade-off, and identify the regimes in which they are most effective.
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Sebastian Lee, Stefano Sarao Mannelli, Claudia Clopath, Sebastian Goldt, Andrew Saxe
| null | null | 2,022 |
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Query-Efficient and Scalable Black-Box Adversarial Attacks on Discrete Sequential Data via Bayesian Optimization
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We focus on the problem of adversarial attacks against models on discrete sequential data in the black-box setting where the attacker aims to craft adversarial examples with limited query access to the victim model. Existing black-box attacks, mostly based on greedy algorithms, find adversarial examples using pre-computed key positions to perturb, which severely limits the search space and might result in suboptimal solutions. To this end, we propose a query-efficient black-box attack using Bayesian optimization, which dynamically computes important positions using an automatic relevance determination (ARD) categorical kernel. We introduce block decomposition and history subsampling techniques to improve the scalability of Bayesian optimization when an input sequence becomes long. Moreover, we develop a post-optimization algorithm that finds adversarial examples with smaller perturbation size. Experiments on natural language and protein classification tasks demonstrate that our method consistently achieves higher attack success rate with significant reduction in query count and modification rate compared to the previous state-of-the-art methods.
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Deokjae Lee, Seungyong Moon, Junhyeok Lee, Hyun Oh Song
| null | null | 2,022 |
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Entropic Gromov-Wasserstein between Gaussian Distributions
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We study the entropic Gromov-Wasserstein and its unbalanced version between (unbalanced) Gaussian distributions with different dimensions. When the metric is the inner product, which we refer to as inner product Gromov-Wasserstein (IGW), we demonstrate that the optimal transportation plans of entropic IGW and its unbalanced variant are (unbalanced) Gaussian distributions. Via an application of von Neumann’s trace inequality, we obtain closed-form expressions for the entropic IGW between these Gaussian distributions. Finally, we consider an entropic inner product Gromov-Wasserstein barycenter of multiple Gaussian distributions. We prove that the barycenter is a Gaussian distribution when the entropic regularization parameter is small. We further derive a closed-form expression for the covariance matrix of the barycenter.
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Khang Le, Dung Q Le, Huy Nguyen, Dat Do, Tung Pham, Nhat Ho
| null | null | 2,022 |
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Least Squares Estimation using Sketched Data with Heteroskedastic Errors
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Researchers may perform regressions using a sketch of data of size m instead of the full sample of size n for a variety of reasons. This paper considers the case when the regression errors do not have constant variance and heteroskedasticity robust standard errors would normally be needed for test statistics to provide accurate inference. We show that estimates using data sketched by random projections will behave ’as if’ the errors were homoskedastic. Estimation by random sampling would not have this property. The result arises because the sketched estimates in the case of random projections can be expressed as degenerate U-statistics, and under certain conditions, these statistics are asymptotically normal with homoskedastic variance. We verify that the conditions hold not only in the case of least squares regression when the covariates are exogenous, but also in instrumental variables estimation when the covariates are endogenous. The result implies that inference can be simpler than the full sample case if the sketching scheme is appropriately chosen.
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Sokbae Lee, Serena Ng
| null | null | 2,022 |
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Dataset Condensation with Contrastive Signals
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Recent studies have demonstrated that gradient matching-based dataset synthesis, or dataset condensation (DC), methods can achieve state-of-theart performance when applied to data-efficient learning tasks. However, in this study, we prove that the existing DC methods can perform worse than the random selection method when taskirrelevant information forms a significant part of the training dataset. We attribute this to the lack of participation of the contrastive signals between the classes resulting from the class-wise gradient matching strategy. To address this problem, we propose Dataset Condensation with Contrastive signals (DCC) by modifying the loss function to enable the DC methods to effectively capture the differences between classes. In addition, we analyze the new loss function in terms of training dynamics by tracking the kernel velocity. Furthermore, we introduce a bi-level warm-up strategy to stabilize the optimization. Our experimental results indicate that while the existing methods are ineffective for fine-grained image classification tasks, the proposed method can successfully generate informative synthetic datasets for the same tasks. Moreover, we demonstrate that the proposed method outperforms the baselines even on benchmark datasets such as SVHN, CIFAR-10, and CIFAR-100. Finally, we demonstrate the high applicability of the proposed method by applying it to continual learning tasks.
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Saehyung Lee, Sanghyuk Chun, Sangwon Jung, Sangdoo Yun, Sungroh Yoon
| null | null | 2,022 |
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Disentangled Federated Learning for Tackling Attributes Skew via Invariant Aggregation and Diversity Transferring
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Attributes skew hinders the current federated learning (FL) frameworks from consistent optimization directions among the clients, which inevitably leads to performance reduction and unstable convergence. The core problems lie in that: 1) Domain-specific attributes, which are non-causal and only locally valid, are indeliberately mixed into global aggregation. 2) The one-stage optimizations of entangled attributes cannot simultaneously satisfy two conflicting objectives, i.e., generalization and personalization. To cope with these, we proposed disentangled federated learning (DFL) to disentangle the domain-specific and cross-invariant attributes into two complementary branches, which are trained by the proposed alternating local-global optimization independently. Importantly, convergence analysis proves that the FL system can be stably converged even if incomplete client models participate in the global aggregation, which greatly expands the application scope of FL. Extensive experiments verify that DFL facilitates FL with higher performance, better interpretability, and faster convergence rate, compared with SOTA FL methods on both manually synthesized and realistic attributes skew datasets.
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Zhengquan Luo, Yunlong Wang, Zilei Wang, Zhenan Sun, Tieniu Tan
| null | null | 2,022 |
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Multi-slots Online Matching with High Entropy
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Online matching with diversity and fairness pursuit, a common building block in the recommendation and advertising, can be modeled as constrained convex programming with high entropy. While most existing approaches are based on the “single slot” assumption (i.e., assigning one item per iteration), they cannot be directly applied to cases with multiple slots, e.g., stock-aware top-N recommendation and advertising at multiple places. Particularly, the gradient computation and resource allocation are both challenging under this setting due to the absence of a closed-form solution. To overcome these obstacles, we develop a novel algorithm named Online subGradient descent for Multi-slots Allocation (OG-MA). It uses an efficient pooling algorithm to compute closed-form of the gradient then performs a roulette swapping for allocation, yielding a sub-linear regret with linear cost per iteration. Extensive experiments on synthetic and industrial data sets demonstrate that OG-MA is a fast and promising method for multi-slots online matching.
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Xingyu Lu, Qintong Wu, Wenliang Zhong
| null | null | 2,022 |
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A Rigorous Study of Integrated Gradients Method and Extensions to Internal Neuron Attributions
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As deep learning (DL) efficacy grows, concerns for poor model explainability grow also. Attribution methods address the issue of explainability by quantifying the importance of an input feature for a model prediction. Among various methods, Integrated Gradients (IG) sets itself apart by claiming other methods failed to satisfy desirable axioms, while IG and methods like it uniquely satisfy said axioms. This paper comments on fundamental aspects of IG and its applications/extensions: 1) We identify key differences between IG function spaces and the supporting literature’s function spaces which problematize previous claims of IG uniqueness. We show that with the introduction of an additional axiom, non-decreasing positivity, the uniqueness claims can be established. 2) We address the question of input sensitivity by identifying function classes where IG is/is not Lipschitz in the attributed input. 3) We show that axioms for single-baseline methods have analogous properties for methods with probability distribution baselines. 4) We introduce a computationally efficient method of identifying internal neurons that contribute to specified regions of an IG attribution map. Finally, we present experimental results validating this method.
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Daniel D Lundstrom, Tianjian Huang, Meisam Razaviyayn
| null | null | 2,022 |
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Channel Importance Matters in Few-Shot Image Classification
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Few-Shot Learning (FSL) requires vision models to quickly adapt to brand-new classification tasks with a shift in task distribution. Understanding the difficulties posed by this task distribution shift is central to FSL. In this paper, we show that a simple channel-wise feature transformation may be the key to unraveling this secret from a channel perspective. When facing novel few-shot tasks in the test-time datasets, this transformation can greatly improve the generalization ability of learned image representations, while being agnostic to the choice of datasets and training algorithms. Through an in-depth analysis of this transformation, we find that the difficulty of representation transfer in FSL stems from the severe channel bias problem of image representations: channels may have different importance in different tasks, while convolutional neural networks are likely to be insensitive, or respond incorrectly to such a shift. This points out a core problem of the generalization ability of modern vision systems which needs further attention in the future.
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Xu Luo, Jing Xu, Zenglin Xu
| null | null | 2,022 |
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Interpretable Neural Networks with Frank-Wolfe: Sparse Relevance Maps and Relevance Orderings
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We study the effects of constrained optimization formulations and Frank-Wolfe algorithms for obtaining interpretable neural network predictions. Reformulating the Rate-Distortion Explanations (RDE) method for relevance attribution as a constrained optimization problem provides precise control over the sparsity of relevance maps. This enables a novel multi-rate as well as a relevance-ordering variant of RDE that both empirically outperform standard RDE and other baseline methods in a well-established comparison test. We showcase several deterministic and stochastic variants of the Frank-Wolfe algorithm and their effectiveness for RDE.
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Jan Macdonald, Mathieu E. Besançon, Sebastian Pokutta
| null | null | 2,022 |
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On Finite-Sample Identifiability of Contrastive Learning-Based Nonlinear Independent Component Analysis
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Nonlinear independent component analysis (nICA) aims at recovering statistically independent latent components that are mixed by unknown nonlinear functions. Central to nICA is the identifiability of the latent components, which had been elusive until very recently. Specifically, Hyvärinen et al. have shown that the nonlinearly mixed latent components are identifiable (up to often inconsequential ambiguities) under a generalized contrastive learning (GCL) formulation, given that the latent components are independent conditioned on a certain auxiliary variable. The GCL-based identifiability of nICA is elegant, and establishes interesting connections between nICA and popular unsupervised/self-supervised learning paradigms in representation learning, causal learning, and factor disentanglement. However, existing identifiability analyses of nICA all build upon an unlimited sample assumption and the use of ideal universal function learners—which creates a non-negligible gap between theory and practice. Closing the gap is a nontrivial challenge, as there is a lack of established “textbook” routine for finite sample analysis of such unsupervised problems. This work puts forth a finite-sample identifiability analysis of GCL-based nICA. Our analytical framework judiciously combines the properties of the GCL loss function, statistical generalization analysis, and numerical differentiation. Our framework also takes the learning function’s approximation error into consideration, and reveals an intuitive trade-off between the complexity and expressiveness of the employed function learner. Numerical experiments are used to validate the theorems.
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Qi Lyu, Xiao Fu
| null | null | 2,022 |
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Pessimism meets VCG: Learning Dynamic Mechanism Design via Offline Reinforcement Learning
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Dynamic mechanism design has garnered significant attention from both computer scientists and economists in recent years. By allowing agents to interact with the seller over multiple rounds, where agents’ reward functions may change with time and are state-dependent, the framework is able to model a rich class of real-world problems. In these works, the interaction between agents and sellers is often assumed to follow a Markov Decision Process (MDP). We focus on the setting where the reward and transition functions of such an MDP are not known a priori, and we are attempting to recover the optimal mechanism using an a priori collected data set. In the setting where the function approximation is employed to handle large state spaces, with only mild assumptions on the expressiveness of the function class, we are able to design a dynamic mechanism using offline reinforcement learning algorithms. Moreover, learned mechanisms approximately have three key desiderata: efficiency, individual rationality, and truthfulness. Our algorithm is based on the pessimism principle and only requires a mild assumption on the coverage of the offline data set. To the best of our knowledge, our work provides the first offline RL algorithm for dynamic mechanism design without assuming uniform coverage.
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Boxiang Lyu, Zhaoran Wang, Mladen Kolar, Zhuoran Yang
| null | null | 2,022 |
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BAMDT: Bayesian Additive Semi-Multivariate Decision Trees for Nonparametric Regression
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Bayesian additive regression trees (BART; Chipman et al., 2010) have gained great popularity as a flexible nonparametric function estimation and modeling tool. Nearly all existing BART models rely on decision tree weak learners with axis-parallel univariate split rules to partition the Euclidean feature space into rectangular regions. In practice, however, many regression problems involve features with multivariate structures (e.g., spatial locations) possibly lying in a manifold, where rectangular partitions may fail to respect irregular intrinsic geometry and boundary constraints of the structured feature space. In this paper, we develop a new class of Bayesian additive multivariate decision tree models that combine univariate split rules for handling possibly high dimensional features without known multivariate structures and novel multivariate split rules for features with multivariate structures in each weak learner. The proposed multivariate split rules are built upon stochastic predictive spanning tree bipartition models on reference knots, which are capable of achieving highly flexible nonlinear decision boundaries on manifold feature spaces while enabling efficient dimension reduction computations. We demonstrate the superior performance of the proposed method using simulation data and a Sacramento housing price data set.
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Zhao Tang Luo, Huiyan Sang, Bani Mallick
| null | null | 2,022 |
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Quantification and Analysis of Layer-wise and Pixel-wise Information Discarding
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This paper presents a method to explain how the information of each input variable is gradually discarded during the forward propagation in a deep neural network (DNN), which provides new perspectives to explain DNNs. We define two types of entropy-based metrics, i.e. (1) the discarding of pixel-wise information used in the forward propagation, and (2) the uncertainty of the input reconstruction, to measure input information contained by a specific layer from two perspectives. Unlike previous attribution metrics, the proposed metrics ensure the fairness of comparisons between different layers of different DNNs. We can use these metrics to analyze the efficiency of information processing in DNNs, which exhibits strong connections to the performance of DNNs. We analyze information discarding in a pixel-wise manner, which is different from the information bottleneck theory measuring feature information w.r.t. the sample distribution. Experiments have shown the effectiveness of our metrics in analyzing classic DNNs and explaining existing deep-learning techniques. The code is available at https://github.com/haotianSustc/deepinfo.
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Haotian Ma, Hao Zhang, Fan Zhou, Yinqing Zhang, Quanshi Zhang
| null | null | 2,022 |
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ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias
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Deep learning models are able to approximate one specific dynamical system but struggle at learning generalisable dynamics, where dynamical systems obey the same laws of physics but contain different numbers of elements (e.g., double- and triple-pendulum systems). To relieve this issue, we proposed the Modular Lagrangian Network (ModLaNet), a structural neural network framework with modularity and physical inductive bias. This framework models the energy of each element using modularity and then construct the target dynamical system via Lagrangian mechanics. Modularity is beneficial for reusing trained networks and reducing the scale of networks and datasets. As a result, our framework can learn from the dynamics of simpler systems and extend to more complex ones, which is not feasible using other relevant physics-informed neural networks. We examine our framework for modelling double-pendulum or three-body systems with small training datasets, where our models achieve the best data efficiency and accuracy performance compared with counterparts. We also reorganise our models as extensions to model multi-pendulum and multi-body systems, demonstrating the intriguing reusable feature of our framework.
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Yupu Lu, Shijie Lin, Guanqi Chen, Jia Pan
| null | null | 2,022 |
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Zero-Shot Reward Specification via Grounded Natural Language
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Reward signals in reinforcement learning are expensive to design and often require access to the true state which is not available in the real world. Common alternatives are usually demonstrations or goal images which can be labor-intensive to collect. On the other hand, text descriptions provide a general, natural, and low-effort way of communicating the desired task. However, prior works in learning text-conditioned policies still rely on rewards that are defined using either true state or labeled expert demonstrations. We use recent developments in building large-scale visuolanguage models like CLIP to devise a framework that generates the task reward signal just from goal text description and raw pixel observations which is then used to learn the task policy. We evaluate the proposed framework on control and robotic manipulation tasks. Finally, we distill the individual task policies into a single goal text conditioned policy that can generalize in a zero-shot manner to new tasks with unseen objects and unseen goal text descriptions.
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Parsa Mahmoudieh, Deepak Pathak, Trevor Darrell
| null | null | 2,022 |
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Orchestra: Unsupervised Federated Learning via Globally Consistent Clustering
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Federated learning is generally used in tasks where labels are readily available (e.g., next word prediction). Relaxing this constraint requires design of unsupervised learning techniques that can support desirable properties for federated training: robustness to statistical/systems heterogeneity, scalability with number of participants, and communication efficiency. Prior work on this topic has focused on directly extending centralized self-supervised learning techniques, which are not designed to have the properties listed above. To address this situation, we propose Orchestra, a novel unsupervised federated learning technique that exploits the federation’s hierarchy to orchestrate a distributed clustering task and enforce a globally consistent partitioning of clients’ data into discriminable clusters. We show the algorithmic pipeline in Orchestra guarantees good generalization performance under a linear probe, allowing it to outperform alternative techniques in a broad range of conditions, including variation in heterogeneity, number of clients, participation ratio, and local epochs.
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Ekdeep Lubana, Chi Ian Tang, Fahim Kawsar, Robert Dick, Akhil Mathur
| null | null | 2,022 |
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Versatile Offline Imitation from Observations and Examples via Regularized State-Occupancy Matching
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We propose State Matching Offline DIstribution Correction Estimation (SMODICE), a novel and versatile regression-based offline imitation learning algorithm derived via state-occupancy matching. We show that the SMODICE objective admits a simple optimization procedure through an application of Fenchel duality and an analytic solution in tabular MDPs. Without requiring access to expert actions, SMODICE can be effectively applied to three offline IL settings: (i) imitation from observations (IfO), (ii) IfO with dynamics or morphologically mismatched expert, and (iii) example-based reinforcement learning, which we show can be formulated as a state-occupancy matching problem. We extensively evaluate SMODICE on both gridworld environments as well as on high-dimensional offline benchmarks. Our results demonstrate that SMODICE is effective for all three problem settings and significantly outperforms prior state-of-art.
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Yecheng Ma, Andrew Shen, Dinesh Jayaraman, Osbert Bastani
| null | null | 2,022 |
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Learning Dynamics and Generalization in Deep Reinforcement Learning
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Solving a reinforcement learning (RL) problem poses two competing challenges: fitting a potentially discontinuous value function, and generalizing well to new observations. In this paper, we analyze the learning dynamics of temporal difference algorithms to gain novel insight into the tension between these two objectives. We show theoretically that temporal difference learning encourages agents to fit non-smooth components of the value function early in training, and at the same time induces the second-order effect of discouraging generalization. We corroborate these findings in deep RL agents trained on a range of environments, finding that neural networks trained using temporal difference algorithms on dense reward tasks exhibit weaker generalization between states than randomly initialized networks and networks trained with policy gradient methods. Finally, we investigate how post-training policy distillation may avoid this pitfall, and show that this approach improves generalization to novel environments in the ProcGen suite and improves robustness to input perturbations.
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Clare Lyle, Mark Rowland, Will Dabney, Marta Kwiatkowska, Yarin Gal
| null | null | 2,022 |
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Maximum Likelihood Training for Score-based Diffusion ODEs by High Order Denoising Score Matching
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Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can be used to define an ODE (“score-based diffusion ODE”) for exact likelihood evaluation. However, the relationship between the likelihood of the ODE and the score matching objective is unclear. In this work, we prove that matching the first-order score is not sufficient to maximize the likelihood of the ODE, by showing a gap between the maximum likelihood and score matching objectives. To fill up this gap, we show that the negative likelihood of the ODE can be bounded by controlling the first, second, and third-order score matching errors; and we further present a novel high-order denoising score matching method to enable maximum likelihood training of score-based diffusion ODEs. Our algorithm guarantees that the higher-order matching error is bounded by the training error and the lower-order errors. We empirically observe that by high-order score matching, score-based diffusion ODEs achieve better likelihood on both synthetic data and CIFAR-10, while retaining the high generation quality.
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Cheng Lu, Kaiwen Zheng, Fan Bao, Jianfei Chen, Chongxuan Li, Jun Zhu
| null | null | 2,022 |
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Architecture Agnostic Federated Learning for Neural Networks
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With growing concerns regarding data privacy and rapid increase in data volume, Federated Learning (FL) has become an important learning paradigm. However, jointly learning a deep neural network model in a FL setting proves to be a non-trivial task because of the complexities associated with the neural networks, such as varied architectures across clients, permutation invariance of the neurons, and presence of non-linear transformations in each layer. This work introduces a novel framework, Federated Heterogeneous Neural Networks (FedHeNN), that allows each client to build a personalised model without enforcing a common architecture across clients. This allows each client to optimize with respect to local data and compute constraints, while still benefiting from the learnings of other (potentially more powerful) clients. The key idea of FedHeNN is to use the instance-level representations obtained from peer clients to guide the simultaneous training on each client. The extensive experimental results demonstrate that the FedHeNN framework is capable of learning better performing models on clients in both the settings of homogeneous and heterogeneous architectures across clients.
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Disha Makhija, Xing Han, Nhat Ho, Joydeep Ghosh
| null | null | 2,022 |
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A Tighter Analysis of Spectral Clustering, and Beyond
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This work studies the classical spectral clustering algorithm which embeds the vertices of some graph G=(V_G, E_G) into R^k using k eigenvectors of some matrix of G, and applies k-means to partition V_G into k clusters. Our first result is a tighter analysis on the performance of spectral clustering, and explains why it works under some much weaker condition than the ones studied in the literature. For the second result, we show that, by applying fewer than k eigenvectors to construct the embedding, spectral clustering is able to produce better output for many practical instances; this result is the first of its kind in spectral clustering. Besides its conceptual and theoretical significance, the practical impact of our work is demonstrated by the empirical analysis on both synthetic and real-world data sets, in which spectral clustering produces comparable or better results with fewer than k eigenvectors.
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Peter Macgregor, He Sun
| null | null | 2,022 |
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Knowledge-Grounded Self-Rationalization via Extractive and Natural Language Explanations
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Models that generate extractive rationales (i.e., subsets of features) or natural language explanations (NLEs) for their predictions are important for explainable AI. While an extractive rationale provides a quick view of the features most responsible for a prediction, an NLE allows for a comprehensive description of the decision-making process behind a prediction. However, current models that generate the best extractive rationales or NLEs often fall behind the state-of-the-art (SOTA) in terms of task performance. In this work, we bridge this gap by introducing RExC, a self-rationalizing framework that grounds its predictions and two complementary types of explanations (NLEs and extractive rationales) in background knowledge. Our framework improves over previous methods by: (i) reaching SOTA task performance while also providing explanations, (ii) providing two types of explanations, while existing models usually provide only one type, and (iii) beating by a large margin the previous SOTA in terms of quality of both types of explanations. Furthermore, a perturbation analysis in RExC shows a high degree of association between explanations and predictions, a necessary property of faithful explanations.
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Bodhisattwa Prasad Majumder, Oana Camburu, Thomas Lukasiewicz, Julian Mcauley
| null | null | 2,022 |
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Nonparametric Involutive Markov Chain Monte Carlo
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A challenging problem in probabilistic programming is to develop inference algorithms that work for arbitrary programs in a universal probabilistic programming language (PPL). We present the nonparametric involutive Markov chain Monte Carlo (NP-iMCMC) algorithm as a method for constructing MCMC inference algorithms for nonparametric models expressible in universal PPLs. Building on the unifying involutive MCMC framework, and by providing a general procedure for driving state movement between dimensions, we show that NP-iMCMC can generalise numerous existing iMCMC algorithms to work on nonparametric models. We prove the correctness of the NP-iMCMC sampler. Our empirical study shows that the existing strengths of several iMCMC algorithms carry over to their nonparametric extensions. Applying our method to the recently proposed Nonparametric HMC, an instance of (Multiple Step) NP-iMCMC, we have constructed several nonparametric extensions (all of which new) that exhibit significant performance improvements.
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Carol Mak, Fabian Zaiser, Luke Ong
| null | null | 2,022 |
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Robustness in Multi-Objective Submodular Optimization: a Quantile Approach
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The optimization of multi-objective submodular systems appears in a wide variety of applications. However, there are currently very few techniques which are able to provide a robust allocation to such systems. In this work, we propose to design and analyse novel algorithms for the robust allocation of submodular systems through lens of quantile maximization. We start by observing that identifying an exact solution for this problem is computationally intractable. To tackle this issue, we propose a proxy for the quantile function using a softmax formulation, and show that this proxy is well suited to submodular optimization. Based on this relaxation, we propose a novel and simple algorithm called SOFTSAT. Theoretical properties are provided for this algorithm as well as novel approximation guarantees. Finally, we provide numerical experiments showing the efficiency of our algorithm with regards to state-of-the-art methods in a test bed of real-world applications, and show that SOFTSAT is particularly robust and well-suited to online scenarios.
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Cedric Malherbe, Kevin Scaman
| null | null | 2,022 |
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Feature selection using e-values
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In the context of supervised learning, we introduce the concept of e-value. An e-value is a scalar quantity that represents the proximity of the sampling distribution of parameter estimates in a model trained on a subset of features to that of the model trained on all features (i.e. the full model). Under general conditions, a rank ordering of e-values separates models that contain all essential features from those that do not. For a p-dimensional feature space, this requires fitting only the full model and evaluating p+1 models, as opposed to the traditional requirement of fitting and evaluating 2^p models. The above e-values framework is applicable to a wide range of parametric models. We use data depths and a fast resampling-based algorithm to implement a feature selection procedure, providing consistency results. Through experiments across several model settings and synthetic and real datasets, we establish that the e-values can be a promising general alternative to existing model-specific methods of feature selection.
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Subhabrata Majumdar, Snigdhansu Chatterjee
| null | null | 2,022 |
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Differentially Private Coordinate Descent for Composite Empirical Risk Minimization
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Machine learning models can leak information about the data used to train them. To mitigate this issue, Differentially Private (DP) variants of optimization algorithms like Stochastic Gradient Descent (DP-SGD) have been designed to trade-off utility for privacy in Empirical Risk Minimization (ERM) problems. In this paper, we propose Differentially Private proximal Coordinate Descent (DP-CD), a new method to solve composite DP-ERM problems. We derive utility guarantees through a novel theoretical analysis of inexact coordinate descent. Our results show that, thanks to larger step sizes, DP-CD can exploit imbalance in gradient coordinates to outperform DP-SGD. We also prove new lower bounds for composite DP-ERM under coordinate-wise regularity assumptions, that are nearly matched by DP-CD. For practical implementations, we propose to clip gradients using coordinate-wise thresholds that emerge from our theory, avoiding costly hyperparameter tuning. Experiments on real and synthetic data support our results, and show that DP-CD compares favorably with DP-SGD.
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Paul Mangold, Aurélien Bellet, Joseph Salmon, Marc Tommasi
| null | null | 2,022 |
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Refined Convergence Rates for Maximum Likelihood Estimation under Finite Mixture Models
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We revisit the classical problem of deriving convergence rates for the maximum likelihood estimator (MLE) in finite mixture models. The Wasserstein distance has become a standard loss function for the analysis of parameter estimation in these models, due in part to its ability to circumvent label switching and to accurately characterize the behaviour of fitted mixture components with vanishing weights. However, the Wasserstein distance is only able to capture the worst-case convergence rate among the remaining fitted mixture components. We demonstrate that when the log-likelihood function is penalized to discourage vanishing mixing weights, stronger loss functions can be derived to resolve this shortcoming of the Wasserstein distance. These new loss functions accurately capture the heterogeneity in convergence rates of fitted mixture components, and we use them to sharpen existing pointwise and uniform convergence rates in various classes of mixture models. In particular, these results imply that a subset of the components of the penalized MLE typically converge significantly faster than could have been anticipated from past work. We further show that some of these conclusions extend to the traditional MLE. Our theoretical findings are supported by a simulation study to illustrate these improved convergence rates.
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Tudor Manole, Nhat Ho
| null | null | 2,022 |
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More Efficient Sampling for Tensor Decomposition With Worst-Case Guarantees
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Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes when parameters are chosen to achieve certain worst-case guarantees. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous state-of-the-art. We provide a detailed theoretical analysis and also apply the methods in a feature extraction experiment.
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Osman Asif Malik
| null | null | 2,022 |
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Closed-Form Diffeomorphic Transformations for Time Series Alignment
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Time series alignment methods call for highly expressive, differentiable and invertible warping functions which preserve temporal topology, i.e diffeomorphisms. Diffeomorphic warping functions can be generated from the integration of velocity fields governed by an ordinary differential equation (ODE). Gradient-based optimization frameworks containing diffeomorphic transformations require to calculate derivatives to the differential equation’s solution with respect to the model parameters, i.e. sensitivity analysis. Unfortunately, deep learning frameworks typically lack automatic-differentiation-compatible sensitivity analysis methods; and implicit functions, such as the solution of ODE, require particular care. Current solutions appeal to adjoint sensitivity methods, ad-hoc numerical solvers or ResNet’s Eulerian discretization. In this work, we present a closed-form expression for the ODE solution and its gradient under continuous piecewise-affine (CPA) velocity functions. We present a highly optimized implementation of the results on CPU and GPU. Furthermore, we conduct extensive experiments on several datasets to validate the generalization ability of our model to unseen data for time-series joint alignment. Results show significant improvements both in terms of efficiency and accuracy.
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Iñigo Martinez, Elisabeth Viles, Igor G. Olaizola
| null | null | 2,022 |
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Model-Free Opponent Shaping
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In general-sum games the interaction of self-interested learning agents commonly leads to collectively worst-case outcomes, such as defect-defect in the iterated prisoner’s dilemma (IPD). To overcome this, some methods, such as Learning with Opponent-Learning Awareness (LOLA), directly shape the learning process of their opponents. However, these methods are myopic since only a small number of steps can be anticipated, are asymmetric since they treat other agents as naive learners, and require the use of higher-order derivatives, which are calculated through white-box access to an opponent’s differentiable learning algorithm. To address these issues, we propose Model-Free Opponent Shaping (M-FOS). M-FOS learns in a meta-game in which each meta-step is an episode of the underlying game. The meta-state consists of the policies in the underlying game and the meta-policy produces a new policy to be used in the next episode. M-FOS then uses generic model-free optimisation methods to learn meta-policies that accomplish long-horizon opponent shaping. Empirically, M-FOS near-optimally exploits naive learners and other, more sophisticated algorithms from the literature. For example, to the best of our knowledge, it is the first method to learn the well-known ZD extortion strategy in the IPD. In the same settings, M-FOS leads to socially optimal outcomes under meta-self-play. Finally, we show that M-FOS can be scaled to high-dimensional settings.
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Christopher Lu, Timon Willi, Christian A Schroeder De Witt, Jakob Foerster
| null | null | 2,022 |
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