Related papers: A Kernel Two-Sample Test for Functional Data

Machine learning and deep learning have been used extensively to classify physical surfaces through images and time-series contact data. However, these methods rely on human expertise and entail the time-consuming processes of data and…

In the statistical literature, as well as in artificial intelligence and machine learning, measures of discrepancy between two probability distributions are largely used to develop measures of goodness-of-fit. We concentrate on quadratic…

The two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification…

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

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…

Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean…

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

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…

Modern data analyses frequently encounter settings where samples of variables are contaminated by measurement error. Ignoring measurement noise can substantially degrade statistical inference, while existing correction techniques are often…

The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able…

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…

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…

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…

In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why…

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…

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…

In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…

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…

We consider the problem of two-sample testing in a semi-supervised setting with abundant unlabeled covariate data. Standard two-sample tests neglect covariate information, which has the potential to significantly boost performance. However,…