Related papers: Kernel based method for the $k$-sample problem
This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…
In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed…
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to…
We introduce the Kernel Calibration Conditional Stein Discrepancy test (KCCSD test), a non-parametric, kernel-based test for assessing the calibration of probabilistic models with well-defined scores. In contrast to previous methods, our…
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…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…
In this work we consider the problem of numerical integration, i.e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand. We focus on the setting in which the target…
The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that…
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…
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…
In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…
The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…
There are plenty of applications and analysis for time-independent elliptic partial differential equations in the literature hinting at the benefits of overtesting by using more collocation conditions than the number of basis functions.…
We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…
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 two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification…
This paper adresses the problem of testing for the equality of $k$ probability distributions on Hilbert spaces, with $k\geqslant 2$. We introduce a generalization of the maximum variance discrepancy called multiple maximum variance…
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…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…