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Related papers: Minimax Optimal Goodness-of-Fit Testing with Kerne…

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Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to goodness-of-fit testing. Existing convergence-determining Stein…

Machine Learning · Statistics 2021-10-12 Jonathan H. Huggins , Lester Mackey

In the statistical literature, as well as in artificial intelligence and machine learning, measures of discrepancy between two probability distributions are largely used to develop measures of goodness-of-fit. We concentrate on quadratic…

Methodology · Statistics 2025-10-01 Marianthi Markatou , Giovanni Saraceno

Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. In each…

Machine Learning · Statistics 2025-03-26 Alessandro Barp , Carl-Johann Simon-Gabriel , Mark Girolami , Lester Mackey

We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum…

Machine Learning · Statistics 2019-03-19 Shengyu Zhu , Biao Chen , Pengfei Yang , Zhitang Chen

We introduce the Kernel Calibration Conditional Stein Discrepancy test (KCCSD test), a non-parametric, kernel-based test for assessing the calibration of probabilistic models with well-defined scores. In contrast to previous methods, our…

Machine Learning · Statistics 2025-10-17 Pierre Glaser , David Widmann , Fredrik Lindsten , Arthur Gretton

Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…

Statistics Theory · Mathematics 2025-10-17 Soumya Mukherjee , Bharath K. Sriperumbudur

In many fields, data appears in the form of direction (unit vector) and usual statistical procedures are not applicable to such directional data. In this study, we propose non-parametric goodness-of-fit testing procedures for general…

Methodology · Statistics 2020-02-18 Wenkai Xu , Takeru Matsuda

Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…

Machine Learning · Statistics 2020-07-21 Raghav Singhal , Xintian Han , Saad Lahlou , Rajesh Ranganath

This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…

Machine Learning · Statistics 2025-12-30 Antonin Schrab

Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…

Statistics Theory · Mathematics 2020-07-14 Sandra Schluttenhofer , Jan Johannes

Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…

Computation · Statistics 2025-12-17 Clémentine Chazal , Heishiro Kanagawa , Zheyang Shen , Anna Korba , Chris. J. Oates

Distributional approximation is a fundamental problem in machine learning with numerous applications across all fields of science and engineering and beyond. The key challenge in most approximation methods is the need to tackle the…

Statistics Theory · Mathematics 2024-09-19 Xiaoda Qu , Xiran Fan , Baba C. Vemuri

Sliced Stein discrepancy (SSD) and its kernelized variants have demonstrated promising successes in goodness-of-fit tests and model learning in high dimensions. Despite their theoretical elegance, their empirical performance depends…

Machine Learning · Computer Science 2021-07-22 Wenbo Gong , Kaibo Zhang , Yingzhen Li , José Miguel Hernández-Lobato

A new goodness-of-fit test for normality in high-dimension (and Reproducing Kernel Hilbert Space) is proposed. It shares common ideas with the Maximum Mean Discrepancy (MMD) it outperforms both in terms of computation time and applicability…

Statistics Theory · Mathematics 2014-04-14 Jérémie Kellner , Alain Celisse

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the…

Machine Learning · Statistics 2017-10-25 Wittawat Jitkrittum , Wenkai Xu , Zoltan Szabo , Kenji Fukumizu , Arthur Gretton

Distributional comparison is a fundamental problem in statistical data analysis with numerous applications in a variety of scientific and engineering fields. Numerous methods exist for distributional comparison but kernel Stein's method has…

Statistics Theory · Mathematics 2025-06-12 Xiaoda Qu , Baba C. Vemuri

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we…

Statistics Theory · Mathematics 2017-07-03 Sivaraman Balakrishnan , Larry Wasserman

We propose a novel method for measuring the discrepancy between a set of samples and a desired posterior distribution for Bayesian inference. Classical methods for assessing sample quality like the effective sample size are not appropriate…

Machine Learning · Statistics 2026-05-01 Narayan Srinivasan , Matthew Sutton , Christopher Drovandi , Leah F South

Nonparametric tests via kernel embedding of distributions have witnessed a great deal of practical successes in recent years. However, statistical properties of these tests are largely unknown beyond consistency against a fixed alternative.…

Statistics Theory · Mathematics 2019-09-10 Tong Li , Ming Yuan

Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While…

Machine Learning · Computer Science 2020-10-20 Jonas M. Kübler , Wittawat Jitkrittum , Bernhard Schölkopf , Krikamol Muandet