相关论文: The Alpha-Beta-Symetric Divergence and their Posit…

In this paper, we consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on $[0,\infty)$. To this end we use the class of kernel estimators with asymmetric gamma…

We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…

The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…

Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special…

Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…

Bregman divergences play a pivotal role in statistics, machine learning and computational information geometry. Particularly in the context of machine learning, they are central to clustering, exponential families, parameter estimation and…

Let X be a strictly pseudoconcave domain in a closed polarized complex manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given Hermitian metric on L, together with a volume form, induces by restriction to X a Hilbert space…

Classifying points in high dimensional spaces is a fundamental geometric problem in machine learning. In this paper, we address classifying points in the $d$-dimensional Hilbert polygonal metric. The Hilbert metric is a generalization of…

We study the problem of binary classification from the point of view of learning convex polyhedra in Hilbert spaces, to which one can reduce any binary classification problem. The problem of learning convex polyhedra in finite-dimensional…

Divergences are fundamental to the information criteria that underpin most signal processing algorithms. The alpha-beta family of divergences, designed for non-negative data, offers a versatile framework that parameterizes and continuously…

Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…

Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…

Measuring and testing dependence between complex objects is of great importance in modern statistics. Most existing work relied on the distance between random variables, which inevitably required the moment conditions to guarantee the…

The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…

We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…

In modern data analysis, nonparametric measures of discrepancies between random variables are particularly important. The subject is well-studied in the frequentist literature, while the development in the Bayesian setting is limited where…

Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view…

Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure:…