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Partitioning a set of elements into subsets of a priori unknown sizes isessential in many applications. These subset sizes are rarely explicitlylearned - be it the cluster sizes in clustering applications or the number ofshared versus independent generative latent factors in weakly-supervisedlearning. Probability distributions over correct combinations of subset sizesare non-differentiable due to hard constraints, which prohibit gradient-basedoptimization. In this work, we propose the differentiable hypergeometricdistribution. The hypergeometric distribution models the probability ofdifferent group sizes based on their relative importance. We introducereparameterizable gradients to learn the importance between groups andhighlight the advantage of explicitly learning the size of subsets in twotypical applications: weakly-supervised learning and clustering. In bothapplications, we outperform previous approaches, which rely on suboptimalheuristics to model the unknown size of groups.

Learning Group Importance using the Differentiable Hypergeometric Distribution