NorMatch: Matching Normalizing Flows with Discriminative Classifiers for Semi-Supervised Learning

Semi-Supervised Learning (SSL) aims to learn a model using a tiny labeled set and massive amounts of unlabeled data. To better exploit the unlabeled data the latest SSL methods use pseudo-labels predicted from a single discriminative classifier. However, the generated pseudo-labels are inevitably linked to inherent confirmation bias and noise which greatly affects the model performance. In this work we introduce a new framework for SSL named NorMatch. Firstly, we introduce a new uncertainty estimation scheme based on normalizing flows, as an auxiliary classifier, to enforce highly certain pseudo-labels yielding a boost of the discriminative classifiers. Secondly, we introduce a threshold-free sample weighting strategy to exploit better both high and low confidence pseudo-labels. Furthermore, we utilize normalizing flows to model, in an unsupervised fashion, the distribution of unlabeled data. This modelling assumption can further improve the performance of generative classifiers via unlabeled data, and thus, implicitly contributing to training a better discriminative classifier. We demonstrate, through numerical and visual results, that NorMatch achieves state-of-the-art performance on several datasets.Comment: Accepted to Transactions on Machine Learning Researc

Auxiliary Deep Generative Models

Deep generative models parameterized by neural networks have recently achieved state-of-the-art performance in unsupervised and semi-supervised learning. We extend deep generative models with auxiliary variables which improves the variational approximation. The auxiliary variables leave the generative model unchanged but make the variational distribution more expressive. Inspired by the structure of the auxiliary variable we also propose a model with two stochastic layers and skip connections. Our findings suggest that more expressive and properly specified deep generative models converge faster with better results. We show state-of-the-art performance within semi-supervised learning on MNIST, SVHN and NORB datasets.Comment: Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA, 2016, JMLR: Workshop and Conference Proceedings volume 48, Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA, 201

Hybrid Models with Deep and Invertible Features

We propose a neural hybrid model consisting of a linear model defined on a set of features computed by a deep, invertible transformation (i.e. a normalizing flow). An attractive property of our model is that both p(features), the density of the features, and p(targets | features), the predictive distribution, can be computed exactly in a single feed-forward pass. We show that our hybrid model, despite the invertibility constraints, achieves similar accuracy to purely predictive models. Moreover the generative component remains a good model of the input features despite the hybrid optimization objective. This offers additional capabilities such as detection of out-of-distribution inputs and enabling semi-supervised learning. The availability of the exact joint density p(targets, features) also allows us to compute many quantities readily, making our hybrid model a useful building block for downstream applications of probabilistic deep learning.Comment: ICML 201

Semi-Supervised Generation with Cluster-aware Generative Models

Deep generative models trained with large amounts of unlabelled data have proven to be powerful within the domain of unsupervised learning. Many real life data sets contain a small amount of labelled data points, that are typically disregarded when training generative models. We propose the Cluster-aware Generative Model, that uses unlabelled information to infer a latent representation that models the natural clustering of the data, and additional labelled data points to refine this clustering. The generative performances of the model significantly improve when labelled information is exploited, obtaining a log-likelihood of -79.38 nats on permutation invariant MNIST, while also achieving competitive semi-supervised classification accuracies. The model can also be trained fully unsupervised, and still improve the log-likelihood performance with respect to related methods