Learning Group Importance using the Differentiable Hypergeometric Distribution

TL;DR

This paper introduces a differentiable hypergeometric distribution that enables gradient-based learning of group importance and sizes, improving performance in clustering and weakly-supervised learning tasks.

Contribution

The paper proposes a novel differentiable hypergeometric distribution with reparameterizable gradients for learning group importance and sizes, addressing non-differentiability issues in subset size modeling.

Findings

Outperforms previous methods in clustering tasks.

Enhances weakly-supervised learning by explicitly modeling group sizes.

Provides a new tool for gradient-based optimization over subset sizes.

Abstract

Partitioning a set of elements into subsets of a priori unknown sizes is essential in many applications. These subset sizes are rarely explicitly learned - be it the cluster sizes in clustering applications or the number of shared versus independent generative latent factors in weakly-supervised learning. Probability distributions over correct combinations of subset sizes are non-differentiable due to hard constraints, which prohibit gradient-based optimization. In this work, we propose the differentiable hypergeometric distribution. The hypergeometric distribution models the probability of different group sizes based on their relative importance. We introduce reparameterizable gradients to learn the importance between groups and highlight the advantage of explicitly learning the size of subsets in two typical applications: weakly-supervised learning and clustering. In both applications, we outperform previous approaches, which rely on suboptimal heuristics to model the unknown size of groups.