Related papers: Volterra Kernel Identification using Regularized O…
We consider a distributed system with persistent memory of a type which is often encountered in viscoelasticity or in the study of diffusion processes with memory. The relaxation kernel, i.e. the kernel of the memory term, is scarcely known…
In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods…
A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using the reservoir…
We investigate memory dependent asymptotic growth in scalar Volterra equations with sublinear nonlinearity. To obtain precise results we utilise the powerful theory of regular variation extensively. By computing the growth rate in terms of…
We review current methods for building PSF-matching kernels for the purposes of image subtraction or coaddition. Such methods use a linear decomposition of the kernel on a series of basis functions. The correct choice of these basis…
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by…
We construct the basis of a stochastic calculus for so-called Volterra processes, i.e., processes which are defined as the stochastic integral of a time-dependent kernel with respect to a standard Brownian motion. For these processes which…
In this paper, indirect collocation approach based on compactly supported radial basis function is applied for solving Volterras population model. The method reduces the solution of this problem to the solution of a system of algebraic…
In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…
The purpose of this paper is to establish the convergence in distribution of the normalized error in the Euler approximation scheme for stochastic Volterra equations driven by a standard Brownian motion, with a kernel of the form…
Normalization techniques have become a basic component in modern convolutional neural networks (ConvNets). In particular, many recent works demonstrate that promoting the orthogonality of the weights helps train deep models and improve…
This article is devoted to the extension of the theory of rough paths in the context of Volterra equations with possibly singular kernels. We begin to describe a class of two parameter functions defined on the simplex called Volterra paths.…
Predicting the conditional evolution of Volterra processes with stochastic volatility is a crucial challenge in mathematical finance. While deep neural network models offer promise in approximating the conditional law of such processes,…
A simple nonlinear system modeling algorithm designed to work with limited \emph{a priori }knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an $l_{q}$-constrained least…
This study aims to discuss the existence and uniqueness of solution of fuzzy Volterra integral equation with piecewise continuous kernel. Such problems appears in many balance problems for hereditary dynamic systems, e.g. in electric load…
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the…
Despite several algorithmic advances in the training of convolutional neural networks (CNNs) over the years, their generalization capabilities are still subpar across several pertinent domains, particularly within open-set tasks often found…
The damage detection problem becomes a more difficult task when the intrinsically nonlinear behavior of the structures and the natural data variation are considered in the analysis because both phenomena can be confused with damage if…
We develop a kernel-based approach for estimating the spatially varying Sobolev regularity~$s$ of an unknown $d$-variate function~$f$ from scattered sampling data, which quantifies the degree of local differentiability supported by the…
We present a dimension-incremental algorithm for the nonlinear approximation of high-dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to detect a suitable truncation of the basis expansion of the…