相关论文: Testing for Homogeneity with Kernel Fisher Discrim…

This article presents a homogeneity test for testing the equality of several high-dimensional covariance matrices for stationary processes with ignoring the assumption of normality. We give the asymptotic distribution of the proposed test.…

In recent years, transfer learning has garnered significant attention. Its ability to leverage knowledge from related studies to improve generalization performance in a target study has made it highly appealing. This paper focuses on…

Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…

Kernel-weighted test statistics have been widely used in a variety of settings including non-stationary regression, inference on propensity score and panel data models. We develop the limit theory for a kernel-based specification test of a…

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…

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 test of homogeneity for normal mixtures has been conducted in diverse research areas, but constructing a theory of the test of homogeneity is challenging because the parameter set for the null hypothesis corresponds to singular points…

Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…

This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…

The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of $L^2(\C, \, d^2z/\pi)$ based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family…

In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…

Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive…

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…

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of…

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 study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…

Handling incomplete and heterogeneous data remains a central challenge in real-world machine learning, where missing values may follow complex mechanisms (MCAR, MAR, MNAR) and features can be of mixed types (numerical and categorical).…

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…

Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models…

Kernel-based methods have been recently introduced for linear system identification as an alternative to parametric prediction error methods. Adopting the Bayesian perspective, the impulse response is modeled as a non-stationary Gaussian…