English
Related papers

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

200 papers

We study distributed goodness-of-fit testing for discrete distribution under bandwidth and differential privacy constraints. Information constraint distributed goodness-of-fit testing is a problem that has received considerable attention…

Statistics Theory · Mathematics 2024-11-05 Lasse Vuursteen

We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on…

Methodology · Statistics 2025-01-07 Xiaotong Lin , Weihao Li , Fangqiao Tian , Dongming Huang

When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as…

Statistics Theory · Mathematics 2022-10-07 Alessandro Barp , Francois-Xavier Briol , Andrew B. Duncan , Mark Girolami , Lester Mackey

We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model's log-density. We estimate the Stein discrepancy between the data density $p(x)$…

Machine Learning · Statistics 2020-08-17 Will Grathwohl , Kuan-Chieh Wang , Jorn-Henrik Jacobsen , David Duvenaud , Richard Zemel

We propose two novel nonparametric two-sample kernel tests based on the Maximum Mean Discrepancy (MMD). First, for a fixed kernel, we construct an MMD test using either permutations or a wild bootstrap, two popular numerical procedures to…

Machine Learning · Statistics 2023-08-22 Antonin Schrab , Ilmun Kim , Mélisande Albert , Béatrice Laurent , Benjamin Guedj , Arthur Gretton

In this paper, we investigate the minimax properties of Stein block thresholding in any dimension $d$ with a particular emphasis on $d=2$. Towards this goal, we consider a frame coefficient space over which minimaxity is proved. The choice…

Statistics Theory · Mathematics 2009-09-29 Christophe Chesneau , Jalal Fadili , Jean-Luc Starck

Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions. Applying these methods in practice can require…

Machine Learning · Statistics 2025-12-17 Aaron Wei , Milad Jalali , Danica J. Sutherland

We consider the goodness of fit testing problem for linear stochastic differential equation (Ornstein-Uhlenbeck process). The basic hypothesis is supposed to be composite with two-dimensional unknown parameter. We study two goodness of fit…

Statistics Theory · Mathematics 2013-05-16 Yury A. Kutoyants

This article provides a practical introduction to kernel discrepancies, focusing on the Maximum Mean Discrepancy (MMD), the Hilbert-Schmidt Independence Criterion (HSIC), and the Kernel Stein Discrepancy (KSD). Various estimators for these…

Machine Learning · Statistics 2025-11-03 Antonin Schrab

This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation error are established for posterior…

Statistics Theory · Mathematics 2022-01-12 Alessandro Barp , Chris. J. Oates , Emilio Porcu , Mark Girolami

Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…

Machine Learning · Statistics 2026-04-21 Antoine Chatalic , Marco Letizia , Nicolas Schreuder , Lorenzo Rosasco

Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare…

Machine Learning · Computer Science 2013-05-03 Somayeh Danafar , Paola M. V. Rancoita , Tobias Glasmachers , Kevin Whittingstall , Juergen Schmidhuber

We propose a novel supervised learning method to optimize the kernel in the maximum mean discrepancy generative adversarial networks (MMD GANs), and the kernel support vector machines (SVMs). Specifically, we characterize a distributionally…

Machine Learning · Computer Science 2020-02-25 Masoud Badiei Khuzani , Liyue Shen , Shahin Shahrampour , Lei Xing

This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These…

Statistics Theory · Mathematics 2019-02-12 Gilles R. Ducharme , Pierre Lafaye de Micheaux

As modern precision cosmological measurements continue to show agreement with the broad features of the standard $\Lambda$-Cold Dark Matter ($\Lambda$CDM) cosmological model, we are increasingly motivated to look for small departures from…

Cosmology and Nongalactic Astrophysics · Physics 2017-05-11 Andrew Arrasmith , Brent Follin , Ethan Anderes , Lloyd Knox

Despite a substantial literature on nonparametric two-sample goodness-of-fit testing in arbitrary dimensions spanning decades, there is no mention there of any curse of dimensionality. Only more recently Ramdas et al. (2015) have discussed…

Statistics Theory · Mathematics 2018-09-13 Ery Arias-Castro , Bruno Pelletier , Venkatesh Saligrama

We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test…

Statistics Theory · Mathematics 2015-07-13 Jérémie Kellner , Alain Celisse

This paper proposes a goodness of fit test for the generalized Pareto distribution (GPD). Firstly, we provide two characterizations of GPD based on Stein's identity and dynamic survival extropy. These characterizations are used to test GPD…

Methodology · Statistics 2025-06-03 Gaurav Kandpal , Nitin Gupta

We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…

Machine Learning · Statistics 2020-07-01 Wittawat Jitkrittum , Heishiro Kanagawa , Bernhard Schölkopf

We consider a Gaussian sequence model that contains ill-posed inverse problems as special cases. We assume that the associated operator is partially unknown in the sense that its singular functions are known and the corresponding singular…

Statistics Theory · Mathematics 2015-06-22 Clément Marteau , Theofanis Sapatinas