The assumption that data samples are independently identically distributed is the backbone of many learning algorithms. Nevertheless, datasets often exhibit rich structures in practice, and we argue that there exist some unknown orders within the data instances. Aiming to find such orders, we introduce a novel Generative Markov Network (GMN) which we use to extract the order of data instances automatically. Specifically, we assume that the instances are sampled from a Markov chain. Our goal is to learn the transitional operator of the chain as well as the generation order by maximizing the generation probability under all possible data permutations. One of our key ideas is to use neural networks as a soft lookup table for approximating the possibly huge, but discrete transition matrix. This strategy allows us to amortize the space complexity with a single model and make the transitional operator generalizable to unseen instances. To ensure the learned Markov chain is ergodic, we propose a greedy batch-wise permutation scheme that allows fast training.   Empirically, we evaluate the learned Markov chain by showing that GMNs are able to discover orders among data instances and also perform comparably well to state-of-the-art methods on the one-shot recognition benchmark task.
Propose to observe implicit orders in datasets in a generative model viewpoint. The authors deal with the problem of implicit ordering in a dataset and the challenge of recovering it and propose to learn a distance-metric-free model that assumes a Markov chain as the generative mechanism of the data  The paper proposes “Generative Markov Networks” - a deep-learning-based approach to modeling sequences and discovering order in datasets. Proposes learning the order of an unordered data sample by learning a Markov chain.