Learning Group Importance using the Differentiable Hypergeometric Distribution
This addresses a fundamental challenge in machine learning for applications like clustering and weakly-supervised learning, offering a more principled solution compared to incremental improvements.
The paper tackles the problem of partitioning elements into subsets of unknown sizes, which is non-differentiable due to hard constraints, by proposing the differentiable hypergeometric distribution to model group importance. It outperforms previous heuristic-based approaches in weakly-supervised learning and clustering applications.
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.