Related papers: On using Reproducible Hilbert Spaces for the analy…
In this note, we describe the backward shift invariant subspaces for a large class of reproducing kernel Hilbert spaces. This class includes in particular de Branges-Rovnyak spaces (the non-extreme case) and the range space of co-analytic…
In statistical learning theory, interpolation spaces of the form $[\mathrm{L}^2,H]_{\theta,r}$, where $H$ is a reproducing kernel Hilbert space, are in widespread use. So far, however, they are only well understood for fine index $r=2$. We…
In this paper we propose a novel variable selection method for two-view settings, or for vector-valued supervised learning problems. Our framework is able to handle extremely large scale selection tasks, where number of data samples could…
Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation…
This article is concerned with an approximate analytical solution for the time fractional Kudryashov Sinelshchikov equation by using the reproducing kernel Hilbert space method. The main tools of this method are reproducing kernel theory,…
We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a…
We present a method to construct a chain of reproducing kernel Hilbert spaces controlled by a first-order system of differential equations from a given unimodular function satisfying several conditions. One of the applications of that…
In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…
This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and…
The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and…
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…
Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…
We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors.…
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…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with large datasets or high-dimensional data. It is well recognized…
The Ginibre point process is one of the main examples of deter- minantal point processes on the complex plane. It forms a recurring model in stochastic matrix theory as well as in pratical applications. However, this model has mostly been…
The field of quantum machine learning is a promising way to lead to a revolution in intelligent data processing methods. In this way, a hybrid learning method based on classic kernel methods is proposed. This proposal also requires the…
Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…