Related papers: A Kernelized Stein Discrepancy for Goodness-of-fit…

We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

Methods of performing anomaly detection on high-dimensional data sets are needed, since algorithms which are trained on data are only expected to perform well on data that is similar to the training data. There are theoretical results on…

Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of…

We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish that testing for the \emph{equality} of two non-atomic…

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

In this paper we present a general framework for Stein's method for multivariate continuous distributions. The approach gives a collection of Stein characterisations, among which we highlight score-Stein operators and kernel Stein…

In the present paper, we develop a new goodness-of-fit test for the Birnbaum- Saunders distribution based on the probability plot. We utilize the sample correlation coefficient from the Birnbaum-Saunders probability plot as a measure of…

Stein importance sampling is a widely applicable technique based on kernelized Stein discrepancy, which corrects the output of approximate sampling algorithms by reweighting the empirical distribution of the samples. A general analysis of…

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…

This work is motivated by the study of local protein structure, which is defined by two variable dihedral angles that take values from probability distributions on the flat torus. Our goal is to provide the space…

We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we…

We consider the problem of goodness-of-fit testing for a model that has at least one unknown parameter that cannot be eliminated by transformation. Examples of such problems can be as simple as testing whether a sample consists of…

Goodness-of-fit (GoF) tests are fundamental for assessing model adequacy. Score-based tests are appealing because they require fitting the model only once under the null. However, extending them to powerful nonparametric alternatives is…

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between…

We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…

We develop a systematic, omnibus approach to goodness-of-fit testing for parametric distributional models when the variable of interest is only partially observed due to censoring and/or truncation. In many such designs, tests based on the…

A consistent goodness-of-fit test for distributional regression is introduced. The test statistic is based on a process that traces the difference between a nonparametric and a semi-parametric estimate of the marginal distribution function…

Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…