Related papers: On the Finite-Sample Performance of Measure Transp…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
A variant of the classical optimal transportation problem is: among all joint measures with fixed marginals and which are dominated by a given density, find the optimal one. Existence and uniqueness of solutions to this variant were…
Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
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…
It is common to rank different categories by means of preferences that are revealed through data on choices. A prominent example is the ranking of political candidates or parties using the estimated share of support each one receives in…
Graph-based tests are a class of non-parametric two-sample tests useful for analyzing high-dimensional data. The test statistics are constructed from similarity graphs (such as K-minimum spanning tree), and consequently, their performance…
We are deriving optimal rank-based tests for the adequacy of a vector autoregressive-moving average (VARMA) model with elliptically contoured innovation density. These tests are based on the ranks of pseudo-Mahalanobis distances and on…
In complex scale-free networks, ranking the individual nodes based upon their importance has useful applications, such as the identification of hubs for epidemic control, or bottlenecks for controlling traffic congestion. However, in most…
The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
A depth-based rank sum statistic for multivariate data introduced by Liu and Singh [J. Amer. Statist. Assoc. 88 (1993) 252--260] as an extension of the Wilcoxon rank sum statistic for univariate data has been used in multivariate rank tests…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…
Symmetry arises often when learning from high dimensional data. For example, data sets consisting of point clouds, graphs, and unordered sets appear routinely in contemporary applications, and exhibit rich underlying symmetries.…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
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,…
Distribution-free tests such as the Wilcoxon rank sum test are popular for testing the equality of two univariate distributions. Among the important reasons for their popularity are the striking results of Hodges-Lehmann (1956) and…