# A Stein Identity for q-Gaussians with Bounded Support Source: [A Stein Identity for q-Gaussians with Bounded Support]() Collection index: [llms.txt]() Data updated: 2026-03-06T05:00:05.534Z Authors: Sophia Sklaviadis, Thomas Moellenhoff, Andre F. T. Martins, Mario A. T. Figueiredo, Mohammad Emtiyaz Khan Published: 2026-03-04T03:00:49.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on CIFAR-10 (test) (Accuracy, Calibration, and Uncertainty Metrics)](): Image Classification; CIFAR-10 (test); Accuracy: 92.6. ## Original sources and implementation [Original paper]() [PDF]()