Related papers: A Kernel Method for the Two-Sample Problem
We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
We introduce a divergence measure between data distributions based on operators in reproducing kernel Hilbert spaces defined by kernels. The empirical estimator of the divergence is computed using the eigenvalues of positive definite Gram…
In clinical and neuroscientific studies, systematic differences between two populations of brain networks are investigated in order to characterize mental diseases or processes. Those networks are usually represented as graphs built from…
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…
The nonparametric problem of detecting existence of an anomalous interval over a one dimensional line network is studied. Nodes corresponding to an anomalous interval (if exists) receive samples generated by a distribution q, which is…
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…
The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We…
This paper explores methods for estimating or approximating the total variation distance and the chi-squared divergence of probability measures within topological sample spaces, using independent and identically distributed samples. Our…
Representations of probability measures in reproducing kernel Hilbert spaces provide a flexible framework for fully nonparametric hypothesis tests of independence, which can capture any type of departure from independence, including…
Covariate shift occurs prevalently in practice, where the input distributions of the source and target data are substantially different. Despite its practical importance in various learning problems, most of the existing methods only focus…
Two-sample and independence tests with the kernel-based MMD and HSIC have shown remarkable results on i.i.d. data and stationary random processes. However, these statistics are not directly applicable to non-stationary random processes, a…
Given $M \geq 2$ distributions defined on a general measurable space, we introduce a nonparametric (kernel) measure of multi-sample dissimilarity (KMD) -- a parameter that quantifies the difference between the $M$ distributions. The…
In this article, we consider the problem of testing whether two latent position random graphs are correlated. We propose a test statistic based on the kernel method and introduce the estimation procedure based on the spectral decomposition…
In this paper, we study the angle testing problem in the context of similarity search in high-dimensional Euclidean spaces and propose two projection-based probabilistic kernel functions, one designed for angle comparison and the other for…
We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The…
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…
In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…
In the statistical literature, as well as in artificial intelligence and machine learning, measures of discrepancy between two probability distributions are largely used to develop measures of goodness-of-fit. We concentrate on quadratic…
Score-based kernelised Stein discrepancy (KSD) tests have emerged as a powerful tool for the goodness of fit tests, especially in high dimensions; however, the test performance may depend on the choice of kernels in an underlying…