Stabilizing the Kumaraswamy Distribution

Max Wasserman, Gonzalo Mateos

Keywords: Latent variable models, Stochastic variational inference, Kumaraswamy distribution, Bounded interval distributions, Reparameterization trick, Contextual multi-armed bandits, Thompson Sampling

TL;DR: We resolve instabilities in the Kumaraswamy distribution to power scalable latent variable models for important large-scale ML tasks.

Abstract: 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 to improve exploration-exploitation trade-offs in contextual multi-armed bandits and enhance uncertainty quantification for link prediction with graph neural networks. We find these models to be most performant when paired with the stable KS. Our results support the stabilized KS distribution as a core component in scalable variational models for bounded latent variables.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 8118