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Conditional Maximum Mean Discrepancy (CMMD) can capture the discrepancy between conditional distributions by drawing support from nonlinear kernel functions, thus it has been successfully used for pattern classification. However, CMMD does…

Computer Vision and Pattern Recognition · Computer Science 2020-08-25 Chuan-Xian Ren , Pengfei Ge , Dao-Qing Dai , Hong Yan

We introduce a kernel-based goodness-of-fit test for censored data, where observations may be missing in random time intervals: a common occurrence in clinical trials and industrial life-testing. The test statistic is straightforward to…

Methodology · Statistics 2018-10-11 Tamara Fernández , Arthur Gretton

Comparing conditional distributions is a fundamental challenge in statistics and machine learning, with applications across a wide range of domains. While proposed methods for measuring discrepancies using kernel embeddings of distributions…

Machine Learning · Statistics 2026-05-05 Peter Moskvichev , Siu Lun Chau , Dino Sejdinovic

We present a novel neural network Maximum Mean Discrepancy (MMD) statistic by identifying a new connection between neural tangent kernel (NTK) and MMD. This connection enables us to develop a computationally efficient and memory-efficient…

Machine Learning · Statistics 2021-10-19 Xiuyuan Cheng , Yao Xie

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

There exist some testing procedures based on the maximum mean discrepancy (MMD) to address the challenge of model specification. However, they ignore the presence of estimated parameters in the case of composite null hypotheses. In this…

Methodology · Statistics 2024-12-10 Florian Brück , Jean-David Fermanian , Aleksey Min

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

Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…

Machine Learning · Statistics 2025-04-22 Oscar Key , Arthur Gretton , François-Xavier Briol , Tamara Fernandez

Two-sample tests have been extensively employed in various scientific fields and machine learning such as evaluation on the effectiveness of drugs and A/B testing on different marketing strategies to discriminate whether two sets of samples…

Quantum Physics · Physics 2025-11-27 Yu Terada , Yugo Ogio , Ken Arai , Hiroyuki Tezuka , Yu Tanaka

The widespread adoption of the \emph{maximum mean discrepancy} (MMD) in goodness-of-fit testing has spurred extensive research on its statistical performance. However, recent studies indicate that the inherent structure of MMD may constrain…

Methodology · Statistics 2025-11-11 Shiwei Sang , Shao-Bo Lin , Xuehu Zhu

The Maximum Mean Discrepancy (MMD) is a widely used multivariate distance metric for two-sample testing. The standard MMD test statistic has an intractable null distribution typically requiring costly resampling or permutation approaches…

Methodology · Statistics 2026-02-24 Anirban Chatterjee , Aaditya Ramdas

Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…

Machine Learning · Computer Science 2024-12-02 Oleksii Kachaiev , Stefano Recanatesi

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

Nonparametric two sample testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. We refer to the most common…

Statistics Theory · Mathematics 2015-08-05 Aaditya Ramdas , Sashank J. Reddi , Barnabas Poczos , Aarti Singh , Larry Wasserman

Kernel methods underpin many of the most successful approaches in data science and statistics, and they allow representing probability measures as elements of a reproducing kernel Hilbert space without loss of information. Recently, the…

Machine Learning · Statistics 2025-03-19 Florian Kalinke , Zoltan Szabo , Bharath K. Sriperumbudur

We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb{P}$ more effectively than i.i.d. sampling or standard thinning. Given a suitable reproducing kernel $\mathbf{k}_{\star}$ and $O(n^2)$ time, kernel…

Machine Learning · Statistics 2024-05-14 Raaz Dwivedi , Lester Mackey

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

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

Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…

Statistics Theory · Mathematics 2022-10-18 Zhen Huang , Bodhisattva Sen

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