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2302.13319
|
Matth\"aus Kleindessner
|
Efficient fair PCA for fair representation learning
|
stat.ML cs.CY cs.LG
|
We revisit the problem of fair principal component analysis (PCA), where the
goal is to learn the best low-rank linear approximation of the data that
obfuscates demographic information. We propose a conceptually simple approach
that allows for an analytic solution similar to standard PCA and can be
kernelized. Our methods have the same complexity as standard PCA, or kernel
PCA, and run much faster than existing methods for fair PCA based on
semidefinite programming or manifold optimization, while achieving similar
results.
|
Machine Learning, Computers and Society, Machine Learning
|
Statistics
|
2105.04087
|
Pengcheng Ren
|
Latency Analysis of Consortium Blockchained Federated Learning
|
stat.ML cs.DC cs.LG
|
A decentralized federated learning architecture is proposed to apply to the
Businesses-to-Businesses scenarios by introducing the consortium blockchain in
this paper. We introduce a model verification mechanism to ensure the quality
of local models trained by participators. To analyze the latency of the system,
a latency model is constructed by considering the work flow of the
architecture. Finally the experiment results show that our latency model does
well in quantifying the actual delays.
|
Machine Learning, Distributed, Parallel, and Cluster Computing, Machine Learning
|
Statistics
|
1912.07820
|
Sainyam Galhotra Mr
|
Balancing the Tradeoff Between Clustering Value and Interpretability
|
stat.ML cs.DS cs.LG
|
Graph clustering groups entities -- the vertices of a graph -- based on their
similarity, typically using a complex distance function over a large number of
features. Successful integration of clustering approaches in automated
decision-support systems hinges on the interpretability of the resulting
clusters. This paper addresses the problem of generating interpretable
clusters, given features of interest that signify interpretability to an
end-user, by optimizing interpretability in addition to common clustering
objectives. We propose a $\beta$-interpretable clustering algorithm that
ensures that at least $\beta$ fraction of nodes in each cluster share the same
feature value. The tunable parameter $\beta$ is user-specified. We also present
a more efficient algorithm for scenarios with $\beta\!=\!1$ and analyze the
theoretical guarantees of the two algorithms. Finally, we empirically
demonstrate the benefits of our approaches in generating interpretable clusters
using four real-world datasets. The interpretability of the clusters is
complemented by generating simple explanations denoting the feature values of
the nodes in the clusters, using frequent pattern mining.
|
Machine Learning, Data Structures and Algorithms, Machine Learning
|
Statistics
|
1505.05007
|
Paul Blomstedt PhD
|
Modelling-based experiment retrieval: A case study with gene expression
clustering
|
stat.ML cs.IR cs.LG
|
Motivation: Public and private repositories of experimental data are growing
to sizes that require dedicated methods for finding relevant data. To improve
on the state of the art of keyword searches from annotations, methods for
content-based retrieval have been proposed. In the context of gene expression
experiments, most methods retrieve gene expression profiles, requiring each
experiment to be expressed as a single profile, typically of case vs. control.
A more general, recently suggested alternative is to retrieve experiments whose
models are good for modelling the query dataset. However, for very noisy and
high-dimensional query data, this retrieval criterion turns out to be very
noisy as well.
Results: We propose doing retrieval using a denoised model of the query
dataset, instead of the original noisy dataset itself. To this end, we
introduce a general probabilistic framework, where each experiment is modelled
separately and the retrieval is done by finding related models. For retrieval
of gene expression experiments, we use a probabilistic model called product
partition model, which induces a clustering of genes that show similar
expression patterns across a number of samples. The suggested metric for
retrieval using clusterings is the normalized information distance. Empirical
results finally suggest that inference for the full probabilistic model can be
approximated with good performance using computationally faster heuristic
clustering approaches (e.g. $k$-means). The method is highly scalable and
straightforward to apply to construct a general-purpose gene expression
experiment retrieval method.
Availability: The method can be implemented using standard clustering
algorithms and normalized information distance, available in many statistical
software packages.
|
Machine Learning, Information Retrieval, Machine Learning
|
Statistics
|
2206.14278
|
Karan Srivastava
|
A Perturbation Bound on the Subspace Estimator from Canonical
Projections
|
stat.ML cs.IT cs.LG math.IT
|
This paper derives a perturbation bound on the optimal subspace estimator
obtained from a subset of its canonical projections contaminated by noise. This
fundamental result has important implications in matrix completion, subspace
clustering, and related problems.
|
Machine Learning, Information Theory, Machine Learning, Information Theory
|
Statistics
|
2006.00402
|
Boris Landa
|
Doubly-Stochastic Normalization of the Gaussian Kernel is Robust to
Heteroskedastic Noise
|
stat.ML cs.IT cs.LG math.IT
|
A fundamental step in many data-analysis techniques is the construction of an
affinity matrix describing similarities between data points. When the data
points reside in Euclidean space, a widespread approach is to from an affinity
matrix by the Gaussian kernel with pairwise distances, and to follow with a
certain normalization (e.g. the row-stochastic normalization or its symmetric
variant). We demonstrate that the doubly-stochastic normalization of the
Gaussian kernel with zero main diagonal (i.e., no self loops) is robust to
heteroskedastic noise. That is, the doubly-stochastic normalization is
advantageous in that it automatically accounts for observations with different
noise variances. Specifically, we prove that in a suitable high-dimensional
setting where heteroskedastic noise does not concentrate too much in any
particular direction in space, the resulting (doubly-stochastic) noisy affinity
matrix converges to its clean counterpart with rate $m^{-1/2}$, where $m$ is
the ambient dimension. We demonstrate this result numerically, and show that in
contrast, the popular row-stochastic and symmetric normalizations behave
unfavorably under heteroskedastic noise. Furthermore, we provide examples of
simulated and experimental single-cell RNA sequence data with intrinsic
heteroskedasticity, where the advantage of the doubly-stochastic normalization
for exploratory analysis is evident.
|
Machine Learning, Information Theory, Machine Learning, Information Theory
|
Statistics
|
2009.06966
|
Sattar Vakili
|
On Information Gain and Regret Bounds in Gaussian Process Bandits
|
stat.ML cs.IT cs.LG math.IT
|
Consider the sequential optimization of an expensive to evaluate and possibly
non-convex objective function $f$ from noisy feedback, that can be considered
as a continuum-armed bandit problem. Upper bounds on the regret performance of
several learning algorithms (GP-UCB, GP-TS, and their variants) are known under
both a Bayesian (when $f$ is a sample from a Gaussian process (GP)) and a
frequentist (when $f$ lives in a reproducing kernel Hilbert space) setting. The
regret bounds often rely on the maximal information gain $\gamma_T$ between $T$
observations and the underlying GP (surrogate) model. We provide general bounds
on $\gamma_T$ based on the decay rate of the eigenvalues of the GP kernel,
whose specialisation for commonly used kernels, improves the existing bounds on
$\gamma_T$, and subsequently the regret bounds relying on $\gamma_T$ under
numerous settings. For the Mat\'ern family of kernels, where the lower bounds
on $\gamma_T$, and regret under the frequentist setting, are known, our results
close a huge polynomial in $T$ gap between the upper and lower bounds (up to
logarithmic in $T$ factors).
|
Machine Learning, Information Theory, Machine Learning, Information Theory
|
Statistics
|
2212.09396
|
Daesung Kim
|
Rank-1 Matrix Completion with Gradient Descent and Small Random
Initialization
|
stat.ML cs.IT cs.LG math.IT
|
The nonconvex formulation of matrix completion problem has received
significant attention in recent years due to its affordable complexity compared
to the convex formulation. Gradient descent (GD) is the simplest yet efficient
baseline algorithm for solving nonconvex optimization problems. The success of
GD has been witnessed in many different problems in both theory and practice
when it is combined with random initialization. However, previous works on
matrix completion require either careful initialization or regularizers to
prove the convergence of GD. In this work, we study the rank-1 symmetric matrix
completion and prove that GD converges to the ground truth when small random
initialization is used. We show that in logarithmic amount of iterations, the
trajectory enters the region where local convergence occurs. We provide an
upper bound on the initialization size that is sufficient to guarantee the
convergence and show that a larger initialization can be used as more samples
are available. We observe that implicit regularization effect of GD plays a
critical role in the analysis, and for the entire trajectory, it prevents each
entry from becoming much larger than the others.
|
Machine Learning, Information Theory, Machine Learning, Information Theory
|
Statistics
|
1810.11571
|
Puning Zhao
|
Analysis of KNN Information Estimators for Smooth Distributions
|
stat.ML cs.IT cs.LG math.IT math.ST stat.TH
|
KSG mutual information estimator, which is based on the distances of each
sample to its k-th nearest neighbor, is widely used to estimate mutual
information between two continuous random variables. Existing work has analyzed
the convergence rate of this estimator for random variables whose densities are
bounded away from zero in its support. In practice, however, KSG estimator also
performs well for a much broader class of distributions, including not only
those with bounded support and densities bounded away from zero, but also those
with bounded support but densities approaching zero, and those with unbounded
support. In this paper, we analyze the convergence rate of the error of KSG
estimator for smooth distributions, whose support of density can be both
bounded and unbounded. As KSG mutual information estimator can be viewed as an
adaptive recombination of KL entropy estimators, in our analysis, we also
provide convergence analysis of KL entropy estimator for a broad class of
distributions.
|
Machine Learning, Information Theory, Machine Learning, Information Theory, Statistics Theory, Statistics Theory
|
Statistics
|
1508.07648
|
Mehdi Korki
|
Dictionary Learning for Blind One Bit Compressed Sensing
|
stat.ML cs.IT math.IT
|
This letter proposes a dictionary learning algorithm for blind one bit
compressed sensing. In the blind one bit compressed sensing framework, the
original signal to be reconstructed from one bit linear random measurements is
sparse in an unknown domain. In this context, the multiplication of measurement
matrix $\Ab$ and sparse domain matrix $\Phi$, \ie $\Db=\Ab\Phi$, should be
learned. Hence, we use dictionary learning to train this matrix. Towards that
end, an appropriate continuous convex cost function is suggested for one bit
compressed sensing and a simple steepest-descent method is exploited to learn
the rows of the matrix $\Db$. Experimental results show the effectiveness of
the proposed algorithm against the case of no dictionary learning, specially
with increasing the number of training signals and the number of sign
measurements.
|
Machine Learning, Information Theory, Information Theory
|
Statistics
|
2005.11770
|
Junjie Liang
|
Longitudinal Deep Kernel Gaussian Process Regression
|
stat.ML cs.LG
|
Gaussian processes offer an attractive framework for predictive modeling from
longitudinal data, i.e., irregularly sampled, sparse observations from a set of
individuals over time. However, such methods have two key shortcomings: (i)
They rely on ad hoc heuristics or expensive trial and error to choose the
effective kernels, and (ii) They fail to handle multilevel correlation
structure in the data. We introduce Longitudinal deep kernel Gaussian process
regression (L-DKGPR), which to the best of our knowledge, is the only method to
overcome these limitations by fully automating the discovery of complex
multilevel correlation structure from longitudinal data. Specifically, L-DKGPR
eliminates the need for ad hoc heuristics or trial and error using a novel
adaptation of deep kernel learning that combines the expressive power of deep
neural networks with the flexibility of non-parametric kernel methods. L-DKGPR
effectively learns the multilevel correlation with a novel addictive kernel
that simultaneously accommodates both time-varying and the time-invariant
effects. We derive an efficient algorithm to train L-DKGPR using latent space
inducing points and variational inference. Results of extensive experiments on
several benchmark data sets demonstrate that L-DKGPR significantly outperforms
the state-of-the-art longitudinal data analysis (LDA) methods.
|
Machine Learning, Machine Learning
|
Statistics
|
1406.1853
|
Ian Osband
|
Model-based Reinforcement Learning and the Eluder Dimension
|
stat.ML cs.LG
|
We consider the problem of learning to optimize an unknown Markov decision
process (MDP). We show that, if the MDP can be parameterized within some known
function class, we can obtain regret bounds that scale with the dimensionality,
rather than cardinality, of the system. We characterize this dependence
explicitly as $\tilde{O}(\sqrt{d_K d_E T})$ where $T$ is time elapsed, $d_K$ is
the Kolmogorov dimension and $d_E$ is the \emph{eluder dimension}. These
represent the first unified regret bounds for model-based reinforcement
learning and provide state of the art guarantees in several important settings.
Moreover, we present a simple and computationally efficient algorithm
\emph{posterior sampling for reinforcement learning} (PSRL) that satisfies
these bounds.
|
Machine Learning, Machine Learning
|
Statistics
|
1805.06595
|
Kevin He
|
Covariance-Insured Screening
|
stat.ML cs.LG
|
Modern bio-technologies have produced a vast amount of high-throughput data
with the number of predictors far greater than the sample size. In order to
identify more novel biomarkers and understand biological mechanisms, it is
vital to detect signals weakly associated with outcomes among
ultrahigh-dimensional predictors. However, existing screening methods, which
typically ignore correlation information, are likely to miss these weak
signals. By incorporating the inter-feature dependence, we propose a
covariance-insured screening methodology to identify predictors that are
jointly informative but only marginally weakly associated with outcomes. The
validity of the method is examined via extensive simulations and real data
studies for selecting potential genetic factors related to the onset of cancer.
|
Machine Learning, Machine Learning
|
Statistics
|
1905.07540
|
Jungtaek Kim
|
Practical Bayesian Optimization with Threshold-Guided Marginal
Likelihood Maximization
|
stat.ML cs.LG
|
We propose a practical Bayesian optimization method using Gaussian process
regression, of which the marginal likelihood is maximized where the number of
model selection steps is guided by a pre-defined threshold. Since Bayesian
optimization consumes a large portion of its execution time in finding the
optimal free parameters for Gaussian process regression, our simple, but
straightforward method is able to mitigate the time complexity and speed up the
overall Bayesian optimization procedure. Finally, the experimental results show
that our method is effective to reduce the execution time in most of cases,
with less loss of optimization quality.
|
Machine Learning, Machine Learning
|
Statistics
|
2210.05737
|
Miros{\l}awa {\L}ukawska
|
Context-aware Bayesian Mixed Multinomial Logit Model
|
stat.ML cs.LG
|
The mixed multinomial logit model assumes constant preference parameters of a
decision-maker throughout different choice situations, which may be considered
too strong for certain choice modelling applications. This paper proposes an
effective approach to model context-dependent intra-respondent heterogeneity,
thereby introducing the concept of the Context-aware Bayesian mixed multinomial
logit model, where a neural network maps contextual information to
interpretable shifts in the preference parameters of each individual in each
choice occasion. The proposed model offers several key advantages. First, it
supports both continuous and discrete variables, as well as complex non-linear
interactions between both types of variables. Secondly, each context
specification is considered jointly as a whole by the neural network rather
than each variable being considered independently. Finally, since the neural
network parameters are shared across all decision-makers, it can leverage
information from other decision-makers to infer the effect of a particular
context on a particular decision-maker. Even though the context-aware Bayesian
mixed multinomial logit model allows for flexible interactions between
attributes, the increase in computational complexity is minor, compared to the
mixed multinomial logit model. We illustrate the concept and interpretation of
the proposed model in a simulation study. We furthermore present a real-world
case study from the travel behaviour domain - a bicycle route choice model,
based on a large-scale, crowdsourced dataset of GPS trajectories including
119,448 trips made by 8,555 cyclists.
|
Machine Learning, Machine Learning
|
Statistics
|
1210.4276
|
Bertrand Lebichot
|
Semi-Supervised Classification Through the Bag-of-Paths Group
Betweenness
|
stat.ML cs.LG
|
This paper introduces a novel, well-founded, betweenness measure, called the
Bag-of-Paths (BoP) betweenness, as well as its extension, the BoP group
betweenness, to tackle semisupervised classification problems on weighted
directed graphs. The objective of semi-supervised classification is to assign a
label to unlabeled nodes using the whole topology of the graph and the labeled
nodes at our disposal. The BoP betweenness relies on a bag-of-paths framework
assigning a Boltzmann distribution on the set of all possible paths through the
network such that long (high-cost) paths have a low probability of being picked
from the bag, while short (low-cost) paths have a high probability of being
picked. Within that context, the BoP betweenness of node j is defined as the
sum of the a posteriori probabilities that node j lies in-between two arbitrary
nodes i, k, when picking a path starting in i and ending in k. Intuitively, a
node typically receives a high betweenness if it has a large probability of
appearing on paths connecting two arbitrary nodes of the network. This quantity
can be computed in closed form by inverting a n x n matrix where n is the
number of nodes. For the group betweenness, the paths are constrained to start
and end in nodes within the same class, therefore defining a group betweenness
for each class. Unlabeled nodes are then classified according to the class
showing the highest group betweenness. Experiments on various real-world data
sets show that BoP group betweenness outperforms all the tested state
of-the-art methods. The benefit of the BoP betweenness is particularly
noticeable when only a few labeled nodes are available.
|
Machine Learning, Machine Learning
|
Statistics
|
2009.03017
|
Pierre Alquier
|
Non-exponentially weighted aggregation: regret bounds for unbounded loss
functions
|
stat.ML cs.LG
|
We tackle the problem of online optimization with a general, possibly
unbounded, loss function. It is well known that when the loss is bounded, the
exponentially weighted aggregation strategy (EWA) leads to a regret in
$\sqrt{T}$ after $T$ steps. In this paper, we study a generalized aggregation
strategy, where the weights no longer depend exponentially on the losses. Our
strategy is based on Follow The Regularized Leader (FTRL): we minimize the
expected losses plus a regularizer, that is here a $\phi$-divergence. When the
regularizer is the Kullback-Leibler divergence, we obtain EWA as a special
case. Using alternative divergences enables unbounded losses, at the cost of a
worst regret bound in some cases.
|
Machine Learning, Machine Learning
|
Statistics
|
2404.18769
|
Fanghui Liu
|
Learning with Norm Constrained, Over-parameterized, Two-layer Neural
Networks
|
stat.ML cs.LG
|
Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a
suitable space to model functions by neural networks as the curse of
dimensionality (CoD) cannot be evaded when trying to approximate even a single
ReLU neuron (Bach, 2017). In this paper, we study a suitable function space for
over-parameterized two-layer neural networks with bounded norms (e.g., the path
norm, the Barron norm) in the perspective of sample complexity and
generalization properties. First, we show that the path norm (as well as the
Barron norm) is able to obtain width-independence sample complexity bounds,
which allows for uniform convergence guarantees. Based on this result, we
derive the improved result of metric entropy for $\epsilon$-covering up to
$O(\epsilon^{-\frac{2d}{d+2}})$ ($d$ is the input dimension and the depending
constant is at most linear order of $d$) via the convex hull technique, which
demonstrates the separation with kernel methods with $\Omega(\epsilon^{-d})$ to
learn the target function in a Barron space. Second, this metric entropy result
allows for building a sharper generalization bound under a general moment
hypothesis setting, achieving the rate at $O(n^{-\frac{d+2}{2d+2}})$. Our
analysis is novel in that it offers a sharper and refined estimation for metric
entropy with a linear dimension dependence and unbounded sampling in the
estimation of the sample error and the output error.
|
Machine Learning, Machine Learning
|
Statistics
|
1805.10965
|
Kevin Scaman
|
Lipschitz regularity of deep neural networks: analysis and efficient
estimation
|
stat.ML cs.LG
|
Deep neural networks are notorious for being sensitive to small well-chosen
perturbations, and estimating the regularity of such architectures is of utmost
importance for safe and robust practical applications. In this paper, we
investigate one of the key characteristics to assess the regularity of such
methods: the Lipschitz constant of deep learning architectures. First, we show
that, even for two layer neural networks, the exact computation of this
quantity is NP-hard and state-of-art methods may significantly overestimate it.
Then, we both extend and improve previous estimation methods by providing
AutoLip, the first generic algorithm for upper bounding the Lipschitz constant
of any automatically differentiable function. We provide a power method
algorithm working with automatic differentiation, allowing efficient
computations even on large convolutions. Second, for sequential neural
networks, we propose an improved algorithm named SeqLip that takes advantage of
the linear computation graph to split the computation per pair of consecutive
layers. Third we propose heuristics on SeqLip in order to tackle very large
networks. Our experiments show that SeqLip can significantly improve on the
existing upper bounds. Finally, we provide an implementation of AutoLip in the
PyTorch environment that may be used to better estimate the robustness of a
given neural network to small perturbations or regularize it using more precise
Lipschitz estimations.
|
Machine Learning, Machine Learning
|
Statistics
|
2209.07787
|
Pawe{\l} Teisseyre
|
Double logistic regression approach to biased positive-unlabeled data
|
stat.ML cs.LG
|
Positive and unlabelled learning is an important problem which arises
naturally in many applications. The significant limitation of almost all
existing methods lies in assuming that the propensity score function is
constant (SCAR assumption), which is unrealistic in many practical situations.
Avoiding this assumption, we consider parametric approach to the problem of
joint estimation of posterior probability and propensity score functions. We
show that under mild assumptions when both functions have the same parametric
form (e.g. logistic with different parameters) the corresponding parameters are
identifiable. Motivated by this, we propose two approaches to their estimation:
joint maximum likelihood method and the second approach based on alternating
maximization of two Fisher consistent expressions. Our experimental results
show that the proposed methods are comparable or better than the existing
methods based on Expectation-Maximisation scheme.
|
Machine Learning, Machine Learning
|
Statistics
|
2106.06573
|
Xiang Wang
|
Understanding Deflation Process in Over-parametrized Tensor
Decomposition
|
stat.ML cs.LG
|
In this paper we study the training dynamics for gradient flow on
over-parametrized tensor decomposition problems. Empirically, such training
process often first fits larger components and then discovers smaller
components, which is similar to a tensor deflation process that is commonly
used in tensor decomposition algorithms. We prove that for orthogonally
decomposable tensor, a slightly modified version of gradient flow would follow
a tensor deflation process and recover all the tensor components. Our proof
suggests that for orthogonal tensors, gradient flow dynamics works similarly as
greedy low-rank learning in the matrix setting, which is a first step towards
understanding the implicit regularization effect of over-parametrized models
for low-rank tensors.
|
Machine Learning, Machine Learning
|
Statistics
|
2011.12651
|
Stefan Klus
|
Feature space approximation for kernel-based supervised learning
|
stat.ML cs.LG
|
We propose a method for the approximation of high- or even
infinite-dimensional feature vectors, which play an important role in
supervised learning. The goal is to reduce the size of the training data,
resulting in lower storage consumption and computational complexity.
Furthermore, the method can be regarded as a regularization technique, which
improves the generalizability of learned target functions. We demonstrate
significant improvements in comparison to the computation of data-driven
predictions involving the full training data set. The method is applied to
classification and regression problems from different application areas such as
image recognition, system identification, and oceanographic time series
analysis.
|
Machine Learning, Machine Learning
|
Statistics
|
2406.09567
|
Carlos Fern\'andez-Lor\'ia
|
Causal Fine-Tuning and Effect Calibration of Non-Causal Predictive
Models
|
stat.ML cs.LG
|
This paper proposes techniques to enhance the performance of non-causal
models for causal inference using data from randomized experiments. In domains
like advertising, customer retention, and precision medicine, non-causal models
that predict outcomes under no intervention are often used to score individuals
and rank them according to the expected effectiveness of an intervention (e.g,
an ad, a retention incentive, a nudge). However, these scores may not perfectly
correspond to intervention effects due to the inherent non-causal nature of the
models. To address this limitation, we propose causal fine-tuning and effect
calibration, two techniques that leverage experimental data to refine the
output of non-causal models for different causal tasks, including effect
estimation, effect ordering, and effect classification. They are underpinned by
two key advantages. First, they can effectively integrate the predictive
capabilities of general non-causal models with the requirements of a causal
task in a specific context, allowing decision makers to support diverse causal
applications with a "foundational" scoring model. Second, through simulations
and an empirical example, we demonstrate that they can outperform the
alternative of building a causal-effect model from scratch, particularly when
the available experimental data is limited and the non-causal scores already
capture substantial information about the relative sizes of causal effects.
Overall, this research underscores the practical advantages of combining
experimental data with non-causal models to support causal applications.
|
Machine Learning, Machine Learning
|
Statistics
|
2004.10629
|
Stefan T. Radev
|
Amortized Bayesian model comparison with evidential deep learning
|
stat.ML cs.LG
|
Comparing competing mathematical models of complex natural processes is a
shared goal among many branches of science. The Bayesian probabilistic
framework offers a principled way to perform model comparison and extract
useful metrics for guiding decisions. However, many interesting models are
intractable with standard Bayesian methods, as they lack a closed-form
likelihood function or the likelihood is computationally too expensive to
evaluate. With this work, we propose a novel method for performing Bayesian
model comparison using specialized deep learning architectures. Our method is
purely simulation-based and circumvents the step of explicitly fitting all
alternative models under consideration to each observed dataset. Moreover, it
requires no hand-crafted summary statistics of the data and is designed to
amortize the cost of simulation over multiple models and observable datasets.
This makes the method particularly effective in scenarios where model fit needs
to be assessed for a large number of datasets, so that per-dataset inference is
practically infeasible.Finally, we propose a novel way to measure epistemic
uncertainty in model comparison problems. We demonstrate the utility of our
method on toy examples and simulated data from non-trivial models from
cognitive science and single-cell neuroscience. We show that our method
achieves excellent results in terms of accuracy, calibration, and efficiency
across the examples considered in this work. We argue that our framework can
enhance and enrich model-based analysis and inference in many fields dealing
with computational models of natural processes. We further argue that the
proposed measure of epistemic uncertainty provides a unique proxy to quantify
absolute evidence even in a framework which assumes that the true
data-generating model is within a finite set of candidate models.
|
Machine Learning, Machine Learning
|
Statistics
|
2002.07246
|
Huijie Feng
|
Regularized Training and Tight Certification for Randomized Smoothed
Classifier with Provable Robustness
|
stat.ML cs.LG
|
Recently smoothing deep neural network based classifiers via isotropic
Gaussian perturbation is shown to be an effective and scalable way to provide
state-of-the-art probabilistic robustness guarantee against $\ell_2$ norm
bounded adversarial perturbations. However, how to train a good base classifier
that is accurate and robust when smoothed has not been fully investigated. In
this work, we derive a new regularized risk, in which the regularizer can
adaptively encourage the accuracy and robustness of the smoothed counterpart
when training the base classifier. It is computationally efficient and can be
implemented in parallel with other empirical defense methods. We discuss how to
implement it under both standard (non-adversarial) and adversarial training
scheme. At the same time, we also design a new certification algorithm, which
can leverage the regularization effect to provide tighter robustness lower
bound that holds with high probability. Our extensive experimentation
demonstrates the effectiveness of the proposed training and certification
approaches on CIFAR-10 and ImageNet datasets.
|
Machine Learning, Machine Learning
|
Statistics
|
1811.10154
|
Cynthia Rudin
|
Stop Explaining Black Box Machine Learning Models for High Stakes
Decisions and Use Interpretable Models Instead
|
stat.ML cs.LG
|
Black box machine learning models are currently being used for high stakes
decision-making throughout society, causing problems throughout healthcare,
criminal justice, and in other domains. People have hoped that creating methods
for explaining these black box models will alleviate some of these problems,
but trying to \textit{explain} black box models, rather than creating models
that are \textit{interpretable} in the first place, is likely to perpetuate bad
practices and can potentially cause catastrophic harm to society. There is a
way forward -- it is to design models that are inherently interpretable. This
manuscript clarifies the chasm between explaining black boxes and using
inherently interpretable models, outlines several key reasons why explainable
black boxes should be avoided in high-stakes decisions, identifies challenges
to interpretable machine learning, and provides several example applications
where interpretable models could potentially replace black box models in
criminal justice, healthcare, and computer vision.
|
Machine Learning, Machine Learning
|
Statistics
|
2111.00034
|
Alexander Atanasov
|
Neural Networks as Kernel Learners: The Silent Alignment Effect
|
stat.ML cs.LG
|
Neural networks in the lazy training regime converge to kernel machines. Can
neural networks in the rich feature learning regime learn a kernel machine with
a data-dependent kernel? We demonstrate that this can indeed happen due to a
phenomenon we term silent alignment, which requires that the tangent kernel of
a network evolves in eigenstructure while small and before the loss appreciably
decreases, and grows only in overall scale afterwards. We show that such an
effect takes place in homogenous neural networks with small initialization and
whitened data. We provide an analytical treatment of this effect in the linear
network case. In general, we find that the kernel develops a low-rank
contribution in the early phase of training, and then evolves in overall scale,
yielding a function equivalent to a kernel regression solution with the final
network's tangent kernel. The early spectral learning of the kernel depends on
the depth. We also demonstrate that non-whitened data can weaken the silent
alignment effect.
|
Machine Learning, Machine Learning
|
Statistics
|
2206.01163
|
Chen Xu
|
Invertible Neural Networks for Graph Prediction
|
stat.ML cs.LG
|
Graph prediction problems prevail in data analysis and machine learning. The
inverse prediction problem, namely to infer input data from given output
labels, is of emerging interest in various applications. In this work, we
develop \textit{invertible graph neural network} (iGNN), a deep generative
model to tackle the inverse prediction problem on graphs by casting it as a
conditional generative task. The proposed model consists of an invertible
sub-network that maps one-to-one from data to an intermediate encoded feature,
which allows forward prediction by a linear classification sub-network as well
as efficient generation from output labels via a parametric mixture model. The
invertibility of the encoding sub-network is ensured by a Wasserstein-2
regularization which allows free-form layers in the residual blocks. The model
is scalable to large graphs by a factorized parametric mixture model of the
encoded feature and is computationally scalable by using GNN layers. The
existence of invertible flow mapping is backed by theories of optimal transport
and diffusion process, and we prove the expressiveness of graph convolution
layers to approximate the theoretical flows of graph data. The proposed iGNN
model is experimentally examined on synthetic data, including the example on
large graphs, and the empirical advantage is also demonstrated on
real-application datasets of solar ramping event data and traffic flow anomaly
detection.
|
Machine Learning, Machine Learning
|
Statistics
|
2003.14286
|
Nicolas Donati
|
Deep Geometric Functional Maps: Robust Feature Learning for Shape
Correspondence
|
stat.ML cs.LG
|
We present a novel learning-based approach for computing correspondences
between non-rigid 3D shapes. Unlike previous methods that either require
extensive training data or operate on handcrafted input descriptors and thus
generalize poorly across diverse datasets, our approach is both accurate and
robust to changes in shape structure. Key to our method is a feature-extraction
network that learns directly from raw shape geometry, combined with a novel
regularized map extraction layer and loss, based on the functional map
representation. We demonstrate through extensive experiments in challenging
shape matching scenarios that our method can learn from less training data than
existing supervised approaches and generalizes significantly better than
current descriptor-based learning methods. Our source code is available at:
https://github.com/LIX-shape-analysis/GeomFmaps.
|
Machine Learning, Machine Learning
|
Statistics
|
1910.05534
|
Ian Gallagher
|
Spectral embedding of weighted graphs
|
stat.ML cs.LG
|
When analyzing weighted networks using spectral embedding, a judicious
transformation of the edge weights may produce better results. To formalize
this idea, we consider the asymptotic behavior of spectral embedding for
different edge-weight representations, under a generic low rank model. We
measure the quality of different embeddings -- which can be on entirely
different scales -- by how easy it is to distinguish communities, in an
information-theoretic sense. For common types of weighted graphs, such as count
networks or p-value networks, we find that transformations such as tempering or
thresholding can be highly beneficial, both in theory and in practice.
|
Machine Learning, Machine Learning
|
Statistics
|
1809.02157
|
Dino Oglic
|
Scalable Learning in Reproducing Kernel Krein Spaces
|
stat.ML cs.LG
|
We provide the first mathematically complete derivation of the Nystr\"om
method for low-rank approximation of indefinite kernels and propose an
efficient method for finding an approximate eigendecomposition of such kernel
matrices. Building on this result, we devise highly scalable methods for
learning in reproducing kernel Kre\u{\i}n spaces. The devised approaches
provide a principled and theoretically well-founded means to tackle large scale
learning problems with indefinite kernels. The main motivation for our work
comes from problems with structured representations (e.g., graphs, strings,
time-series), where it is relatively easy to devise a pairwise (dis)similarity
function based on intuition and/or knowledge of domain experts. Such functions
are typically not positive definite and it is often well beyond the expertise
of practitioners to verify this condition. The effectiveness of the devised
approaches is evaluated empirically using indefinite kernels defined on
structured and vectorial data representations.
|
Machine Learning, Machine Learning
|
Statistics
|
2108.00230
|
Flore Sentenac
|
Pure Exploration and Regret Minimization in Matching Bandits
|
stat.ML cs.LG
|
Finding an optimal matching in a weighted graph is a standard combinatorial
problem. We consider its semi-bandit version where either a pair or a full
matching is sampled sequentially. We prove that it is possible to leverage a
rank-1 assumption on the adjacency matrix to reduce the sample complexity and
the regret of off-the-shelf algorithms up to reaching a linear dependency in
the number of vertices (up to poly log terms).
|
Machine Learning, Machine Learning
|
Statistics
|
2310.11431
|
David Klindt
|
Identifying Interpretable Visual Features in Artificial and Biological
Neural Systems
|
stat.ML cs.LG
|
Single neurons in neural networks are often interpretable in that they
represent individual, intuitively meaningful features. However, many neurons
exhibit $\textit{mixed selectivity}$, i.e., they represent multiple unrelated
features. A recent hypothesis proposes that features in deep networks may be
represented in $\textit{superposition}$, i.e., on non-orthogonal axes by
multiple neurons, since the number of possible interpretable features in
natural data is generally larger than the number of neurons in a given network.
Accordingly, we should be able to find meaningful directions in activation
space that are not aligned with individual neurons. Here, we propose (1) an
automated method for quantifying visual interpretability that is validated
against a large database of human psychophysics judgments of neuron
interpretability, and (2) an approach for finding meaningful directions in
network activation space. We leverage these methods to discover directions in
convolutional neural networks that are more intuitively meaningful than
individual neurons, as we confirm and investigate in a series of analyses.
Moreover, we apply the same method to three recent datasets of visual neural
responses in the brain and find that our conclusions largely transfer to real
neural data, suggesting that superposition might be deployed by the brain. This
also provides a link with disentanglement and raises fundamental questions
about robust, efficient and factorized representations in both artificial and
biological neural systems.
|
Machine Learning, Machine Learning
|
Statistics
|
1611.06534
|
Marc Abeille
|
Linear Thompson Sampling Revisited
|
stat.ML cs.LG
|
We derive an alternative proof for the regret of Thompson sampling (\ts) in
the stochastic linear bandit setting. While we obtain a regret bound of order
$\widetilde{O}(d^{3/2}\sqrt{T})$ as in previous results, the proof sheds new
light on the functioning of the \ts. We leverage on the structure of the
problem to show how the regret is related to the sensitivity (i.e., the
gradient) of the objective function and how selecting optimal arms associated
to \textit{optimistic} parameters does control it. Thus we show that \ts can be
seen as a generic randomized algorithm where the sampling distribution is
designed to have a fixed probability of being optimistic, at the cost of an
additional $\sqrt{d}$ regret factor compared to a UCB-like approach.
Furthermore, we show that our proof can be readily applied to regularized
linear optimization and generalized linear model problems.
|
Machine Learning, Machine Learning
|
Statistics
|
2209.07230
|
Chen Amiraz
|
Recovery Guarantees for Distributed-OMP
|
stat.ML cs.LG
|
We study distributed schemes for high-dimensional sparse linear regression,
based on orthogonal matching pursuit (OMP). Such schemes are particularly
suited for settings where a central fusion center is connected to end machines,
that have both computation and communication limitations. We prove that under
suitable assumptions, distributed-OMP schemes recover the support of the
regression vector with communication per machine linear in its sparsity and
logarithmic in the dimension. Remarkably, this holds even at low
signal-to-noise-ratios, where individual machines are unable to detect the
support. Our simulations show that distributed-OMP schemes are competitive with
more computationally intensive methods, and in some cases even outperform them.
|
Machine Learning, Machine Learning
|
Statistics
|
2303.15074
|
Francisco Caldas
|
Conjunction Data Messages for Space Collision Behave as a Poisson
Process
|
stat.ML cs.LG
|
Space debris is a major problem in space exploration. International bodies
continuously monitor a large database of orbiting objects and emit warnings in
the form of conjunction data messages. An important question for satellite
operators is to estimate when fresh information will arrive so that they can
react timely but sparingly with satellite maneuvers. We propose a statistical
learning model of the message arrival process, allowing us to answer two
important questions: (1) Will there be any new message in the next specified
time interval? (2) When exactly and with what uncertainty will the next message
arrive? The average prediction error for question (2) of our Bayesian Poisson
process model is smaller than the baseline in more than 4 hours in a test set
of 50k close encounter events.
|
Machine Learning, Machine Learning
|
Statistics
|
2304.04258
|
Jiachen T. Wang
|
A Note on "Efficient Task-Specific Data Valuation for Nearest Neighbor
Algorithms"
|
stat.ML cs.LG
|
Data valuation is a growing research field that studies the influence of
individual data points for machine learning (ML) models. Data Shapley, inspired
by cooperative game theory and economics, is an effective method for data
valuation. However, it is well-known that the Shapley value (SV) can be
computationally expensive. Fortunately, Jia et al. (2019) showed that for
K-Nearest Neighbors (KNN) models, the computation of Data Shapley is
surprisingly simple and efficient.
In this note, we revisit the work of Jia et al. (2019) and propose a more
natural and interpretable utility function that better reflects the performance
of KNN models. We derive the corresponding calculation procedure for the Data
Shapley of KNN classifiers/regressors with the new utility functions. Our new
approach, dubbed soft-label KNN-SV, achieves the same time complexity as the
original method. We further provide an efficient approximation algorithm for
soft-label KNN-SV based on locality sensitive hashing (LSH). Our experimental
results demonstrate that Soft-label KNN-SV outperforms the original method on
most datasets in the task of mislabeled data detection, making it a better
baseline for future work on data valuation.
|
Machine Learning, Machine Learning
|
Statistics
|
1905.12407
|
Ayman Boustati
|
Non-linear Multitask Learning with Deep Gaussian Processes
|
stat.ML cs.LG
|
We present a multi-task learning formulation for Deep Gaussian processes
(DGPs), through non-linear mixtures of latent processes. The latent space is
composed of private processes that capture within-task information and shared
processes that capture across-task dependencies. We propose two different
methods for segmenting the latent space: through hard coding shared and
task-specific processes or through soft sharing with Automatic Relevance
Determination kernels. We show that our formulation is able to improve the
learning performance and transfer information between the tasks, outperforming
other probabilistic multi-task learning models across real-world and
benchmarking settings.
|
Machine Learning, Machine Learning
|
Statistics
|
1708.05789
|
Kumar Sricharan
|
Semi-supervised Conditional GANs
|
stat.ML cs.LG
|
We introduce a new model for building conditional generative models in a
semi-supervised setting to conditionally generate data given attributes by
adapting the GAN framework. The proposed semi-supervised GAN (SS-GAN) model
uses a pair of stacked discriminators to learn the marginal distribution of the
data, and the conditional distribution of the attributes given the data
respectively. In the semi-supervised setting, the marginal distribution (which
is often harder to learn) is learned from the labeled + unlabeled data, and the
conditional distribution is learned purely from the labeled data. Our
experimental results demonstrate that this model performs significantly better
compared to existing semi-supervised conditional GAN models.
|
Machine Learning, Machine Learning
|
Statistics
|
2011.05231
|
Elliott Gordon-Rodriguez
|
Uses and Abuses of the Cross-Entropy Loss: Case Studies in Modern Deep
Learning
|
stat.ML cs.LG
|
Modern deep learning is primarily an experimental science, in which empirical
advances occasionally come at the expense of probabilistic rigor. Here we focus
on one such example; namely the use of the categorical cross-entropy loss to
model data that is not strictly categorical, but rather takes values on the
simplex. This practice is standard in neural network architectures with label
smoothing and actor-mimic reinforcement learning, amongst others. Drawing on
the recently discovered continuous-categorical distribution, we propose
probabilistically-inspired alternatives to these models, providing an approach
that is more principled and theoretically appealing. Through careful
experimentation, including an ablation study, we identify the potential for
outperformance in these models, thereby highlighting the importance of a proper
probabilistic treatment, as well as illustrating some of the failure modes
thereof.
|
Machine Learning, Machine Learning
|
Statistics
|
1704.07352
|
Pratik Jawanpuria
|
Structured low-rank matrix learning: algorithms and applications
|
stat.ML cs.LG
|
We consider the problem of learning a low-rank matrix, constrained to lie in
a linear subspace, and introduce a novel factorization for modeling such
matrices. A salient feature of the proposed factorization scheme is it
decouples the low-rank and the structural constraints onto separate factors. We
formulate the optimization problem on the Riemannian spectrahedron manifold,
where the Riemannian framework allows to develop computationally efficient
conjugate gradient and trust-region algorithms. Experiments on problems such as
standard/robust/non-negative matrix completion, Hankel matrix learning and
multi-task learning demonstrate the efficacy of our approach. A shorter version
of this work has been published in ICML'18.
|
Machine Learning, Machine Learning
|
Statistics
|
1907.02571
|
Stefano Trac\`a
|
Reducing Exploration of Dying Arms in Mortal Bandits
|
stat.ML cs.LG
|
Mortal bandits have proven to be extremely useful for providing news article
recommendations, running automated online advertising campaigns, and for other
applications where the set of available options changes over time. Previous
work on this problem showed how to regulate exploration of new arms when they
have recently appeared, but they do not adapt when the arms are about to
disappear. Since in most applications we can determine either exactly or
approximately when arms will disappear, we can leverage this information to
improve performance: we should not be exploring arms that are about to
disappear. We provide adaptations of algorithms, regret bounds, and experiments
for this study, showing a clear benefit from regulating greed
(exploration/exploitation) for arms that will soon disappear. We illustrate
numerical performance on the Yahoo! Front Page Today Module User Click Log
Dataset.
|
Machine Learning, Machine Learning
|
Statistics
|
1906.11426
|
Prashant Shekhar
|
Hierarchical Data Reduction and Learning
|
stat.ML cs.LG
|
This paper describes a hierarchical learning strategy for generating sparse
representations of multivariate datasets. The hierarchy arises from
approximation spaces considered at successively finer scales. A detailed
analysis of stability, convergence and behavior of error functionals associated
with the approximations are presented, along with a well chosen set of
applications. Results show the performance of the approach as a data reduction
mechanism for both synthetic (univariate and multivariate) and real datasets
(geospatial and numerical model outcomes). The sparse representation generated
is shown to efficiently reconstruct data and minimize error in prediction.
|
Machine Learning, Machine Learning
|
Statistics
|
1811.12323
|
C\'edric Beaulac
|
A Deep Latent-Variable Model Application to Select Treatment Intensity
in Survival Analysis
|
stat.ML cs.LG
|
In the following short article we adapt a new and popular machine learning
model for inference on medical data sets. Our method is based on the
Variational AutoEncoder (VAE) framework that we adapt to survival analysis on
small data sets with missing values. In our model, the true health status
appears as a set of latent variables that affects the observed covariates and
the survival chances. We show that this flexible model allows insightful
decision-making using a predicted distribution and outperforms a classic
survival analysis model.
|
Machine Learning, Machine Learning
|
Statistics
|
1303.3664
|
Weicong Ding
|
Topic Discovery through Data Dependent and Random Projections
|
stat.ML cs.LG
|
We present algorithms for topic modeling based on the geometry of
cross-document word-frequency patterns. This perspective gains significance
under the so called separability condition. This is a condition on existence of
novel-words that are unique to each topic. We present a suite of highly
efficient algorithms based on data-dependent and random projections of
word-frequency patterns to identify novel words and associated topics. We will
also discuss the statistical guarantees of the data-dependent projections
method based on two mild assumptions on the prior density of topic document
matrix. Our key insight here is that the maximum and minimum values of
cross-document frequency patterns projected along any direction are associated
with novel words. While our sample complexity bounds for topic recovery are
similar to the state-of-art, the computational complexity of our random
projection scheme scales linearly with the number of documents and the number
of words per document. We present several experiments on synthetic and
real-world datasets to demonstrate qualitative and quantitative merits of our
scheme.
|
Machine Learning, Machine Learning
|
Statistics
|
2006.07036
|
Yohan Jung
|
Approximate Inference for Spectral Mixture Kernel
|
stat.ML cs.LG
|
A spectral mixture (SM) kernel is a flexible kernel used to model any
stationary covariance function. Although it is useful in modeling data, the
learning of the SM kernel is generally difficult because optimizing a large
number of parameters for the SM kernel typically induces an over-fitting,
particularly when a gradient-based optimization is used. Also, a longer
training time is required. To improve the training, we propose an approximate
Bayesian inference for the SM kernel. Specifically, we employ the variational
distribution of the spectral points to approximate SM kernel with a random
Fourier feature. We optimize the variational parameters by applying a
sampling-based variational inference to the derived evidence lower bound (ELBO)
estimator constructed from the approximate kernel. To improve the inference, we
further propose two additional strategies: (1) a sampling strategy of spectral
points to estimate the ELBO estimator reliably and thus its associated
gradient, and (2) an approximate natural gradient to accelerate the convergence
of the parameters. The proposed inference combined with two strategies
accelerates the convergence of the parameters and leads to better optimal
parameters.
|
Machine Learning, Machine Learning
|
Statistics
|
2404.01883
|
Yanyan Dong
|
Adversarial Combinatorial Bandits with Switching Costs
|
stat.ML cs.LG
|
We study the problem of adversarial combinatorial bandit with a switching
cost $\lambda$ for a switch of each selected arm in each round, considering
both the bandit feedback and semi-bandit feedback settings. In the oblivious
adversarial case with $K$ base arms and time horizon $T$, we derive lower
bounds for the minimax regret and design algorithms to approach them. To prove
these lower bounds, we design stochastic loss sequences for both feedback
settings, building on an idea from previous work in Dekel et al. (2014). The
lower bound for bandit feedback is $ \tilde{\Omega}\big( (\lambda
K)^{\frac{1}{3}} (TI)^{\frac{2}{3}}\big)$ while that for semi-bandit feedback
is $ \tilde{\Omega}\big( (\lambda K I)^{\frac{1}{3}} T^{\frac{2}{3}}\big)$
where $I$ is the number of base arms in the combinatorial arm played in each
round. To approach these lower bounds, we design algorithms that operate in
batches by dividing the time horizon into batches to restrict the number of
switches between actions. For the bandit feedback setting, where only the total
loss of the combinatorial arm is observed, we introduce the Batched-Exp2
algorithm which achieves a regret upper bound of $\tilde{O}\big((\lambda
K)^{\frac{1}{3}}T^{\frac{2}{3}}I^{\frac{4}{3}}\big)$ as $T$ tends to infinity.
In the semi-bandit feedback setting, where all losses for the combinatorial arm
are observed, we propose the Batched-BROAD algorithm which achieves a regret
upper bound of $\tilde{O}\big( (\lambda K)^{\frac{1}{3}}
(TI)^{\frac{2}{3}}\big)$.
|
Machine Learning, Machine Learning
|
Statistics
|
1606.00856
|
Jesus Malo
|
Sequential Principal Curves Analysis
|
stat.ML cs.LG
|
This work includes all the technical details of the Sequential Principal
Curves Analysis (SPCA) in a single document. SPCA is an unsupervised nonlinear
and invertible feature extraction technique. The identified curvilinear
features can be interpreted as a set of nonlinear sensors: the response of each
sensor is the projection onto the corresponding feature. Moreover, it can be
easily tuned for different optimization criteria; e.g. infomax, error
minimization, decorrelation; by choosing the right way to measure distances
along each curvilinear feature. Even though proposed in [Laparra et al. Neural
Comp. 12] and shown to work in multiple modalities in [Laparra and Malo
Frontiers Hum. Neuro. 15], the SPCA framework has its original roots in the
nonlinear ICA algorithm in [Malo and Gutierrez Network 06]. Later on, the SPCA
philosophy for nonlinear generalization of PCA originated substantially faster
alternatives at the cost of introducing different constraints in the model.
Namely, the Principal Polynomial Analysis (PPA) [Laparra et al. IJNS 14], and
the Dimensionality Reduction via Regression (DRR) [Laparra et al. IEEE TGRS
15]. This report illustrates the reasons why we developed such family and is
the appropriate technical companion for the missing details in [Laparra et al.,
NeCo 12, Laparra and Malo, Front.Hum.Neuro. 15]. See also the data, code and
examples in the dedicated sites http://isp.uv.es/spca.html and
http://isp.uv.es/after effects.html
|
Machine Learning, Machine Learning
|
Statistics
|
2203.13911
|
Benyamin Ghojogh
|
Theoretical Connection between Locally Linear Embedding, Factor
Analysis, and Probabilistic PCA
|
stat.ML cs.LG
|
Locally Linear Embedding (LLE) is a nonlinear spectral dimensionality
reduction and manifold learning method. It has two main steps which are linear
reconstruction and linear embedding of points in the input space and embedding
space, respectively. In this work, we look at the linear reconstruction step
from a stochastic perspective where it is assumed that every data point is
conditioned on its linear reconstruction weights as latent factors. The
stochastic linear reconstruction of LLE is solved using expectation
maximization. We show that there is a theoretical connection between three
fundamental dimensionality reduction methods, i.e., LLE, factor analysis, and
probabilistic Principal Component Analysis (PCA). The stochastic linear
reconstruction of LLE is formulated similar to the factor analysis and
probabilistic PCA. It is also explained why factor analysis and probabilistic
PCA are linear and LLE is a nonlinear method. This work combines and makes a
bridge between two broad approaches of dimensionality reduction, i.e., the
spectral and probabilistic algorithms.
|
Machine Learning, Machine Learning
|
Statistics
|
1808.03253
|
Adarsh Subbaswamy
|
Counterfactual Normalization: Proactively Addressing Dataset Shift and
Improving Reliability Using Causal Mechanisms
|
stat.ML cs.LG
|
Predictive models can fail to generalize from training to deployment
environments because of dataset shift, posing a threat to model reliability and
the safety of downstream decisions made in practice. Instead of using samples
from the target distribution to reactively correct dataset shift, we use
graphical knowledge of the causal mechanisms relating variables in a prediction
problem to proactively remove relationships that do not generalize across
environments, even when these relationships may depend on unobserved variables
(violations of the "no unobserved confounders" assumption). To accomplish this,
we identify variables with unstable paths of statistical influence and remove
them from the model. We also augment the causal graph with latent
counterfactual variables that isolate unstable paths of statistical influence,
allowing us to retain stable paths that would otherwise be removed. Our
experiments demonstrate that models that remove vulnerable variables and use
estimates of the latent variables transfer better, often outperforming in the
target domain despite some accuracy loss in the training domain.
|
Machine Learning, Machine Learning
|
Statistics
|
1202.5514
|
Simplice Dossou-Gb\'et\'e
|
Classification approach based on association rules mining for unbalanced
data
|
stat.ML cs.LG
|
This paper deals with the binary classification task when the target class
has the lower probability of occurrence. In such situation, it is not possible
to build a powerful classifier by using standard methods such as logistic
regression, classification tree, discriminant analysis, etc. To overcome this
short-coming of these methods which yield classifiers with low sensibility, we
tackled the classification problem here through an approach based on the
association rules learning. This approach has the advantage of allowing the
identification of the patterns that are well correlated with the target class.
Association rules learning is a well known method in the area of data-mining.
It is used when dealing with large database for unsupervised discovery of local
patterns that expresses hidden relationships between input variables. In
considering association rules from a supervised learning point of view, a
relevant set of weak classifiers is obtained from which one derives a
classifier that performs well.
|
Machine Learning, Machine Learning
|
Statistics
|
2403.10929
|
Aidan Scannell
|
Function-space Parameterization of Neural Networks for Sequential
Learning
|
stat.ML cs.LG
|
Sequential learning paradigms pose challenges for gradient-based deep
learning due to difficulties incorporating new data and retaining prior
knowledge. While Gaussian processes elegantly tackle these problems, they
struggle with scalability and handling rich inputs, such as images. To address
these issues, we introduce a technique that converts neural networks from
weight space to function space, through a dual parameterization. Our
parameterization offers: (i) a way to scale function-space methods to large
data sets via sparsification, (ii) retention of prior knowledge when access to
past data is limited, and (iii) a mechanism to incorporate new data without
retraining. Our experiments demonstrate that we can retain knowledge in
continual learning and incorporate new data efficiently. We further show its
strengths in uncertainty quantification and guiding exploration in model-based
RL. Further information and code is available on the project website.
|
Machine Learning, Machine Learning
|
Statistics
|
1409.0797
|
Jian Yang
|
Feature Engineering for Map Matching of Low-Sampling-Rate GPS
Trajectories in Road Network
|
stat.ML cs.LG
|
Map matching of GPS trajectories from a sequence of noisy observations serves
the purpose of recovering the original routes in a road network. In this work
in progress, we attempt to share our experience of feature construction in a
spatial database by reporting our ongoing experiment of feature extrac-tion in
Conditional Random Fields (CRFs) for map matching. Our preliminary results are
obtained from real-world taxi GPS trajectories.
|
Machine Learning, Machine Learning
|
Statistics
|
2404.17442
|
Benjamin Dupuis
|
Uniform Generalization Bounds on Data-Dependent Hypothesis Sets via
PAC-Bayesian Theory on Random Sets
|
stat.ML cs.LG
|
We propose data-dependent uniform generalization bounds by approaching the
problem from a PAC-Bayesian perspective. We first apply the PAC-Bayesian
framework on `random sets' in a rigorous way, where the training algorithm is
assumed to output a data-dependent hypothesis set after observing the training
data. This approach allows us to prove data-dependent bounds, which can be
applicable in numerous contexts. To highlight the power of our approach, we
consider two main applications. First, we propose a PAC-Bayesian formulation of
the recently developed fractal-dimension-based generalization bounds. The
derived results are shown to be tighter and they unify the existing results
around one simple proof technique. Second, we prove uniform bounds over the
trajectories of continuous Langevin dynamics and stochastic gradient Langevin
dynamics. These results provide novel information about the generalization
properties of noisy algorithms.
|
Machine Learning, Machine Learning
|
Statistics
|
2307.05789
|
Mihaela Rosca
|
Implicit regularisation in stochastic gradient descent: from
single-objective to two-player games
|
stat.ML cs.LG
|
Recent years have seen many insights on deep learning optimisation being
brought forward by finding implicit regularisation effects of commonly used
gradient-based optimisers. Understanding implicit regularisation can not only
shed light on optimisation dynamics, but it can also be used to improve
performance and stability across problem domains, from supervised learning to
two-player games such as Generative Adversarial Networks. An avenue for finding
such implicit regularisation effects has been quantifying the discretisation
errors of discrete optimisers via continuous-time flows constructed by backward
error analysis (BEA). The current usage of BEA is not without limitations,
since not all the vector fields of continuous-time flows obtained using BEA can
be written as a gradient, hindering the construction of modified losses
revealing implicit regularisers. In this work, we provide a novel approach to
use BEA, and show how our approach can be used to construct continuous-time
flows with vector fields that can be written as gradients. We then use this to
find previously unknown implicit regularisation effects, such as those induced
by multiple stochastic gradient descent steps while accounting for the exact
data batches used in the updates, and in generally differentiable two-player
games.
|
Machine Learning, Machine Learning
|
Statistics
|
2202.02943
|
Kunwoong Kim
|
Learning fair representation with a parametric integral probability
metric
|
stat.ML cs.LG
|
As they have a vital effect on social decision-making, AI algorithms should
be not only accurate but also fair. Among various algorithms for fairness AI,
learning fair representation (LFR), whose goal is to find a fair representation
with respect to sensitive variables such as gender and race, has received much
attention. For LFR, the adversarial training scheme is popularly employed as is
done in the generative adversarial network type algorithms. The choice of a
discriminator, however, is done heuristically without justification. In this
paper, we propose a new adversarial training scheme for LFR, where the integral
probability metric (IPM) with a specific parametric family of discriminators is
used. The most notable result of the proposed LFR algorithm is its theoretical
guarantee about the fairness of the final prediction model, which has not been
considered yet. That is, we derive theoretical relations between the fairness
of representation and the fairness of the prediction model built on the top of
the representation (i.e., using the representation as the input). Moreover, by
numerical experiments, we show that our proposed LFR algorithm is
computationally lighter and more stable, and the final prediction model is
competitive or superior to other LFR algorithms using more complex
discriminators.
|
Machine Learning, Machine Learning
|
Statistics
|
1506.07721
|
Kazuto Fukuchi
|
Fairness-Aware Learning with Restriction of Universal Dependency using
f-Divergences
|
stat.ML cs.LG
|
Fairness-aware learning is a novel framework for classification tasks. Like
regular empirical risk minimization (ERM), it aims to learn a classifier with a
low error rate, and at the same time, for the predictions of the classifier to
be independent of sensitive features, such as gender, religion, race, and
ethnicity. Existing methods can achieve low dependencies on given samples, but
this is not guaranteed on unseen samples. The existing fairness-aware learning
algorithms employ different dependency measures, and each algorithm is
specifically designed for a particular one. Such diversity makes it difficult
to theoretically analyze and compare them. In this paper, we propose a general
framework for fairness-aware learning that uses f-divergences and that covers
most of the dependency measures employed in the existing methods. We introduce
a way to estimate the f-divergences that allows us to give a unified analysis
for the upper bound of the estimation error; this bound is tighter than that of
the existing convergence rate analysis of the divergence estimation. With our
divergence estimate, we propose a fairness-aware learning algorithm, and
perform a theoretical analysis of its generalization error. Our analysis
reveals that, under mild assumptions and even with enforcement of fairness, the
generalization error of our method is $O(\sqrt{1/n})$, which is the same as
that of the regular ERM. In addition, and more importantly, we show that, for
any f-divergence, the upper bound of the estimation error of the divergence is
$O(\sqrt{1/n})$. This indicates that our fairness-aware learning algorithm
guarantees low dependencies on unseen samples for any dependency measure
represented by an f-divergence.
|
Machine Learning, Machine Learning
|
Statistics
|
2206.05828
|
Mathieu Molina
|
Bounding and Approximating Intersectional Fairness through Marginal
Fairness
|
stat.ML cs.LG
|
Discrimination in machine learning often arises along multiple dimensions
(a.k.a. protected attributes); it is then desirable to ensure
\emph{intersectional fairness} -- i.e., that no subgroup is discriminated
against. It is known that ensuring \emph{marginal fairness} for every dimension
independently is not sufficient in general. Due to the exponential number of
subgroups, however, directly measuring intersectional fairness from data is
impossible. In this paper, our primary goal is to understand in detail the
relationship between marginal and intersectional fairness through statistical
analysis. We first identify a set of sufficient conditions under which an exact
relationship can be obtained. Then, we prove bounds (easily computable through
marginal fairness and other meaningful statistical quantities) in
high-probability on intersectional fairness in the general case. Beyond their
descriptive value, we show that these theoretical bounds can be leveraged to
derive a heuristic improving the approximation and bounds of intersectional
fairness by choosing, in a relevant manner, protected attributes for which we
describe intersectional subgroups. Finally, we test the performance of our
approximations and bounds on real and synthetic data-sets.
|
Machine Learning, Machine Learning
|
Statistics
|
2307.06406
|
Luke Duttweiler
|
Testing Sparsity Assumptions in Bayesian Networks
|
stat.ML cs.LG
|
Bayesian network (BN) structure discovery algorithms typically either make
assumptions about the sparsity of the true underlying network, or are limited
by computational constraints to networks with a small number of variables.
While these sparsity assumptions can take various forms, frequently the
assumptions focus on an upper bound for the maximum in-degree of the underlying
graph $\nabla_G$. Theorem 2 in Duttweiler et. al. (2023) demonstrates that the
largest eigenvalue of the normalized inverse covariance matrix ($\Omega$) of a
linear BN is a lower bound for $\nabla_G$. Building on this result, this paper
provides the asymptotic properties of, and a debiasing procedure for, the
sample eigenvalues of $\Omega$, leading to a hypothesis test that may be used
to determine if the BN has max in-degree greater than 1. A linear BN structure
discovery workflow is suggested in which the investigator uses this hypothesis
test to aid in selecting an appropriate structure discovery algorithm. The
hypothesis test performance is evaluated through simulations and the workflow
is demonstrated on data from a human psoriasis study.
|
Machine Learning, Machine Learning
|
Statistics
|
2112.06760
|
Jianhua Zhao
|
Robust factored principal component analysis for matrix-valued outlier
accommodation and detection
|
stat.ML cs.LG
|
Principal component analysis (PCA) is a popular dimension reduction technique
for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for
matrix data, which can substantially reduce the number of parameters in PCA
while yield satisfactory performance. However, FPCA is based on the Gaussian
assumption and thereby susceptible to outliers. Although the multivariate $t$
distribution as a robust modeling tool for vector data has a very long history,
its application to matrix data is very limited. The main reason is that the
dimension of the vectorized matrix data is often very high and the higher the
dimension, the lower the breakdown point that measures the robustness. To solve
the robustness problem suffered by FPCA and make it applicable to matrix data,
in this paper we propose a robust extension of FPCA (RFPCA), which is built
upon a $t$-type distribution called matrix-variate $t$ distribution. Like the
multivariate $t$ distribution, the matrix-variate $t$ distribution can
adaptively down-weight outliers and yield robust estimates. We develop a fast
EM-type algorithm for parameter estimation. Experiments on synthetic and
real-world datasets reveal that RFPCA is compared favorably with several
related methods and RFPCA is a simple but powerful tool for matrix-valued
outlier detection.
|
Machine Learning, Machine Learning
|
Statistics
|
1810.10425
|
Gaetano Manzo
|
A Deep Learning Mechanism for Efficient Information Dissemination in
Vehicular Floating Content
|
stat.ML cs.LG
|
Handling the tremendous amount of network data, produced by the explosive
growth of mobile traffic volume, is becoming of main priority to achieve
desired performance targets efficiently. Opportunistic communication such as
FloatingContent (FC), can be used to offload part of the cellular traffic
volume to vehicular-to-vehicular communication (V2V), leaving the
infrastructure the task of coordinating the communication. Existing FC
dimensioning approaches have limitations, mainly due to unrealistic assumptions
and on a coarse partitioning of users, which results in over-dimensioning.
Shaping the opportunistic communication area is a crucial task to achieve
desired application performance efficiently. In this work, we propose a
solution for this open challenge. In particular, the broadcasting areas called
Anchor Zone (AZ), are selected via a deep learning approach to minimize
communication resources achieving desired message availability. No assumption
required to fit the classifier in both synthetic and real mobility. A numerical
study is made to validate the effectiveness and efficiency of the proposed
method. The predicted AZ configuration can achieve an accuracy of 89.7%within
98% of confidence level. By cause of the learning approach, the method performs
even better in real scenarios, saving up to 27% of resources compared to
previous work analytically modelled
|
Machine Learning, Machine Learning
|
Statistics
|
1802.04865
|
Terrance DeVries
|
Learning Confidence for Out-of-Distribution Detection in Neural Networks
|
stat.ML cs.LG
|
Modern neural networks are very powerful predictive models, but they are
often incapable of recognizing when their predictions may be wrong. Closely
related to this is the task of out-of-distribution detection, where a network
must determine whether or not an input is outside of the set on which it is
expected to safely perform. To jointly address these issues, we propose a
method of learning confidence estimates for neural networks that is simple to
implement and produces intuitively interpretable outputs. We demonstrate that
on the task of out-of-distribution detection, our technique surpasses recently
proposed techniques which construct confidence based on the network's output
distribution, without requiring any additional labels or access to
out-of-distribution examples. Additionally, we address the problem of
calibrating out-of-distribution detectors, where we demonstrate that
misclassified in-distribution examples can be used as a proxy for
out-of-distribution examples.
|
Machine Learning, Machine Learning
|
Statistics
|
1905.00507
|
Antoine Dedieu
|
Learning higher-order sequential structure with cloned HMMs
|
stat.ML cs.LG
|
Variable order sequence modeling is an important problem in artificial and
natural intelligence. While overcomplete Hidden Markov Models (HMMs), in
theory, have the capacity to represent long-term temporal structure, they often
fail to learn and converge to local minima. We show that by constraining HMMs
with a simple sparsity structure inspired by biology, we can make it learn
variable order sequences efficiently. We call this model cloned HMM (CHMM)
because the sparsity structure enforces that many hidden states map
deterministically to the same emission state. CHMMs with over 1 billion
parameters can be efficiently trained on GPUs without being severely affected
by the credit diffusion problem of standard HMMs. Unlike n-grams and sequence
memoizers, CHMMs can model temporal dependencies at arbitrarily long distances
and recognize contexts with 'holes' in them. Compared to Recurrent Neural
Networks and their Long Short-Term Memory extensions (LSTMs), CHMMs are
generative models that can natively deal with uncertainty. Moreover, CHMMs
return a higher-order graph that represents the temporal structure of the data
which can be useful for community detection, and for building hierarchical
models. Our experiments show that CHMMs can beat n-grams, sequence memoizers,
and LSTMs on character-level language modeling tasks. CHMMs can be a viable
alternative to these methods in some tasks that require variable order sequence
modeling and the handling of uncertainty.
|
Machine Learning, Machine Learning
|
Statistics
|
2110.10518
|
Alejandro David De La Concha Duarte
|
Online non-parametric change-point detection for heterogeneous data
streams observed over graph nodes
|
stat.ML cs.LG
|
Consider a heterogeneous data stream being generated by the nodes of a graph.
The data stream is in essence composed by multiple streams, possibly of
different nature that depends on each node. At a given moment $\tau$, a
change-point occurs for a subset of nodes $C$, signifying the change in the
probability distribution of their associated streams. In this paper we propose
an online non-parametric method to infer $\tau$ based on the direct estimation
of the likelihood-ratio between the post-change and the pre-change distribution
associated with the data stream of each node. We propose a kernel-based method,
under the hypothesis that connected nodes of the graph are expected to have
similar likelihood-ratio estimates when there is no change-point. We
demonstrate the quality of our method on synthetic experiments and real-world
applications.
|
Machine Learning, Machine Learning
|
Statistics
|
1702.01824
|
Franziska Horn
|
Predicting Pairwise Relations with Neural Similarity Encoders
|
stat.ML cs.LG
|
Matrix factorization is at the heart of many machine learning algorithms, for
example, dimensionality reduction (e.g. kernel PCA) or recommender systems
relying on collaborative filtering. Understanding a singular value
decomposition (SVD) of a matrix as a neural network optimization problem
enables us to decompose large matrices efficiently while dealing naturally with
missing values in the given matrix. But most importantly, it allows us to learn
the connection between data points' feature vectors and the matrix containing
information about their pairwise relations. In this paper we introduce a novel
neural network architecture termed Similarity Encoder (SimEc), which is
designed to simultaneously factorize a given target matrix while also learning
the mapping to project the data points' feature vectors into a similarity
preserving embedding space. This makes it possible to, for example, easily
compute out-of-sample solutions for new data points. Additionally, we
demonstrate that SimEc can preserve non-metric similarities and even predict
multiple pairwise relations between data points at once.
|
Machine Learning, Machine Learning
|
Statistics
|
1806.04577
|
Abhishek Bansal
|
Using Inherent Structures to design Lean 2-layer RBMs
|
stat.ML cs.LG
|
Understanding the representational power of Restricted Boltzmann Machines
(RBMs) with multiple layers is an ill-understood problem and is an area of
active research. Motivated from the approach of \emph{Inherent Structure
formalism} (Stillinger & Weber, 1982), extensively used in analysing Spin
Glasses, we propose a novel measure called \emph{Inherent Structure Capacity}
(ISC), which characterizes the representation capacity of a fixed architecture
RBM by the expected number of modes of distributions emanating from the RBM
with parameters drawn from a prior distribution. Though ISC is intractable, we
show that for a single layer RBM architecture ISC approaches a finite constant
as number of hidden units are increased and to further improve the ISC, one
needs to add a second layer. Furthermore, we introduce \emph{Lean} RBMs, which
are multi-layer RBMs where each layer can have at-most $O(n)$ units with the
number of visible units being n. We show that for every single layer RBM with
$\Omega(n^{2+r}), r \ge 0$, hidden units there exists a two-layered \emph{lean}
RBM with $\Theta(n^2)$ parameters with the same ISC, establishing that 2 layer
RBMs can achieve the same representational power as single-layer RBMs but using
far fewer number of parameters. To the best of our knowledge, this is the first
result which quantitatively establishes the need for layering.
|
Machine Learning, Machine Learning
|
Statistics
|
2110.13891
|
Virginia Aglietti
|
Dynamic Causal Bayesian Optimization
|
stat.ML cs.LG
|
This paper studies the problem of performing a sequence of optimal
interventions in a causal dynamical system where both the target variable of
interest and the inputs evolve over time. This problem arises in a variety of
domains e.g. system biology and operational research. Dynamic Causal Bayesian
Optimization (DCBO) brings together ideas from sequential decision making,
causal inference and Gaussian process (GP) emulation. DCBO is useful in
scenarios where all causal effects in a graph are changing over time. At every
time step DCBO identifies a local optimal intervention by integrating both
observational and past interventional data collected from the system. We give
theoretical results detailing how one can transfer interventional information
across time steps and define a dynamic causal GP model which can be used to
quantify uncertainty and find optimal interventions in practice. We demonstrate
how DCBO identifies optimal interventions faster than competing approaches in
multiple settings and applications.
|
Machine Learning, Machine Learning
|
Statistics
|
1807.02089
|
Claire Vernade
|
Linear Bandits with Stochastic Delayed Feedback
|
stat.ML cs.LG
|
Stochastic linear bandits are a natural and well-studied model for structured
exploration/exploitation problems and are widely used in applications such as
online marketing and recommendation. One of the main challenges faced by
practitioners hoping to apply existing algorithms is that usually the feedback
is randomly delayed and delays are only partially observable. For example,
while a purchase is usually observable some time after the display, the
decision of not buying is never explicitly sent to the system. In other words,
the learner only observes delayed positive events. We formalize this problem as
a novel stochastic delayed linear bandit and propose ${\tt OTFLinUCB}$ and
${\tt OTFLinTS}$, two computationally efficient algorithms able to integrate
new information as it becomes available and to deal with the permanently
censored feedback. We prove optimal $\tilde O(\smash{d\sqrt{T}})$ bounds on the
regret of the first algorithm and study the dependency on delay-dependent
parameters. Our model, assumptions and results are validated by experiments on
simulated and real data.
|
Machine Learning, Machine Learning
|
Statistics
|
2007.05627
|
Shaofeng Deng
|
A Performance Guarantee for Spectral Clustering
|
stat.ML cs.LG
|
The two-step spectral clustering method, which consists of the Laplacian
eigenmap and a rounding step, is a widely used method for graph partitioning.
It can be seen as a natural relaxation to the NP-hard minimum ratio cut
problem. In this paper we study the central question: when is spectral
clustering able to find the global solution to the minimum ratio cut problem?
First we provide a condition that naturally depends on the intra- and
inter-cluster connectivities of a given partition under which we may certify
that this partition is the solution to the minimum ratio cut problem. Then we
develop a deterministic two-to-infinity norm perturbation bound for the the
invariant subspace of the graph Laplacian that corresponds to the $k$ smallest
eigenvalues. Finally by combining these two results we give a condition under
which spectral clustering is guaranteed to output the global solution to the
minimum ratio cut problem, which serves as a performance guarantee for spectral
clustering.
|
Machine Learning, Machine Learning
|
Statistics
|
2210.07278
|
Marvin Schmitt
|
Meta-Uncertainty in Bayesian Model Comparison
|
stat.ML cs.LG
|
Bayesian model comparison (BMC) offers a principled probabilistic approach to
study and rank competing models. In standard BMC, we construct a discrete
probability distribution over the set of possible models, conditional on the
observed data of interest. These posterior model probabilities (PMPs) are
measures of uncertainty, but -- when derived from a finite number of
observations -- are also uncertain themselves. In this paper, we conceptualize
distinct levels of uncertainty which arise in BMC. We explore a fully
probabilistic framework for quantifying meta-uncertainty, resulting in an
applied method to enhance any BMC workflow. Drawing on both Bayesian and
frequentist techniques, we represent the uncertainty over the uncertain PMPs
via meta-models which combine simulated and observed data into a predictive
distribution for PMPs on new data. We demonstrate the utility of the proposed
method in the context of conjugate Bayesian regression, likelihood-based
inference with Markov chain Monte Carlo, and simulation-based inference with
neural networks.
|
Machine Learning, Machine Learning
|
Statistics
|
1702.06832
|
Jernej Kos
|
Adversarial examples for generative models
|
stat.ML cs.LG
|
We explore methods of producing adversarial examples on deep generative
models such as the variational autoencoder (VAE) and the VAE-GAN. Deep learning
architectures are known to be vulnerable to adversarial examples, but previous
work has focused on the application of adversarial examples to classification
tasks. Deep generative models have recently become popular due to their ability
to model input data distributions and generate realistic examples from those
distributions. We present three classes of attacks on the VAE and VAE-GAN
architectures and demonstrate them against networks trained on MNIST, SVHN and
CelebA. Our first attack leverages classification-based adversaries by
attaching a classifier to the trained encoder of the target generative model,
which can then be used to indirectly manipulate the latent representation. Our
second attack directly uses the VAE loss function to generate a target
reconstruction image from the adversarial example. Our third attack moves
beyond relying on classification or the standard loss for the gradient and
directly optimizes against differences in source and target latent
representations. We also motivate why an attacker might be interested in
deploying such techniques against a target generative network.
|
Machine Learning, Machine Learning
|
Statistics
|
1701.02386
|
Ilya Tolstikhin
|
AdaGAN: Boosting Generative Models
|
stat.ML cs.LG
|
Generative Adversarial Networks (GAN) (Goodfellow et al., 2014) are an
effective method for training generative models of complex data such as natural
images. However, they are notoriously hard to train and can suffer from the
problem of missing modes where the model is not able to produce examples in
certain regions of the space. We propose an iterative procedure, called AdaGAN,
where at every step we add a new component into a mixture model by running a
GAN algorithm on a reweighted sample. This is inspired by boosting algorithms,
where many potentially weak individual predictors are greedily aggregated to
form a strong composite predictor. We prove that such an incremental procedure
leads to convergence to the true distribution in a finite number of steps if
each step is optimal, and convergence at an exponential rate otherwise. We also
illustrate experimentally that this procedure addresses the problem of missing
modes.
|
Machine Learning, Machine Learning
|
Statistics
|
2003.13491
|
Giuseppe Di Benedetto
|
Non-exchangeable feature allocation models with sublinear growth of the
feature sizes
|
stat.ML cs.LG
|
Feature allocation models are popular models used in different applications
such as unsupervised learning or network modeling. In particular, the Indian
buffet process is a flexible and simple one-parameter feature allocation model
where the number of features grows unboundedly with the number of objects. The
Indian buffet process, like most feature allocation models, satisfies a
symmetry property of exchangeability: the distribution is invariant under
permutation of the objects. While this property is desirable in some cases, it
has some strong implications. Importantly, the number of objects sharing a
particular feature grows linearly with the number of objects. In this article,
we describe a class of non-exchangeable feature allocation models where the
number of objects sharing a given feature grows sublinearly, where the rate can
be controlled by a tuning parameter. We derive the asymptotic properties of the
model, and show that such model provides a better fit and better predictive
performances on various datasets.
|
Machine Learning, Machine Learning
|
Statistics
|
1705.10924
|
Feng Nan
|
Sequential Dynamic Decision Making with Deep Neural Nets on a Test-Time
Budget
|
stat.ML cs.LG
|
Deep neural network (DNN) based approaches hold significant potential for
reinforcement learning (RL) and have already shown remarkable gains over
state-of-art methods in a number of applications. The effectiveness of DNN
methods can be attributed to leveraging the abundance of supervised data to
learn value functions, Q-functions, and policy function approximations without
the need for feature engineering. Nevertheless, the deployment of DNN-based
predictors with very deep architectures can pose an issue due to computational
and other resource constraints at test-time in a number of applications. We
propose a novel approach for reducing the average latency by learning a
computationally efficient gating function that is capable of recognizing states
in a sequential decision process for which policy prescriptions of a shallow
network suffices and deeper layers of the DNN have little marginal utility. The
overall system is adaptive in that it dynamically switches control actions
based on state-estimates in order to reduce average latency without sacrificing
terminal performance. We experiment with a number of alternative loss-functions
to train gating functions and shallow policies and show that in a number of
applications a speed-up of up to almost 5X can be obtained with little loss in
performance.
|
Machine Learning, Machine Learning
|
Statistics
|
1807.09089
|
Sattar Vakili
|
Decision Variance in Online Learning
|
stat.ML cs.LG
|
Online learning has traditionally focused on the expected rewards. In this
paper, a risk-averse online learning problem under the performance measure of
the mean-variance of the rewards is studied. Both the bandit and full
information settings are considered. The performance of several existing
policies is analyzed, and new fundamental limitations on risk-averse learning
is established. In particular, it is shown that although a logarithmic
distribution-dependent regret in time $T$ is achievable (similar to the
risk-neutral problem), the worst-case (i.e. minimax) regret is lower bounded by
$\Omega(T)$ (in contrast to the $\Omega(\sqrt{T})$ lower bound in the
risk-neutral problem). This sharp difference from the risk-neutral counterpart
is caused by the the variance in the player's decisions, which, while absent in
the regret under the expected reward criterion, contributes to excess
mean-variance due to the non-linearity of this risk measure. The role of the
decision variance in regret performance reflects a risk-averse player's desire
for robust decisions and outcomes.
|
Machine Learning, Machine Learning
|
Statistics
|
2005.09047
|
Saeed Saremi
|
Learning and Inference in Imaginary Noise Models
|
stat.ML cs.LG
|
Inspired by recent developments in learning smoothed densities with empirical
Bayes, we study variational autoencoders with a decoder that is tailored for
the random variable $Y=X+N(0,\sigma^2 I_d)$. A notion of smoothed variational
inference emerges where the smoothing is implicitly enforced by the noise model
of the decoder; "implicit", since during training the encoder only sees clean
samples. This is the concept of imaginary noise model, where the noise model
dictates the functional form of the variational lower bound
$\mathcal{L}(\sigma)$, but the noisy data are never seen during learning. The
model is named $\sigma$-VAE. We prove that all $\sigma$-VAEs are equivalent to
each other via a simple $\beta$-VAE expansion: $\mathcal{L}(\sigma_2) \equiv
\mathcal{L}(\sigma_1,\beta)$, where $\beta=\sigma_2^2/\sigma_1^2$. We prove a
similar result for the Laplace distribution in exponential families.
Empirically, we report an intriguing power law $\mathcal{D}_{\rm KL} \sim
\sigma^{-\nu}$ for the learned models and we study the inference in the
$\sigma$-VAE for unseen noisy data. The experiments were performed on MNIST,
where we show that quite remarkably the model can make reasonable inferences on
extremely noisy samples even though it has not seen any during training. The
vanilla VAE completely breaks down in this regime. We finish with a hypothesis
(the XYZ hypothesis) on the findings here.
|
Machine Learning, Machine Learning
|
Statistics
|
2206.09513
|
Yuka Hashimoto
|
$C^*$-algebra Net: A New Approach Generalizing Neural Network Parameters
to $C^*$-algebra
|
stat.ML cs.LG
|
We propose a new framework that generalizes the parameters of neural network
models to $C^*$-algebra-valued ones. $C^*$-algebra is a generalization of the
space of complex numbers. A typical example is the space of continuous
functions on a compact space. This generalization enables us to combine
multiple models continuously and use tools for functions such as regression and
integration. Consequently, we can learn features of data efficiently and adapt
the models to problems continuously. We apply our framework to practical
problems such as density estimation and few-shot learning and show that our
framework enables us to learn features of data even with a limited number of
samples. Our new framework highlights the potential possibility of applying the
theory of $C^*$-algebra to general neural network models.
|
Machine Learning, Machine Learning
|
Statistics
|
2112.12194
|
Martin Jankowiak
|
Surrogate Likelihoods for Variational Annealed Importance Sampling
|
stat.ML cs.LG
|
Variational inference is a powerful paradigm for approximate Bayesian
inference with a number of appealing properties, including support for model
learning and data subsampling. By contrast MCMC methods like Hamiltonian Monte
Carlo do not share these properties but remain attractive since, contrary to
parametric methods, MCMC is asymptotically unbiased. For these reasons
researchers have sought to combine the strengths of both classes of algorithms,
with recent approaches coming closer to realizing this vision in practice.
However, supporting data subsampling in these hybrid methods can be a
challenge, a shortcoming that we address by introducing a surrogate likelihood
that can be learned jointly with other variational parameters. We argue
theoretically that the resulting algorithm permits the user to make an
intuitive trade-off between inference fidelity and computational cost. In an
extensive empirical comparison we show that our method performs well in
practice and that it is well-suited for black-box inference in probabilistic
programming frameworks.
|
Machine Learning, Machine Learning
|
Statistics
|
2110.14800
|
Chengkuan Hong
|
Convolutional Deep Exponential Families
|
stat.ML cs.LG
|
We describe convolutional deep exponential families (CDEFs) in this paper.
CDEFs are built based on deep exponential families, deep probabilistic models
that capture the hierarchical dependence between latent variables. CDEFs
greatly reduce the number of free parameters by tying the weights of DEFs. Our
experiments show that CDEFs are able to uncover time correlations with a small
amount of data.
|
Machine Learning, Machine Learning
|
Statistics
|
2302.11294
|
Seunghwan An
|
Distributional Learning of Variational AutoEncoder: Application to
Synthetic Data Generation
|
stat.ML cs.LG
|
The Gaussianity assumption has been consistently criticized as a main
limitation of the Variational Autoencoder (VAE) despite its efficiency in
computational modeling. In this paper, we propose a new approach that expands
the model capacity (i.e., expressive power of distributional family) without
sacrificing the computational advantages of the VAE framework. Our VAE model's
decoder is composed of an infinite mixture of asymmetric Laplace distribution,
which possesses general distribution fitting capabilities for continuous
variables. Our model is represented by a special form of a nonparametric
M-estimator for estimating general quantile functions, and we theoretically
establish the relevance between the proposed model and quantile estimation. We
apply the proposed model to synthetic data generation, and particularly, our
model demonstrates superiority in easily adjusting the level of data privacy.
|
Machine Learning, Machine Learning
|
Statistics
|
2009.11285
|
Kazuma Tsuji
|
Estimation error analysis of deep learning on the regression problem on
the variable exponent Besov space
|
stat.ML cs.LG
|
Deep learning has achieved notable success in various fields, including image
and speech recognition. One of the factors in the successful performance of
deep learning is its high feature extraction ability. In this study, we focus
on the adaptivity of deep learning; consequently, we treat the variable
exponent Besov space, which has a different smoothness depending on the input
location $x$. In other words, the difficulty of the estimation is not uniform
within the domain. We analyze the general approximation error of the variable
exponent Besov space and the approximation and estimation errors of deep
learning. We note that the improvement based on adaptivity is remarkable when
the region upon which the target function has less smoothness is small and the
dimension is large. Moreover, the superiority to linear estimators is shown
with respect to the convergence rate of the estimation error.
|
Machine Learning, Machine Learning
|
Statistics
|
2107.12783
|
Drona Khurana
|
Statistical Guarantees for Fairness Aware Plug-In Algorithms
|
stat.ML cs.LG
|
A plug-in algorithm to estimate Bayes Optimal Classifiers for fairness-aware
binary classification has been proposed in (Menon & Williamson, 2018). However,
the statistical efficacy of their approach has not been established. We prove
that the plug-in algorithm is statistically consistent. We also derive finite
sample guarantees associated with learning the Bayes Optimal Classifiers via
the plug-in algorithm. Finally, we propose a protocol that modifies the plug-in
approach, so as to simultaneously guarantee fairness and differential privacy
with respect to a binary feature deemed sensitive.
|
Machine Learning, Machine Learning
|
Statistics
|
1512.08887
|
Farhad Pourkamali-Anaraki
|
Estimation of the sample covariance matrix from compressive measurements
|
stat.ML cs.LG
|
This paper focuses on the estimation of the sample covariance matrix from
low-dimensional random projections of data known as compressive measurements.
In particular, we present an unbiased estimator to extract the covariance
structure from compressive measurements obtained by a general class of random
projection matrices consisting of i.i.d. zero-mean entries and finite first
four moments. In contrast to previous works, we make no structural assumptions
about the underlying covariance matrix such as being low-rank. In fact, our
analysis is based on a non-Bayesian data setting which requires no
distributional assumptions on the set of data samples. Furthermore, inspired by
the generality of the projection matrices, we propose an approach to covariance
estimation that utilizes sparse Rademacher matrices. Therefore, our algorithm
can be used to estimate the covariance matrix in applications with limited
memory and computation power at the acquisition devices. Experimental results
demonstrate that our approach allows for accurate estimation of the sample
covariance matrix on several real-world data sets, including video data.
|
Machine Learning, Machine Learning
|
Statistics
|
2011.07607
|
Uri Shaham
|
Deep Ordinal Regression using Optimal Transport Loss and Unimodal Output
Probabilities
|
stat.ML cs.LG
|
It is often desired that ordinal regression models yield unimodal
predictions. However, in many recent works this characteristic is either
absent, or implemented using soft targets, which do not guarantee unimodal
outputs at inference. In addition, we argue that the standard maximum
likelihood objective is not suitable for ordinal regression problems, and that
optimal transport is better suited for this task, as it naturally captures the
order of the classes. In this work, we propose a framework for deep ordinal
regression, based on unimodal output distribution and optimal transport loss.
Inspired by the well-known Proportional Odds model, we propose to modify its
design by using an architectural mechanism which guarantees that the model
output distribution will be unimodal. We empirically analyze the different
components of our proposed approach and demonstrate their contribution to the
performance of the model. Experimental results on eight real-world datasets
demonstrate that our proposed approach consistently performs on par with and
often better than several recently proposed deep learning approaches for deep
ordinal regression with unimodal output probabilities, while having guarantee
on the output unimodality. In addition, we demonstrate that proposed approach
is less overconfident than current baselines.
|
Machine Learning, Machine Learning
|
Statistics
|
1312.5921
|
Arto Klami
|
Group-sparse Embeddings in Collective Matrix Factorization
|
stat.ML cs.LG
|
CMF is a technique for simultaneously learning low-rank representations based
on a collection of matrices with shared entities. A typical example is the
joint modeling of user-item, item-property, and user-feature matrices in a
recommender system. The key idea in CMF is that the embeddings are shared
across the matrices, which enables transferring information between them. The
existing solutions, however, break down when the individual matrices have
low-rank structure not shared with others. In this work we present a novel CMF
solution that allows each of the matrices to have a separate low-rank structure
that is independent of the other matrices, as well as structures that are
shared only by a subset of them. We compare MAP and variational Bayesian
solutions based on alternating optimization algorithms and show that the model
automatically infers the nature of each factor using group-wise sparsity. Our
approach supports in a principled way continuous, binary and count observations
and is efficient for sparse matrices involving missing data. We illustrate the
solution on a number of examples, focusing in particular on an interesting
use-case of augmented multi-view learning.
|
Machine Learning, Machine Learning
|
Statistics
|
1810.09184
|
Peter Bloem
|
Learning sparse transformations through backpropagation
|
stat.ML cs.LG
|
Many transformations in deep learning architectures are sparsely connected.
When such transformations cannot be designed by hand, they can be learned, even
through plain backpropagation, for instance in attention mechanisms. However,
during learning, such sparse structures are often represented in a dense form,
as we do not know beforehand which elements will eventually become non-zero. We
introduce the adaptive, sparse hyperlayer, a method for learning a sparse
transformation, paramatrized sparsely: as index-tuples with associated values.
To overcome the lack of gradients from such a discrete structure, we introduce
a method of randomly sampling connections, and backpropagating over the
randomly wired computation graph. To show that this approach allows us to train
a model to competitive performance on real data, we use it to build two
architectures. First, an attention mechanism for visual classification. Second,
we implement a method for differentiable sorting: specifically, learning to
sort unlabeled MNIST digits, given only the correct order.
|
Machine Learning, Machine Learning
|
Statistics
|
1905.04654
|
Shi Dong
|
On the Performance of Thompson Sampling on Logistic Bandits
|
stat.ML cs.LG
|
We study the logistic bandit, in which rewards are binary with success
probability $\exp(\beta a^\top \theta) / (1 + \exp(\beta a^\top \theta))$ and
actions $a$ and coefficients $\theta$ are within the $d$-dimensional unit ball.
While prior regret bounds for algorithms that address the logistic bandit
exhibit exponential dependence on the slope parameter $\beta$, we establish a
regret bound for Thompson sampling that is independent of $\beta$.
Specifically, we establish that, when the set of feasible actions is identical
to the set of possible coefficient vectors, the Bayesian regret of Thompson
sampling is $\tilde{O}(d\sqrt{T})$. We also establish a $\tilde{O}(\sqrt{d\eta
T}/\lambda)$ bound that applies more broadly, where $\lambda$ is the worst-case
optimal log-odds and $\eta$ is the "fragility dimension," a new statistic we
define to capture the degree to which an optimal action for one model fails to
satisfice for others. We demonstrate that the fragility dimension plays an
essential role by showing that, for any $\epsilon > 0$, no algorithm can
achieve $\mathrm{poly}(d, 1/\lambda)\cdot T^{1-\epsilon}$ regret.
|
Machine Learning, Machine Learning
|
Statistics
|
1806.01619
|
Changyong Oh
|
BOCK : Bayesian Optimization with Cylindrical Kernels
|
stat.ML cs.LG
|
A major challenge in Bayesian Optimization is the boundary issue (Swersky,
2017) where an algorithm spends too many evaluations near the boundary of its
search space. In this paper, we propose BOCK, Bayesian Optimization with
Cylindrical Kernels, whose basic idea is to transform the ball geometry of the
search space using a cylindrical transformation. Because of the transformed
geometry, the Gaussian Process-based surrogate model spends less budget
searching near the boundary, while concentrating its efforts relatively more
near the center of the search region, where we expect the solution to be
located. We evaluate BOCK extensively, showing that it is not only more
accurate and efficient, but it also scales successfully to problems with a
dimensionality as high as 500. We show that the better accuracy and scalability
of BOCK even allows optimizing modestly sized neural network layers, as well as
neural network hyperparameters.
|
Machine Learning, Machine Learning
|
Statistics
|
1702.07552
|
Muhammad Farooq
|
Learning Rates for Kernel-Based Expectile Regression
|
stat.ML cs.LG
|
Conditional expectiles are becoming an increasingly important tool in finance
as well as in other areas of applications. We analyse a support vector machine
type approach for estimating conditional expectiles and establish learning
rates that are minimax optimal modulo a logarithmic factor if Gaussian RBF
kernels are used and the desired expectile is smooth in a Besov sense. As a
special case, our learning rates improve the best known rates for kernel-based
least squares regression in this scenario. Key ingredients of our statistical
analysis are a general calibration inequality for the asymmetric least squares
loss, a corresponding variance bound as well as an improved entropy number
bound for Gaussian RBF kernels.
|
Machine Learning, Machine Learning
|
Statistics
|
1909.09621
|
Elena Smirnova
|
On the Convergence of Approximate and Regularized Policy Iteration
Schemes
|
stat.ML cs.LG
|
Entropy regularized algorithms such as Soft Q-learning and Soft Actor-Critic,
recently showed state-of-the-art performance on a number of challenging
reinforcement learning (RL) tasks. The regularized formulation modifies the
standard RL objective and thus generally converges to a policy different from
the optimal greedy policy of the original RL problem. Practically, it is
important to control the sub-optimality of the regularized optimal policy. In
this paper, we establish sufficient conditions for convergence of a large class
of regularized dynamic programming algorithms, unified under regularized
modified policy iteration (MPI) and conservative value iteration (VI) schemes.
We provide explicit convergence rates to the optimality depending on the
decrease rate of the regularization parameter. Our experiments show that the
empirical error closely follows the established theoretical convergence rates.
In addition to optimality, we demonstrate two desirable behaviours of the
regularized algorithms even in the absence of approximations: robustness to
stochasticity of environment and safety of trajectories induced by the policy
iterates.
|
Machine Learning, Machine Learning
|
Statistics
|
2310.11837
|
Jonathan So
|
Optimising Distributions with Natural Gradient Surrogates
|
stat.ML cs.LG
|
Natural gradient methods have been used to optimise the parameters of
probability distributions in a variety of settings, often resulting in
fast-converging procedures. Unfortunately, for many distributions of interest,
computing the natural gradient has a number of challenges. In this work we
propose a novel technique for tackling such issues, which involves reframing
the optimisation as one with respect to the parameters of a surrogate
distribution, for which computing the natural gradient is easy. We give several
examples of existing methods that can be interpreted as applying this
technique, and propose a new method for applying it to a wide variety of
problems. Our method expands the set of distributions that can be efficiently
targeted with natural gradients. Furthermore, it is fast, easy to understand,
simple to implement using standard autodiff software, and does not require
lengthy model-specific derivations. We demonstrate our method on maximum
likelihood estimation and variational inference tasks.
|
Machine Learning, Machine Learning
|
Statistics
|
2302.04759
|
Matias Altamirano
|
Robust and Scalable Bayesian Online Changepoint Detection
|
stat.ML cs.LG
|
This paper proposes an online, provably robust, and scalable Bayesian
approach for changepoint detection. The resulting algorithm has key advantages
over previous work: it provides provable robustness by leveraging the
generalised Bayesian perspective, and also addresses the scalability issues of
previous attempts. Specifically, the proposed generalised Bayesian formalism
leads to conjugate posteriors whose parameters are available in closed form by
leveraging diffusion score matching. The resulting algorithm is exact, can be
updated through simple algebra, and is more than 10 times faster than its
closest competitor.
|
Machine Learning, Machine Learning
|
Statistics
|
2007.12420
|
Lorena Romero-Medrano
|
Multinomial Sampling for Hierarchical Change-Point Detection
|
stat.ML cs.LG
|
Bayesian change-point detection, together with latent variable models, allows
to perform segmentation over high-dimensional time-series. We assume that
change-points lie on a lower-dimensional manifold where we aim to infer subsets
of discrete latent variables. For this model, full inference is computationally
unfeasible and pseudo-observations based on point-estimates are used instead.
However, if estimation is not certain enough, change-point detection gets
affected. To circumvent this problem, we propose a multinomial sampling
methodology that improves the detection rate and reduces the delay while
keeping complexity stable and inference analytically tractable. Our experiments
show results that outperform the baseline method and we also provide an example
oriented to a human behavior study.
|
Machine Learning, Machine Learning
|
Statistics
|
1903.07082
|
Maryam Aziz
|
On Multi-Armed Bandit Designs for Dose-Finding Clinical Trials
|
stat.ML cs.LG
|
We study the problem of finding the optimal dosage in early stage clinical
trials through the multi-armed bandit lens. We advocate the use of the Thompson
Sampling principle, a flexible algorithm that can accommodate different types
of monotonicity assumptions on the toxicity and efficacy of the doses. For the
simplest version of Thompson Sampling, based on a uniform prior distribution
for each dose, we provide finite-time upper bounds on the number of sub-optimal
dose selections, which is unprecedented for dose-finding algorithms. Through a
large simulation study, we then show that variants of Thompson Sampling based
on more sophisticated prior distributions outperform state-of-the-art dose
identification algorithms in different types of dose-finding studies that occur
in phase I or phase I/II trials.
|
Machine Learning, Machine Learning
|
Statistics
|
2103.12866
|
Deividas Eringis
|
PAC-Bayesian theory for stochastic LTI systems
|
stat.ML cs.LG
|
In this paper we derive a PAC-Bayesian error bound for autonomous stochastic
LTI state-space models. The motivation for deriving such error bounds is that
they will allow deriving similar error bounds for more general dynamical
systems, including recurrent neural networks. In turn, PACBayesian error bounds
are known to be useful for analyzing machine learning algorithms and for
deriving new ones.
|
Machine Learning, Machine Learning
|
Statistics
|
2107.07494
|
Tian Zhou
|
Mid-flight Forecasting for CPA Lines in Online Advertising
|
stat.ML cs.LG
|
For Verizon MediaDemand Side Platform(DSP), forecasting of ad campaign
performance not only feeds key information to the optimization server to allow
the system to operate on a high-performance mode, but also produces actionable
insights to the advertisers. In this paper, the forecasting problem for CPA
lines in the middle of the flight is investigated by taking the bidding
mechanism into account. The proposed methodology generates relationships
between various key performance metrics and optimization signals. It can also
be used to estimate the sensitivity of ad campaign performance metrics to the
adjustments of optimization signal, which is important to the design of a
campaign management system. The relationship between advertiser spends and
effective Cost Per Action(eCPA) is also characterized, which serves as a
guidance for mid-flight line adjustment to the advertisers. Several practical
issues in implementation, such as downsampling of the dataset, are also
discussed in the paper. At last, the forecasting results are validated against
actual deliveries and demonstrates promising accuracy.
|
Machine Learning, Machine Learning
|
Statistics
|
1905.12090
|
Geoffrey Roeder
|
Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear
Dynamical Systems
|
stat.ML cs.LG
|
We introduce a flexible, scalable Bayesian inference framework for nonlinear
dynamical systems characterised by distinct and hierarchical variability at the
individual, group, and population levels. Our model class is a generalisation
of nonlinear mixed-effects (NLME) dynamical systems, the statistical workhorse
for many experimental sciences. We cast parameter inference as stochastic
optimisation of an end-to-end differentiable, block-conditional variational
autoencoder. We specify the dynamics of the data-generating process as an
ordinary differential equation (ODE) such that both the ODE and its solver are
fully differentiable. This model class is highly flexible: the ODE right-hand
sides can be a mixture of user-prescribed or "white-box" sub-components and
neural network or "black-box" sub-components. Using stochastic optimisation,
our amortised inference algorithm could seamlessly scale up to massive data
collection pipelines (common in labs with robotic automation). Finally, our
framework supports interpretability with respect to the underlying dynamics, as
well as predictive generalization to unseen combinations of group components
(also called "zero-shot" learning). We empirically validate our method by
predicting the dynamic behaviour of bacteria that were genetically engineered
to function as biosensors. Our implementation of the framework, the dataset,
and all code to reproduce the experimental results is available at
https://www.github.com/Microsoft/vi-hds .
|
Machine Learning, Machine Learning
|
Statistics
|
2405.06727
|
Owen Davis
|
Approximation Error and Complexity Bounds for ReLU Networks on
Low-Regular Function Spaces
|
stat.ML cs.LG
|
In this work, we consider the approximation of a large class of bounded
functions, with minimal regularity assumptions, by ReLU neural networks. We
show that the approximation error can be bounded from above by a quantity
proportional to the uniform norm of the target function and inversely
proportional to the product of network width and depth. We inherit this
approximation error bound from Fourier features residual networks, a type of
neural network that uses complex exponential activation functions. Our proof is
constructive and proceeds by conducting a careful complexity analysis
associated with the approximation of a Fourier features residual network by a
ReLU network.
|
Machine Learning, Machine Learning
|
Statistics
|
2307.16452
|
Mihir Dhanakshirur
|
A continuous Structural Intervention Distance to compare Causal Graphs
|
stat.ML cs.LG
|
Understanding and adequately assessing the difference between a true and a
learnt causal graphs is crucial for causal inference under interventions. As an
extension to the graph-based structural Hamming distance and structural
intervention distance, we propose a novel continuous-measured metric that
considers the underlying data in addition to the graph structure for its
calculation of the difference between a true and a learnt causal graph. The
distance is based on embedding intervention distributions over each pair of
nodes as conditional mean embeddings into reproducing kernel Hilbert spaces and
estimating their difference by the maximum (conditional) mean discrepancy. We
show theoretical results which we validate with numerical experiments on
synthetic data.
|
Machine Learning, Machine Learning
|
Statistics
|
1609.03544
|
Xin Jiang
|
Online Data Thinning via Multi-Subspace Tracking
|
stat.ML cs.LG
|
In an era of ubiquitous large-scale streaming data, the availability of data
far exceeds the capacity of expert human analysts. In many settings, such data
is either discarded or stored unprocessed in datacenters. This paper proposes a
method of online data thinning, in which large-scale streaming datasets are
winnowed to preserve unique, anomalous, or salient elements for timely expert
analysis. At the heart of this proposed approach is an online anomaly detection
method based on dynamic, low-rank Gaussian mixture models. Specifically, the
high-dimensional covariances matrices associated with the Gaussian components
are associated with low-rank models. According to this model, most observations
lie near a union of subspaces. The low-rank modeling mitigates the curse of
dimensionality associated with anomaly detection for high-dimensional data, and
recent advances in subspace clustering and subspace tracking allow the proposed
method to adapt to dynamic environments. Furthermore, the proposed method
allows subsampling, is robust to missing data, and uses a mini-batch online
optimization approach. The resulting algorithms are scalable, efficient, and
are capable of operating in real time. Experiments on wide-area motion imagery
and e-mail databases illustrate the efficacy of the proposed approach.
|
Machine Learning, Machine Learning
|
Statistics
|
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