Duality in Multi-View Restricted Kernel Machines

We propose a unifying setting that combines existing restricted kernel machine methods into a single primal-dual multi-view framework for kernel principal component analysis in both supervised and unsupervised settings. We derive the primal and dual representations of the framework and relate different training and inference algorithms from a theoretical perspective. We show how to achieve full equivalence in primal and dual formulations by rescaling primal variables. Finally, we experimentally validate the equivalence and provide insight into the relationships between different methods on a number of time series data sets by recursively forecasting unseen test data and visualizing the learned features

The Bures Metric for Generative Adversarial Networks

International audienceGenerative Adversarial Networks (GANs) are performant generative methods yielding high-quality samples. However, under certain circumstances, the training of GANs can lead to mode collapse or mode dropping. To address this problem, we use the last layer of the discriminator as a feature map to study the distribution of the real and the fake data. During training, we propose to match the real batch diversity to the fake batch diversity by using the Bures distance between covariance matrices in this feature space. The computation of the Bures distance can be conveniently done in either feature space or kernel space in terms of the covariance and kernel matrix respectively. We observe that diversity matching reduces mode collapse substantially and has a positive effect on sample quality. On the practical side, a very simple training procedure is proposed and assessed on several data sets

Leverage Score Sampling for Complete Mode Coverage in Generative Adversarial Networks

International audienceCommonly, machine learning models minimize an empirical expectation. As a result, the trained models typically perform well for the majority of the data but the performance may deteriorate in less dense regions of the dataset. This issue also arises in generative modeling. A generative model may overlook underrepresented modes that are less frequent in the empirical data distribution. This problem is known as complete mode coverage. We propose a sampling procedure based on ridge leverage scores which significantly improves mode coverage when compared to standard methods and can easily be combined with any GAN. Ridge leverage scores are computed by using an explicit feature map, associated with the next-to-last layer of a GAN discriminator or of a pre-trained network, or by using an implicit feature map corresponding to a Gaussian kernel. Multiple evaluations against recent approaches of complete mode coverage show a clear improvement when using the proposed sampling strategy