Related papers: Maximum-of-Differences Test for Comparing Multivar…
We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…
Under the null hypothesis, the marginal probability of the positive response is symmetric at any specified correlated coefficient, and the discordance probability is also symmetric to the positive response probability. The marginal…
In many real-world applications of machine learning, we are interested to know if it is possible to train on the data that we have gathered so far, and obtain accurate predictions on a new test data subset that is qualitatively different in…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Domain shift remains a key challenge in deploying machine learning models to the real world. Unsupervised domain adaptation (UDA) aims to address this by minimising domain discrepancy during training, but the discrepancy estimates suffer…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
We discuss a goodness-of-fit method which tests the compatibility between statistically independent data sets. The method gives sensible results even in cases where the chi^2-minima of the individual data sets are very low or when several…
Gaussian mixture models are widely used in Statistics. A fundamental aspect of these distributions is the study of the local maxima of the density, or modes. In particular, it is not known how many modes a mixture of $k$ Gaussians in $d$…
We develop E-variables for testing whether two or more data streams come from the same source or not, and more generally, whether the difference between the sources is larger than some minimal effect size. These E-variables lead to exact,…
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…
Permutation tests enable testing statistical hypotheses in situations when the distribution of the test statistic is complicated or not available. In some situations, the test statistic under investigation is multivariate, with the multiple…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Message identification (M-I) divergence is an important measure of the information distance between probability distributions, similar to Kullback-Leibler (K-L) and Renyi divergence. In fact, M-I divergence with a variable parameter can…
High-dimensional tests are applied to find relevant sets of variables and relevant models. If variables are selected by analyzing the sums of products matrices and a corresponding mean-value test is performed, there is the danger that the…
In this survey, we present and compare different approaches to estimate Mutual Information (MI) from data to analyse general dependencies between variables of interest in a system. We demonstrate the performance difference of MI versus…
This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum…
We propose a new class of distribution-based clustering algorithms, called k-groups, based on energy distance between samples. The energy distance clustering criterion assigns observations to clusters according to a multi-sample energy…
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein…
A method for change point detection is proposed. We consider a univariate sequence of independent random variables with piecewise constant expectation and variance, apart from which the distribution may vary periodically. We aim to detect…