Related papers: Maximum-of-Differences Test for Comparing Multivar…
Suppose one desires to randomly sample a pair of objects such as socks, hoping to get a matching pair. Even in the simplest situation for sampling, which is sampling with replacement, the innocent phrase "the distribution of the color of a…
Mutual information (MI) is a useful information-theoretic measure to quantify the statistical dependence between two random variables: $X$ and $Y$. Often, we are interested in understanding how the dependence between $X$ and $Y$ in one set…
Most existing out-of-distribution (OOD) detection benchmarks classify samples with novel labels as the OOD data. However, some marginal OOD samples actually have close semantic contents to the in-distribution (ID) sample, which makes…
In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number…
We examine the estimation of the Kullback-Leibler (KL) divergence and the use of the goodness-of-fit test for multivariate continuous distributions. Our starting point is the maximum entropy principle for Shannon entropy: among all…
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…
For many applications, it is critical to interpret and validate groups of observations obtained via clustering. A common validation approach involves testing differences in feature means between observations in two estimated clusters. In…
We study two nonparametric tests of the hypothesis that a sequence of independent observations is identically distributed against the alternative that at a single change point the distribution changes. The tests are based on the Cramer-von…
A new interpoint distance-based measure is proposed to identify the optimal number of clusters present in a data set. Designed in nonparametric approach, it is independent of the distribution of given data. Interpoint distances between the…
This paper develops novel conformal methods to test whether a new observation was sampled from the same distribution as a reference set. Blending inductive and transductive conformal inference in an innovative way, the described methods can…
A notorious problem in queueing theory is to compute the worst possible performance of the GI/G/1 queue under mean-dispersion constraints for the interarrival and service time distributions. We address this extremal queue problem by…
Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this paper, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data…
The distribution closeness testing (DCT) assesses whether the distance between a distribution pair is at least $\epsilon$-far. Existing DCT methods mainly measure discrepancies between a distribution pair defined on discrete one-dimensional…
A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of…
The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus…
The identification of peaks or maxima in probability densities, by mode testing or bump hunting, has become an important problem in applied fields. This task has been approached in the statistical literature from different perspectives,…
For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…
Distance-based regression model, as a nonparametric multivariate method, has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic…
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…
Measuring uncertainty is a promising technique for detecting adversarial examples, crafted inputs on which the model predicts an incorrect class with high confidence. But many measures of uncertainty exist, including predictive en- tropy…