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arXiv · 1507.01972

Wasserstein Training of Boltzmann Machines

Grégoire Montavon·Klaus-Robert Müller·Marco Cuturi
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Abstract

The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler (KL) divergence from training samples to the Boltzmann model. We propose in this work a novel approach for Boltzmann training which assumes that a meaningful metric between observations is given. This metric can be represented by the Wasserstein distance between distributions, for which we derive a gradient with respect to the model parameters. Minimization of this new Wasserstein objective leads to generative models that are better when considering the metric and that have a cluster-like structure. We demonstrate the practical potential of these models for data completion and denoising, for which the metric between observations plays a crucial role.

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Grégoire Montavon, Klaus-Robert Müller, Marco Cuturi. 2015-07-07. Wasserstein Training of Boltzmann Machines. https://arxiv.org/abs/1507.01972

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