# Stabilizing the Kumaraswamy Distribution

arXiv: https://arxiv.org/abs/2410.00660 · HTML: https://mlsanity.com/paper/2410.00660/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Builds on (most cited first, 18 of 18)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges](https://mlsanity.com/paper/1507.08025/) (2015)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [A Review on Graph Neural Network Methods in Financial Applications](https://mlsanity.com/paper/2111.15367/) (2021)
- [Scalable Generalized Linear Bandits: Online Computation and Hashing](https://mlsanity.com/paper/1706.00136/) (2017)
- [Stick-Breaking Variational Autoencoders](https://mlsanity.com/paper/1605.06197/) (2016)
- [The continuous Bernoulli: fixing a pervasive error in variational autoencoders](https://mlsanity.com/paper/1907.06845/) (2019)
- [Langevin Monte Carlo for Contextual Bandits](https://mlsanity.com/paper/2206.11254/) (2022)
- [PG-TS: Improved Thompson Sampling for Logistic Contextual Bandits](https://mlsanity.com/paper/1805.07458/) (2018)
- [Variational inference for the multi-armed contextual bandit](https://mlsanity.com/paper/1709.03163/) (2017)
- [VITS : Variational Inference Thompson Sampling for contextual bandits](https://mlsanity.com/paper/2307.10167/) (2023)
- [Graph Structure Learning with Interpretable Bayesian Neural Networks](https://mlsanity.com/paper/2406.14786/) (2024)
- [A New Distribution on the Simplex with Auto-Encoding Applications](https://mlsanity.com/paper/1905.12052/) (2019)

## Built on by (most cited first, 3 of 3)

- [A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2602.00834/) (2026)
- [LLM-Based Test Oracles: Source-of-Authority Taxonomy -- A Systematic Literature Review](https://mlsanity.com/paper/2607.05031/) (2026)
- [Individualized non-uniform quantization for vector search](https://mlsanity.com/paper/2509.18471/) (2025)

## Abstract (arXiv)

Large-scale latent variable models require expressive continuous distributions that support efficient sampling and low-variance differentiation, achievable through the reparameterization trick. The Kumaraswamy (KS) distribution is both expressive and supports the reparameterization trick with a simple closed-form inverse CDF. Yet, its adoption remains limited. We identify and resolve numerical instabilities in the inverse CDF and log-pdf, exposing issues in libraries like PyTorch and TensorFlow. We then introduce simple and scalable latent variable models based on the KS, improving exploration-exploitation trade-offs in contextual multi-armed bandits and enhancing uncertainty quantification for link prediction with graph neural networks. Our results support the stabilized KS distribution as a core component in scalable variational models for bounded latent variables.