# Learning Group Importance using the Differentiable Hypergeometric Distribution

arXiv: https://arxiv.org/abs/2203.01629 · HTML: https://mlsanity.com/paper/2203.01629/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 61 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [Stochastic Beams and Where to Find Them: The Gumbel-Top-k Trick for Sampling Sequences Without Replacement](https://mlsanity.com/paper/1903.06059/) (2019)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Stochastic Optimization of Sorting Networks via Continuous Relaxations](https://mlsanity.com/paper/1903.08850/) (2019)
- [Multi-Level Variational Autoencoder: Learning Disentangled Representations from Grouped Observations](https://mlsanity.com/paper/1705.08841/) (2017)
- [On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset](https://mlsanity.com/paper/1906.03292/) (2019)
- [A Review of the Gumbel-max Trick and its Extensions for Discrete Stochasticity in Machine Learning](https://mlsanity.com/paper/2110.01515/) (2021)
- [Reparameterizable Subset Sampling via Continuous Relaxations](https://mlsanity.com/paper/1901.10517/) (2019)
- [Gradient Estimation with Stochastic Softmax Tricks](https://mlsanity.com/paper/2006.08063/) (2020)
- [Estimating Gradients for Discrete Random Variables by Sampling without Replacement](https://mlsanity.com/paper/2002.06043/) (2020)
- [Submodular Maximization Beyond Non-negativity: Guarantees, Fast Algorithms, and Applications](https://mlsanity.com/paper/1904.09354/) (2019)
- [Deep Conditional Gaussian Mixture Model for Constrained Clustering](https://mlsanity.com/paper/2106.06385/) (2021)
- [Greed is Good: Near-Optimal Submodular Maximization via Greedy Optimization](https://mlsanity.com/paper/1704.01652/) (2017)
- [Query K-means Clustering and the Double Dixie Cup Problem](https://mlsanity.com/paper/1806.05938/) (2018)
- [Group-based Learning of Disentangled Representations with Generalizability for Novel Contents](https://mlsanity.com/paper/1809.02383/) (2018)
- [Generalized Hypergeometric Ensembles: Statistical Hypothesis Testing in Complex Networks](https://mlsanity.com/paper/1607.02441/) (2016)

## Built on by (most cited first, 5 of 5)

- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Unity by Diversity: Improved Representation Learning in Multimodal VAEs](https://mlsanity.com/paper/2403.05300/) (2024)
- [Differentiable Random Partition Models](https://mlsanity.com/paper/2305.16841/) (2023)
- [Estimating Unknown Population Sizes Using the Hypergeometric Distribution](https://mlsanity.com/paper/2402.14220/) (2024)
- [You Only Train Once: Differentiable Subset Selection for Omics Data](https://mlsanity.com/paper/2512.17678/) (2025)

## Abstract (arXiv)

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.