Related papers: Borel Kernels and their Approximation, Categorical…

In this work, we broadly connect kernel-based filtering (e.g. approaches such as the bilateral filters and nonlocal means, but also many more) with general variational formulations of Bayesian regularized least squares, and the related…

For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks,…

In this note, we develop some of the basic theory of s-finite (measures and) kernels, a little-studied class that Staton has recently argued convincingly to be precisely the semantic counterpart of (first-order) probabilistic programs. We…

We develop a unified framework for locating natural properties of algebraic and analytic structures within the Borel hierarchy. Objects are presented as quotients of a universal generator and definability is read directly from the quotient…

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…

Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…

Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear…

We study representations of positive definite kernels $K$ in a general setting, but with view to applications to harmonic analysis, to metric geometry, and to realizations of certain stochastic processes. Our initial results are stated for…

We analyze the Nystr\"om approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nystr\"om approximation with i.i.d. sampling and singular-value…

The main result of this paper is that determinantal point processes on the real line corresponding to projection operators with integrable kernels are quasi-invariant, in the continuous case, under the group of diffeomorphisms with compact…

Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…

In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential equations with weak enforcement of boundary conditions using…

Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…

We study a category of probability spaces and measure-preserving Markov kernels up to almost sure equality. This category contains, among its isomorphisms, mod-zero isomorphisms of probability spaces. It also gives an isomorphism between…

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting…

The present work develops a construction of a CD category of partial kernels from a particular type of Markov category called a partializable Markov category. These are a generalization of earlier models of categories of partial morphisms…

In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of…

We study the mixtures of factorizing probability distributions represented as visible marginal distributions in stochastic layered networks. We take the perspective of kernel transitions of distributions, which gives a unified picture of…

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of…

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…