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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 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

Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…

Methodology · Statistics 2025-10-03 Hoseung Song , Hao Chen

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 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

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

In many real-world applications, it is common that a proportion of the data may be missing or only partially observed. We develop a novel two-sample testing method based on the Maximum Mean Discrepancy (MMD) which accounts for missing data…

Methodology · Statistics 2024-05-27 Yijin Zeng , Niall M. Adams , Dean A. Bodenham

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…

Machine Learning · Statistics 2017-11-07 Ho Chung Leon Law , Christopher Yau , Dino Sejdinovic

In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…

Machine Learning · Computer Science 2025-02-11 Yijin Ni , Xiaoming Huo

Existing domain adaptation methods aim to reduce the distributional difference between the source and target domains and respect their specific discriminative information, by establishing the Maximum Mean Discrepancy (MMD) and the…

Machine Learning · Computer Science 2020-07-03 Wei Wang , Haojie Li , Zhengming Ding , Zhihui Wang

We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the…

Statistics Theory · Mathematics 2023-07-04 Kevin H. Huang , Xing Liu , Andrew B. Duncan , Axel Gandy

In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…

Statistics Theory · Mathematics 2024-10-08 Bilol Banerjee , Anil K. Ghosh

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum…

Methodology · Statistics 2023-05-11 Ayush Bharti , Masha Naslidnyk , Oscar Key , Samuel Kaski , François-Xavier Briol

We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework…

Machine Learning · Statistics 2024-12-23 Jie Wang , Santanu S. Dey , Yao Xie

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

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 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

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

While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we…

Methodology · Statistics 2019-06-17 Francois-Xavier Briol , Alessandro Barp , Andrew B. Duncan , Mark Girolami

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