Related papers: Likelihood Ratio Tests by Kernel Gaussian Embeddin…
In this paper we deal with the problem of testing for the equality of $k$ probability distributions defined on $(\mathcal{X},\mathcal{B})$, where $\mathcal{X}$ is a metric space and $\mathcal{B}$ is the corresponding Borel $\sigma$-field.…
This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…
A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean…
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…
We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…
Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to \emph{one} of the two classes. Special cases of this problem are well-known: with complete knowledge of…
Over the last decade, an approach that has gained a lot of popularity to tackle nonparametric testing problems on general (i.e., non-Euclidean) domains is based on the notion of reproducing kernel Hilbert space (RKHS) embedding of…
In the Gaussian sequence model $Y=\mu+\xi$, we study the likelihood ratio test (LRT) for testing $H_0: \mu=\mu_0$ versus $H_1: \mu \in K$, where $\mu_0 \in K$, and $K$ is a closed convex set in $\mathbb{R}^n$. In particular, we show that…
Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…
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…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method…
Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational…
Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…
We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…
We propose a novel kernel-based two-sample test that leverages the spectral decomposition of the maximum mean discrepancy (MMD) statistic to identify and utilize well-estimated directional components in reproducing kernel Hilbert space…
A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the…
Gaussian mixture models with eigen-decomposed covariance structures make up the most popular family of mixture models for clustering and classification, i.e., the Gaussian parsimonious clustering models (GPCM). Although the GPCM family has…
In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing…
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…