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In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…

Statistics Theory · Mathematics 2020-06-08 Ilmun Kim

Modern large-scale kernel-based tests such as maximum mean discrepancy (MMD) and kernelized Stein discrepancy (KSD) optimize kernel hyperparameters on a held-out sample via data splitting to obtain the most powerful test statistics. While…

Machine Learning · Computer Science 2020-10-20 Jonas M. Kübler , Wittawat Jitkrittum , Bernhard Schölkopf , Krikamol Muandet

We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…

Machine Learning · Statistics 2025-09-16 Leonardo V. Santoro , Victor M. Panaretos

We propose to investigate test statistics for testing homogeneity in reproducing kernel Hilbert spaces. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed and local alternatives is assessed.…

Machine Learning · Statistics 2008-12-18 Zaid Harchaoui , Francis Bach , Eric Moulines

A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…

Statistics Theory · Mathematics 2018-02-20 Meimei Liu , Zuofeng Shang , Guang Cheng

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

We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…

Machine Learning · Statistics 2020-03-11 Matthias Kirchler , Shahryar Khorasani , Marius Kloft , Christoph Lippert

Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector…

Machine Learning · Statistics 2018-08-07 Chenchao Zhao , Jun S. Song

Non-parametric two-sample tests based on energy distance or maximum mean discrepancy are widely used statistical tests for comparing multivariate data from two populations. While these tests enjoy desirable statistical properties, their…

Computation · Statistics 2024-06-11 Elias Chaibub Neto

We present a general framework for hypothesis testing on distributions of sets of individual examples. Sets may represent many common data sources such as groups of observations in time series, collections of words in text or a batch of…

Methodology · Statistics 2021-02-03 Alexis Bellot , Mihaela van der Schaar

Nonparametric two sample testing deals with the question of consistently deciding if two distributions are different, given samples from both, without making any parametric assumptions about the form of the distributions. The current…

Statistics Theory · Mathematics 2014-11-25 Aaditya Ramdas , Sashank J. Reddi , Barnabas Poczos , Aarti Singh , Larry Wasserman

Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data…

Statistics Theory · Mathematics 2023-06-09 Yiting Chen , Wei Lin , Xiaoping Shi

Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…

Methodology · Statistics 2024-01-23 Marija Cuparić , Bruno Ebner , Bojana Milošević

Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…

Machine Learning · Computer Science 2018-07-11 Martin Zaefferer , Thomas Bartz-Beielstein , Günter Rudolph

This study presents an efficient approach for incomplete data classification, where the entries of samples are missing or masked due to privacy preservation. To deal with these incomplete data, a new kernel function with asymmetric…

Machine Learning · Computer Science 2016-11-22 Bo-Wei Chen

We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…

Methodology · Statistics 2025-01-29 Chi Zhang , Peijun Sang , Yingli Qin

Kernel methods provide a flexible and powerful framework for nonparametric statistical testing by embedding probability distributions into a reproducing kernel Hilbert space (RKHS). In this work, we study the kernel two-sample testing…

Statistics Theory · Mathematics 2026-04-09 Perrine Lacroix , Bertrand Michel , Franck Picard , Vincent Rivoirard

Recent years have witnessed growing concerns about the privacy of sensitive data. In response to these concerns, differential privacy has emerged as a rigorous framework for privacy protection, gaining widespread recognition in both…

Statistics Theory · Mathematics 2024-01-09 Ilmun Kim , Antonin Schrab

We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the…

Methodology · Statistics 2021-11-01 Xinran Li , Bo Jiang , Jun S. Liu

We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…

Machine Learning · Statistics 2025-11-07 Chiraag Kaushik , Justin Romberg , Vidya Muthukumar