Related papers: Pitman Efficiency Lower Bounds for Multivariate Di…
Given independent samples from two univariate distributions, the one-sided Wilcoxon-Mann-Whitney statistic may be used to conduct a rank-based test of first-order stochastic dominance. We broaden the scope of applicability of such tests by…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
We study the fundamental problems of (i) uniformity testing of a discrete distribution, and (ii) closeness testing between two discrete distributions with bounded $\ell_2$-norm. These problems have been extensively studied in distribution…
This paper considers the problem of testing for latent structure in large symmetric data matrices. The goal here is to develop statistically principled methodology that is flexible in its applicability, computationally efficient, and…
Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$? This fundamental question has…
The sign and the signed-rank tests for univariate data are perhaps the most popular nonparametric competitors of the t test for paired sample problems. These tests have been extended in various ways for multivariate data in finite…
The traveling salesman problem (TSP) is one of the most challenging NP-hard problems. It has widely applications in various disciplines such as physics, biology, computer science and so forth. The best known approximation algorithm for…
A t-test is considered a standard procedure for inference on population means and is widely used in scientific discovery. However, as a special case of a likelihood-ratio test, t-test often shows drastic performance degradation due to the…
Collecting large labeled data sets is a laborious and expensive task, whose scaling up requires division of the labeling workload between many teachers. When the number of classes is large, miscorrespondences between the labels given by the…
We propose a two-sample test for detecting the difference between mean vectors in a high-dimensional regime based on a ridge-regularized Hotelling's $T^2$. To choose the regularization parameter, a method is derived that aims at maximizing…
This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…
We develop some graph-based tests for spherical symmetry of a multivariate distribution using a method based on data augmentation. These tests are constructed using a new notion of signs and ranks that are computed along a path obtained by…
This paper studies estimation of and inference on a distribution function $F$ that is concave on the nonnegative half line and admits a density function $f$ with potentially unbounded support. When $F$ is strictly concave, we show that the…
Multivariate interaction between two or more classes (or species) has important consequences in many fields and causes multivariate clustering patterns such as segregation or association. The spatial segregation occurs when members of a…
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…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…
We consider distributional approximation by generalized Dickman distributions, which appear in number theory, perpetuities, logarithmic combinatorial structures and many other areas. We prove bounds in the Kolmogorov distance for the…