# A Stein Identity for q-Gaussians with Bounded Support

arXiv: https://arxiv.org/abs/2603.03673 · HTML: https://mlsanity.com/paper/2603.03673/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 4 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam](https://mlsanity.com/paper/1806.04854/) (2018)
- [Variational Learning is Effective for Large Deep Networks](https://mlsanity.com/paper/2402.17641/) (2024)
- [Stein's Lemma for the Reparameterization Trick with Exponential Family Mixtures](https://mlsanity.com/paper/1910.13398/) (2019)
- [Sparse Continuous Distributions and Fenchel-Young Losses](https://mlsanity.com/paper/2108.01988/) (2021)

## Built on by (most cited first, 1 of 1)

- [Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing](https://mlsanity.com/paper/2604.27883/) (2026)

## Abstract (arXiv)

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.