A Stein Identity for q-Gaussians with Bounded Support

Stein's identity is a fundamental tool in machine learning with applications in generative models, stochastic optimization, and other problems involving gradients of expectations under Gaussian distributions. Less attention has been paid to problems with non-Gaussian expectations. Here, we consider the class of bounded-support $q$-Gaussians and derive a new Stein identity leading to gradient estimators which have nearly identical forms to the Gaussian ones, and which are similarly easy to implement. We do this by extending the previous results of Landsman, Vanduffel, and Yao (2013) to prove new Bonnet- and Price-type theorems for q-Gaussians. We also simplify their forms by using escort distributions. Our experiments show that bounded-support distributions can reduce the variance of gradient estimators, which can potentially be useful for Bayesian deep learning and sharpness-aware minimization. Overall, our work simplifies the application of Stein's identity for an important class of non-Gaussian distributions.

• Publication year

  2026

• Venue

  Unknown venue

• Publication date

  2026-03-04

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 2603.03673
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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