Related papers: Kernel Integrated $R^2$: A Measure of Dependence
Kernel techniques are among the most popular and powerful approaches of data science. Among the key features that make kernels ubiquitous are (i) the number of domains they have been designed for, (ii) the Hilbert structure of the function…
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of association between two random variables $X$ and $Y$ taking values in general topological spaces. These nonparametric measures -- defined…
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 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…
A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…
Reliable measurement of dependence between variables is essential in many applications of statistics and machine learning. Current approaches for dependence estimation, especially density-based approaches, lack in precision, robustness…
Dette, Siburg, and Stoimenov (2013) introduced a copula-based measure of dependence, which implies independence if it vanishes and is equal to 1 if one variable is a measurable function of the other. For continuous distributions, the…
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…
We propose an independence test for random variables valued into metric spaces by using a test statistic obtained from appropriately centering and rescaling the squared Hilbert-Schmidt norm of the usual empirical estimator of normalized…
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…
Testing the dependency between two random variables is an important inference problem in statistics since many statistical procedures rely on the assumption that the two samples are independent. To test whether two samples are independent,…
We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…
A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…
We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…
We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test…
We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, this problem is reformulated as an unsupervised learning task…
Mutual information (MI) is an information-theoretic measure of dependency between two random variables. Several methods to estimate MI, from samples of two random variables with unknown underlying probability distributions have been…
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…
Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using…
Kernel-based testing has revolutionized the field of non-parametric tests through the embedding of distributions in an RKHS. This strategy has proven to be powerful and flexible, yet its applicability has been limited to the standard…