Related papers: Positive Definite Multi-Kernels for Scattered Data…
Motivated by multi-distribution divergences, which originate in information theory, we propose a notion of `multi-point' kernels, and study their applications. We study a class of kernels based on Jensen type divergences and show that these…
Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set. Discrete DPPs are parametrized by a positive semidefinite matrix (called the DPP kernel), and estimating this kernel is key…
We present a number of new piecewise-polynomial kernels for image interpolation. The kernels are constructed by optimizing a measure of interpolation quality based on the magnitude of anisotropic artifacts. The kernel design process is…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel…
In this paper we show that the strictly positive definite matrix valued isotropic kernels in the circle and the real dot product kernels in Euclidean spaces are not well behaved with respect to its scalar valued projections. We generalize…
We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…
While direct statements for kernel based interpolation on regions $\Omega \subset \mathbb{R}^d$ are well researched, far less is known about corresponding inverse statements. The available inverse statements for kernel based interpolation…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble…
We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…
Targeting at sparse learning, we construct Banach spaces B of functions on an input space X with the properties that (1) B possesses an l1 norm in the sense that it is isometrically isomorphic to the Banach space of integrable functions on…
This note proposes rapidly convergent computational formulae for evaluating scattering kernels from radiative transfer theory. The approach used here does not rely on Legendre expansions, but rather uses exponentially convergent numerical…
Deep learning methods have predominantly been applied to large artificial neural networks. Despite their state-of-the-art performance, these large networks typically do not generalize well to datasets with limited sample sizes. In this…
It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…
Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…
Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…
In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…