Deep unsupervised clustering with Gaussian mixture variational autoencoders

We study a variant of the variational autoencoder model with a Gaussian mixture as a prior distribution, with the goal of performing unsupervised clustering through deep generative models. We observe that the standard variational approach in these models is unsuited for unsupervised clustering, and mitigate this problem by leveraging a principled information-theoretic regularisation term known as consistency violation. Adding this term to the standard variational optimisation objective yields networks with both meaningful internal representations and well-defined clusters. We demonstrate the performance of this scheme on synthetic data, MNIST and SVHN, showing that the obtained clusters are distinct, interpretable and result in achieving higher performance on unsupervised clustering classification than previous approaches

Deep Divergence-Based Approach to Clustering

A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning, this line of research is in its infancy, and how to design and optimize suitable loss functions to train deep neural networks for clustering is still an open question. Our contribution to this emerging field is a new deep clustering network that leverages the discriminative power of information-theoretic divergence measures, which have been shown to be effective in traditional clustering. We propose a novel loss function that incorporates geometric regularization constraints, thus avoiding degenerate structures of the resulting clustering partition. Experiments on synthetic benchmarks and real datasets show that the proposed network achieves competitive performance with respect to other state-of-the-art methods, scales well to large datasets, and does not require pre-training steps

Group invariance principles for causal generative models

The postulate of independence of cause and mechanism (ICM) has recently led to several new causal discovery algorithms. The interpretation of independence and the way it is utilized, however, varies across these methods. Our aim in this paper is to propose a group theoretic framework for ICM to unify and generalize these approaches. In our setting, the cause-mechanism relationship is assessed by comparing it against a null hypothesis through the application of random generic group transformations. We show that the group theoretic view provides a very general tool to study the structure of data generating mechanisms with direct applications to machine learning.Comment: 16 pages, 6 figure