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We study the comparison problem of distribution equality between two random samples under a right censoring scheme. To address this problem, we design a series of tests based on energy distance and kernel mean embeddings. We calibrate our…

Methodology · Statistics 2019-12-10 Marcos Matabuena , Oscar Hernan Madrid Padilla

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

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

We propose a set of kernel-based tools to evaluate the designs and tune the hyperparameters of conditional sequence models, with a focus on problems in computational biology. The backbone of our tools is a new measure of discrepancy between…

Machine Learning · Statistics 2025-10-20 Pierre Glaser , Steffanie Paul , Alissa M. Hummer , Charlotte M. Deane , Debora S. Marks , Alan N. Amin

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 performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…

Statistics Theory · Mathematics 2026-02-25 Nils Lid Hjort , Nikolai G. Ushakov

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 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

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

The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus…

Methodology · Statistics 2025-09-16 Shubhanshu Shekhar , Ilmun Kim , Aaditya Ramdas

This paper presents a theoretical analysis of sample selection bias correction. The sample bias correction technique commonly used in machine learning consists of reweighting the cost of an error on each training point of a biased sample to…

Machine Learning · Computer Science 2008-12-18 Corinna Cortes , Mehryar Mohri , Michael Riley , Afshin Rostamizadeh

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

Machine Learning · Computer Science 2022-09-13 Paul Scharnhorst , Emilio T. Maddalena , Yuning Jiang , Colin N. Jones

Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…

Machine Learning · Computer Science 2018-10-10 Shahin Shahrampour , Vahid Tarokh

In order to anticipate rare and impactful events, we propose to quantify the worst-case risk under distributional ambiguity using a recent development in kernel methods -- the kernel mean embedding. Specifically, we formulate the…

Optimization and Control · Mathematics 2020-09-08 Jia-Jie Zhu , Wittawat Jitkrittum , Moritz Diehl , Bernhard Schölkopf

We present a sequential version of the kernelized Stein discrepancy goodness-of-fit test, which allows for conducting goodness-of-fit tests for unnormalized densities that are continuously monitored and adaptively stopped. That is, the…

Machine Learning · Statistics 2025-04-18 Diego Martinez-Taboada , Aaditya Ramdas

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

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

Maximum Mean Discrepancy (MMD) is a widely used concept in machine learning research which has gained popularity in recent years as a highly effective tool for comparing (finite-dimensional) distributions. Since it is designed as a…

Machine Learning · Statistics 2025-06-03 Andrew Alden , Blanka Horvath , Zacharia Issa

This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…

Machine Learning · Statistics 2025-12-30 Antonin Schrab

Maximum mean discrepancy (MMD) has enjoyed a lot of success in many machine learning and statistical applications, including non-parametric hypothesis testing, because of its ability to handle non-Euclidean data. Recently, it has been…

Statistics Theory · Mathematics 2025-01-24 Omar Hagrass , Bharath K. Sriperumbudur , Bing Li