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As a promising step, the performance of data analysis and feature learning are able to be improved if certain pattern matching mechanism is available. One of the feasible solutions can refer to the importance estimation of instances, and…

Machine Learning · Computer Science 2020-11-17 Miao Cheng , Xinge You

In the framework of quantum optics, we study the problem of goodness-of-fit testing in a severely ill-posed inverse problem. A novel testing procedure is introduced and its rates of convergence are investigated under various smoothness…

Statistics Theory · Mathematics 2008-12-22 Katia Meziani

High-dimensional data, where the dimension of the feature space is much larger than sample size, arise in a number of statistical applications. In this context, we construct the generalized multivariate sign transformation, defined as a…

Methodology · Statistics 2021-07-05 Subhabrata Majumdar , Snigdhansu Chatterjee

We propose kernel-type smoothed Kolmogorov-Smirnov and Cram\'{e}r-von Mises tests for data on general interval, using bijective transformations. Though not as severe as in the kernel density estimation, utilizing naive kernel method…

Methodology · Statistics 2020-05-29 Rizky Reza Fauzi , Yoshihiko Maesono

Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…

Statistics Theory · Mathematics 2024-03-26 Joydeep Chowdhury , Subhajit Dutta , Marc G. Genton

An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…

Statistics Theory · Mathematics 2025-04-17 Geoffrey Wolfer , Pierre Alquier

Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering…

Methodology · Statistics 2022-08-09 Marcos Matabuena , J. C Vidal , Oscar Hernan Madrid Padilla , Dino Sejdinovic

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them…

Machine Learning · Statistics 2025-07-09 Arturo Castellanos , Anna Korba , Pavlo Mozharovskyi , Hicham Janati

We present a unified approach to goodness-of-fit testing in $\mathbb{R}^d$ and on lower-dimensional manifolds embedded in $\mathbb{R}^d$ based on sums of powers of weighted volumes of $k$-th nearest neighbor spheres. We prove asymptotic…

Methodology · Statistics 2016-12-21 Bruno Ebner , Norbert Henze , Joseph E. Yukich

Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…

Statistics Theory · Mathematics 2014-06-25 Samuel Maistre , Valentin Patilea

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

Machine Learning · Computer Science 2020-02-23 Patrick Heas , Cedric Herzet , Benoit Combes

Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…

Methodology · Statistics 2025-09-04 Jian Yan , Zhuoxi Li , Xianyang Zhang

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

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

Non-parametric goodness-of-fit testing procedures based on kernel Stein discrepancies (KSD) are promising approaches to validate general unnormalised distributions in various scenarios. Existing works focused on studying kernel choices to…

Methodology · Statistics 2022-06-02 Wenkai Xu

Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…

Statistics Theory · Mathematics 2017-10-13 Alain Celisse , Guillemette Marot , Morgane Pierre-Jean , Guillem Rigaill

Under mild assumptions on the kernel, we obtain the best known error rates in a regularized learning scenario taking place in the corresponding reproducing kernel Hilbert space (RKHS). The main novelty in the analysis is a proof that one…

Statistics Theory · Mathematics 2010-01-14 Shahar Mendelson , Joseph Neeman

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

Machine Learning · Statistics 2020-12-15 Krikamol Muandet , Kenji Fukumizu , Bharath Sriperumbudur , Bernhard Schölkopf

In this paper, we study a class of two sample test statistics based on inter-point distances in the high dimensional and low sample size setting. Our test statistics include the well-known energy distance and maximum mean discrepancy with…

Methodology · Statistics 2020-04-13 Changbo Zhu , Xiaofeng Shao