English
Related papers

Related papers: Variable Selection for Kernel Two-Sample Tests

200 papers

Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…

Statistics Theory · Mathematics 2014-11-25 Aaditya Ramdas , Sashank J. Reddi , Barnabas Poczos , Aarti Singh , Larry Wasserman

The maximum mean discrepancy (MMD) is a recently proposed test statistic for two-sample test. Its quadratic time complexity, however, greatly hampers its availability to large-scale applications. To accelerate the MMD calculation, in this…

Artificial Intelligence · Computer Science 2015-06-19 Ji Zhao , Deyu Meng

The maximum mean discrepancy (MMD) is a kernel-based nonparametric statistic for two-sample testing, whose inferential accuracy depends critically on variance characterization. Existing work provides various finite-sample estimators of the…

Machine Learning · Statistics 2026-02-05 Shijie Zhong , Yikun Yang , Da Gong , Jiangfeng Fu

A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice…

Machine Learning · Computer Science 2014-02-11 Wojciech Zaremba , Arthur Gretton , Matthew Blaschko

We propose a novel deterministic sampling method to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD). By employing the general \emph{energetic variational…

Machine Learning · Statistics 2025-03-12 Yindong Chen , Yiwei Wang , Lulu Kang , Chun Liu

We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…

Machine Learning · Statistics 2021-01-15 Feng Liu , Wenkai Xu , Jie Lu , Guangquan Zhang , Arthur Gretton , Danica J. Sutherland

We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…

Machine Learning · Computer Science 2018-09-05 Magda Gregorová , Jason Ramapuram , Alexandros Kalousis , Stéphane Marchand-Maillet

Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…

Statistics Theory · Mathematics 2023-08-29 Hanjia Gao , Xiaofeng Shao

Over the last decade, an approach that has gained a lot of popularity to tackle nonparametric testing problems on general (i.e., non-Euclidean) domains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of…

Statistics Theory · Mathematics 2024-05-03 Omar Hagrass , Bharath K. Sriperumbudur , Bing Li

To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly…

Machine Learning · Computer Science 2025-10-14 Zhijian Zhou , Xunye Tian , Liuhua Peng , Chao Lei , Antonin Schrab , Danica J. Sutherland , Feng Liu

Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…

Machine Learning · Statistics 2024-11-27 Linda Chamakh , Zoltan Szabo

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

Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…

Machine Learning · Statistics 2026-02-26 Masha Naslidnyk

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

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

Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the…

Statistics Theory · Mathematics 2024-10-31 Jian Yan , Xianyang Zhang

Recent years have seen a surge in methods for two-sample testing, among which the Maximum Mean Discrepancy (MMD) test has emerged as an effective tool for handling complex and high-dimensional data. Despite its success and widespread…

Machine Learning · Statistics 2026-05-21 Ikjun Choi , Ilmun Kim

The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able…

Machine Learning · Statistics 2022-11-16 Danica J. Sutherland , Namrata Deka

This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…

Methodology · Statistics 2025-11-05 Yiou Li , Lulu Kang

Modern kernel-based two-sample tests have shown great success in distinguishing complex, high-dimensional distributions with appropriate learned kernels. Previous work has demonstrated that this kernel learning procedure succeeds, assuming…

Machine Learning · Statistics 2022-01-06 Feng Liu , Wenkai Xu , Jie Lu , Danica J. Sutherland