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We propose novel statistics which maximise the power of a two-sample test based on the Maximum Mean Discrepancy (MMD), by adapting over the set of kernels used in defining it. For finite sets, this reduces to combining (normalised) MMD…

Machine Learning · Statistics 2023-10-31 Felix Biggs , Antonin Schrab , Arthur Gretton

We construct a Wasserstein gradient flow of the maximum mean discrepancy (MMD) and study its convergence properties. The MMD is an integral probability metric defined for a reproducing kernel Hilbert space (RKHS), and serves as a metric on…

Machine Learning · Statistics 2019-12-04 Michael Arbel , Anna Korba , Adil Salim , Arthur Gretton

Large language models (LLMs) such as ChatGPT have exhibited remarkable performance in generating human-like texts. However, machine-generated texts (MGTs) may carry critical risks, such as plagiarism issues, misleading information, or…

Computation and Language · Computer Science 2024-03-01 Shuhai Zhang , Yiliao Song , Jiahao Yang , Yuanqing Li , Bo Han , Mingkui Tan

The distribution closeness testing (DCT) assesses whether the distance between a distribution pair is at least $\epsilon$-far. Existing DCT methods mainly measure discrepancies between a distribution pair defined on discrete one-dimensional…

Machine Learning · Computer Science 2025-10-10 Zhijian Zhou , Liuhua Peng , Xunye Tian , Feng Liu

The kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces. In this paper we propose a method to boost the power…

Methodology · Statistics 2024-09-06 Anirban Chatterjee , Bhaswar B. Bhattacharya

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…

Machine Learning · Statistics 2021-02-15 Onur Teymur , Jackson Gorham , Marina Riabiz , Chris. J. Oates

Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…

Optimization and Control · Mathematics 2025-03-18 Zahra Mehraban , Alois Pichler

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

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

A frequent problem in statistical science is how to properly handle missing data in matched paired observations. There is a large body of literature coping with the univariate case. Yet, the ongoing technological progress in measuring…

Methodology · Statistics 2022-06-06 Marcos Matabuena , Paulo Félix , Marc Ditzhaus , Juan Vidal , Francisco Gude

Pre-trained diffusion models have emerged as powerful generative priors for both unconditional and conditional sample generation, yet their outputs often deviate from the characteristics of user-specific target data. Such mismatches are…

Machine Learning · Computer Science 2026-01-14 Matina Mahdizadeh Sani , Nima Jamali , Mohammad Jalali , Farzan Farnia

Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance),…

Machine Learning · Statistics 2019-05-17 Matthieu Lerasle , Zoltan Szabo , Timothee Mathieu , Guillaume Lecue

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

Independence analysis is an indispensable step before regression analysis to find out essential factors that influence the objects. With many applications in machine Learning, medical Learning and a variety of disciplines, statistical…

Methodology · Statistics 2022-07-08 Wenliang Pan , Yujue Li , Jianwu Liu , Pei Dang , Weixiong Mai

We introduce a method, MMD-B-Fair, to learn fair representations of data via kernel two-sample testing. We find neural features of our data where a maximum mean discrepancy (MMD) test cannot distinguish between representations of different…

Machine Learning · Statistics 2023-04-26 Namrata Deka , Danica J. Sutherland

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

Comparing $K$-sample distributions is a fundamental problem in data science that arises in a wide variety of fields and applications. In this article, we introduce a maximum-of-differences approach to make such comparisons. Specifically, we…

Methodology · Statistics 2026-04-13 Wei Lan , Long Feng , Runze Li , Chih-Ling Tsai

The Maximum Mean Discrepancy (MMD) has found numerous applications in statistics and machine learning, most recently as a penalty in the Wasserstein Auto-Encoder (WAE). In this paper we compute closed-form expressions for estimating the…

Machine Learning · Statistics 2020-06-03 Raif M. Rustamov

The Maximum Mean Discrepancy (MMD) is a cornerstone statistic for nonparametric two-sample testing, but its test power is dictated entirely by the chosen kernel. Because any fixed kernel inherently fails to distinguish certain…

Machine Learning · Statistics 2026-05-11 Yijin Ni , Xiaoming Huo

In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a…

Statistics Theory · Mathematics 2019-12-12 Badr-Eddine Chérief-Abdellatif , Pierre Alquier