Related papers: Distance and Kernel-Based Measures for Global and …

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…

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…

We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…

Existing measures and representations for trajectories have two longstanding fundamental shortcomings, i.e., they are computationally expensive and they can not guarantee the `uniqueness' property of a distance function: dist(X,Y) = 0 if…

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…

Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as…

We study the problem of conditional two-sample testing, which aims to determine whether two populations have the same distribution after accounting for confounding factors. This problem commonly arises in various applications, such as…

We propose a novel kernel-based two-sample test that leverages the spectral decomposition of the maximum mean discrepancy (MMD) statistic to identify and utilize well-estimated directional components in reproducing kernel Hilbert space…

In this article a new family of tests is proposed for the comparison problem of the equality of distribution of two-sample under right censoring scheme. The tests are based on energy distance and kernels mean embedding, are calibrated by…

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…

Consider a setting with multiple units (e.g., individuals, cohorts, geographic locations) and outcomes (e.g., treatments, times, items), where the goal is to learn a multivariate distribution for each unit-outcome entry, such as the…

Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…

Kernel two-sample tests have been widely used, and the development of efficient methods for high-dimensional, large-scale data is receiving increasing attention in the big data era. However, existing methods, such as the maximum mean…

When monitoring machine learning systems, two-sample tests of homogeneity form the foundation upon which existing approaches to drift detection build. They are used to test for evidence that the distribution underlying recent deployment…

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…

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…

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…

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, distances between…

We focus on the distribution regression problem: regressing to a real-valued response from a probability distribution. Although there exist a large number of similarity measures between distributions, very little is known about their…

Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do…