Rethinking Generative Mode Coverage: A Pointwise Guaranteed Approach

TL;DR

This paper introduces a game-theoretic approach to ensure complete mode coverage in generative models by using a mixture of generators, providing theoretical guarantees and empirical improvements over existing methods.

Contribution

It proposes a novel algorithm based on the multiplicative weights update rule that guarantees complete mode coverage, addressing limitations of global statistical distances.

Findings

Guarantees complete mode coverage with generator mixtures.

Outperforms recent approaches in mode coverage on real and synthetic datasets.

Provides theoretical proof of the algorithm's effectiveness.

Abstract

Many generative models have to combat $\textit{missing modes}$. The conventional wisdom to this end is by reducing through training a statistical distance (such as $f$-divergence) between the generated distribution and provided data distribution. But this is more of a heuristic than a guarantee. The statistical distance measures a $\textit{global}$, but not $\textit{local}$, similarity between two distributions. Even if it is small, it does not imply a plausible mode coverage. Rethinking this problem from a game-theoretic perspective, we show that a complete mode coverage is firmly attainable. If a generative model can approximate a data distribution moderately well under a global statistical distance measure, then we will be able to find a mixture of generators that collectively covers $\textit{every}$ data point and thus $\textit{every}$ mode, with a lower-bounded generation probability. Constructing the generator mixture has a connection to the multiplicative weights update rule, upon which we propose our algorithm. We prove that our algorithm guarantees complete mode coverage. And our experiments on real and synthetic datasets confirm better mode coverage over recent approaches, ones that also use generator mixtures but rely on global statistical distances.