English
Related papers

Related papers: A Permutation-free Kernel Two-Sample Test

200 papers

We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed through reproducing-kernel maximum mean discrepancy (MMD) penalties, and develop a computational…

Optimization and Control · Mathematics 2026-05-29 Yumiharu Nakano

We investigate the training and performance of generative adversarial networks using the Maximum Mean Discrepancy (MMD) as critic, termed MMD GANs. As our main theoretical contribution, we clarify the situation with bias in GAN loss…

Machine Learning · Statistics 2021-01-15 Mikołaj Bińkowski , Danica J. Sutherland , Michael Arbel , Arthur Gretton

In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed…

Methodology · Statistics 2024-08-30 Anirban Chatterjee , Ziang Niu , Bhaswar B. Bhattacharya

Distance covariance is a popular dependence measure for two random vectors $X$ and $Y$ of possibly different dimensions and types. Recent years have witnessed concentrated efforts in the literature to understand the distributional…

Statistics Theory · Mathematics 2024-08-05 Qiyang Han , Yandi Shen

We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but…

Statistics Theory · Mathematics 2016-11-07 Niklas Pfister , Peter Bühlmann , Bernhard Schölkopf , Jonas Peters

We propose a novel supervised learning method to optimize the kernel in the maximum mean discrepancy generative adversarial networks (MMD GANs), and the kernel support vector machines (SVMs). Specifically, we characterize a distributionally…

Machine Learning · Computer Science 2020-02-25 Masoud Badiei Khuzani , Liyue Shen , Shahin Shahrampour , Lei Xing

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

Statistics Theory · Mathematics 2022-11-15 Loris Michel , Jeffrey Näf , Nicolai Meinshausen

Kernel two-sample testing provides a powerful framework for distinguishing any pair of distributions based on $n$ sample points. However, existing kernel tests either run in $n^2$ time or sacrifice undue power to improve runtime. To address…

Machine Learning · Statistics 2025-03-31 Carles Domingo-Enrich , Raaz Dwivedi , Lester Mackey

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels $K(x,y) = - \|x-y\|^r$, $r \in (0,2)$ have exceptional properties which allow…

Machine Learning · Computer Science 2024-02-21 Johannes Hertrich , Christian Wald , Fabian Altekrüger , Paul Hagemann

We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…

Statistics Theory · Mathematics 2019-11-12 Angshuman Roy , Alok Goswami , C. A. Murthy

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

Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…

Machine Learning · Statistics 2019-10-02 M. Scetbon , G. Varoquaux

High-quality test datasets are crucial for assessing the reliability of Deep Neural Networks (DNNs). Mutation testing evaluates test dataset quality based on their ability to uncover injected faults in DNNs as measured by mutation score…

Software Engineering · Computer Science 2025-03-25 Vivek Vekariya , Mojdeh Golagha , Andrea Stocco , Alexander Pretschner

In many practical transfer learning scenarios, the feature distribution is different across the source and target domains (i.e. non-i.i.d.). Maximum mean discrepancy (MMD), as a domain discrepancy metric, has achieved promising performance…

Computer Vision and Pattern Recognition · Computer Science 2019-03-26 Lei Zhang , Shanshan Wang , Guang-Bin Huang , Wangmeng Zuo , Jian Yang , David Zhang

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

This paper introduces kdiff, a novel kernel-based measure for estimating distances between instances of time series, random fields and other forms of structured data. This measure is based on the idea of matching distributions that only…

Machine Learning · Statistics 2021-10-01 Srinjoy Das , Hrushikesh Mhaskar , Alexander Cloninger

We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over…

Machine Learning · Computer Science 2008-05-16 Arthur Gretton , Karsten Borgwardt , Malte J. Rasch , Bernhard Scholkopf , Alexander J. Smola

Comparing probability distributions is at the crux of many machine learning algorithms. Maximum Mean Discrepancies (MMD) and Wasserstein distances are two classes of distances between probability distributions that have attracted abundant…

Machine Learning · Statistics 2023-06-01 Titouan Vayer , Rémi Gribonval

Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study the distance of a given dataset, viewed as a…

Machine Learning · Computer Science 2025-06-12 Jiří Němeček , Mark Kozdoba , Illia Kryvoviaz , Tomáš Pevný , Jakub Mareček

Distributional comparison is a fundamental problem in statistical data analysis with numerous applications in a variety of scientific and engineering fields. Numerous methods exist for distributional comparison but kernel Stein's method has…

Statistics Theory · Mathematics 2025-06-12 Xiaoda Qu , Baba C. Vemuri