Learning Implicit Generative Models Using Differentiable Graph Tests

TL;DR

This paper introduces a method to learn implicit generative models by smoothing classical two-sample tests using graphical model techniques, enabling their use as differentiable loss functions for training deep models.

Contribution

The paper proposes a novel approach to make classical two-sample tests differentiable using graphical model smoothing, facilitating their integration into deep generative model training.

Findings

Smoothing classical tests increases their statistical power.

The method successfully trains implicit generative models.

Graphical model techniques enable differentiability of non-differentiable tests.

Abstract

Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base measure, and are learned end-to-end using stochastic optimization. One strategy of devising a loss function is through the statistics of two sample tests - if we can fool a statistical test, the learned distribution should be a good model of the true data. However, not all tests can easily fit into this framework, as they might not be differentiable with respect to the data points, and hence with respect to the parameters of the implicit model. Motivated by this problem, in this paper we show how two such classical tests, the Friedman-Rafsky and k-nearest neighbour tests, can be effectively smoothed using ideas from undirected graphical models - the matrix tree theorem and cardinality potentials. Moreover, as we show experimentally, smoothing can significantly increase the power of the test, which might of of independent interest. Finally, we apply our method to learn implicit models.