Related papers: Subinvariant kernel dynamics

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…

We present a new smooth, Gaussian-like kernel that allows the kernel density estimate for an angular distribution to be exactly represented by a finite number of its Fourier series coefficients. Distributions of angular quantities, such as…

One of approaches to quantum gravity is different models of a discrete pregeometry. An example of a discrete pregeometry on a microscopic scale is introduced. This is the particular case of a causal set. The causal set is a locally finite…

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…

Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite…

We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel Granger causality to the multivariate case, here presented,…

We investigate how the training curve of isotropic kernel methods depends on the symmetry of the task to be learned, in several settings. (i) We consider a regression task, where the target function is a Gaussian random field that depends…

We prove some conjectures about vertex algebras which emerge in gauge theory constructions associated to the geometric Langlands program. In particular, we present the conjectural kernel vertex algebra for the $S T^2 S$ duality…

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…

We study horizontal differentiation when the set of feasible products is a structured subset of the Lancasterian characteristics space. Modeling this set as a compact Riemannian manifold, we show that intrinsic geometry governs…

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and $\varepsilon$-support vector regression. By assuming the ground-truth…

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or…

The Bounded Negativity Conjecture predicts that for every complex projective surface $X$ there exists a number $b(X)$ such that $C^2\geq -b(X)$ holds for all reduced curves $C\subset X$. For birational surfaces $f:Y\to X$ there have been…

Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random…

It has been shown that the maximum stable set problem in some infinite graphs, and the kissing number problem in particular, reduces to a minimization problem over the cone of copositive kernels. Optimizing over this infinite dimensional…

In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary…

Controlling the spectral norm of the Jacobian matrix, which is related to the convolution operation, has been shown to improve generalization, training stability and robustness in CNNs. Existing methods for computing the norm either tend to…

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…