Related papers: A Manifold Two-Sample Test Study: Integral Probabi…

Multivariate pattern analyses approaches in neuroimaging are fundamentally concerned with investigating the quantity and type of information processed by various regions of the human brain; typically, estimates of classification accuracy…

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…

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…

A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to…

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…

We propose a two-sample mean test based on the Bayes factor with non-informative priors, specifically designed for scenarios where the dimension $p$ grows with the sample size $n$ with a linear rate $p/n \to c_1 \in (0, \infty)$. We…

This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using…

A class of distance measures on probabilities -- the integral probability metrics (IPMs) -- is addressed: these include the Wasserstein distance, Dudley metric, and Maximum Mean Discrepancy. IPMs have thus far mostly been used in more…

We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view…

This paper introduces a novel two-sample test for a broad class of orthogonally equivalent positive definite symmetric matrix distributions. Our test is the first of its kind and we derive its asymptotic distribution. To estimate the test…

Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=\Sigma^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $\Sigma$ is shared by all…

The integrated conditional moment (ICM) test is a classical and widely used method for assessing the adequacy of regression models. Although it performs well in fixed-dimension settings, its behavior changes dramatically when the predictor…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…

Testing for the equality of two high-dimensional distributions is a challenging problem, and this becomes even more challenging when the sample size is small. Over the last few decades, several graph-based two-sample tests have been…

The manifold hypothesis suggests that high-dimensional data often lie on or near a low-dimensional manifold. Estimating the dimension of this manifold is essential for leveraging its structure, yet existing work on dimension estimation is…

An exciting recent development is the uptake of deep neural networks in many scientific fields, where the main objective is outcome prediction with the black-box nature. Significance testing is promising to address the black-box issue and…

In this article, we propose some two-sample tests based on ball divergence and investigate their high dimensional behavior. First, we study their behavior for High Dimension, Low Sample Size (HDLSS) data, and under appropriate regularity…

The unfolding of detector effects is a key aspect of comparing experimental data with theoretical predictions. In recent years, different Machine-Learning methods have been developed to provide novel features, e.g. high dimensionality or a…

Integrating probability and nonprobability survey samples is an important problem in modern survey sampling. Nonprobability samples often contain rich outcome information but may lack population representativeness, whereas probability…