Related papers: Positive definiteness of real quadratic forms resu…

Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS). For non-Euclidean data spaces, positive-definite…

We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the…

We propose kernel-based approaches for the construction of a single-step and multi-step predictor of the velocity form of nonlinear (NL) systems, which describes the time-difference dynamics of the corresponding NL system and admits a…

We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the multivariate density of the finite dimensional distributions of which we aim to estimate. We assume that we observe the…

We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…

We supply a Fourier characterization for the real, continuous, isotropic and strictly positive definite kernels on a product of circles.

We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…

New approaches to the study of stability of solutions of Set Differential Equations (SDEs) based on convex geometry and the theory of mixed volumes were proposed. The stability of the forms of program solutions of linear SDEs with a stable…

The purpose of this article is to address the issues of dimensional consistency that arise in the process of replacing the ordinary time derivative operator by a fractional derivative operator in order to write a fractional differential…

We develop a method for the efficient verification of neural networks against convolutional perturbations such as blurring or sharpening. To define input perturbations we use well-known camera shake, box blur and sharpen kernels. We…

We prove that the two-step backward differentiation formula (BDF2) method is stable on arbitrary time grids; while the variable-step BDF3 scheme is stable if almost all adjacent step ratios are less than 2.553. These results relax the…

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…

In this paper we study the set of values of quadratic form at points of a cut and project set. We will establish conditions which ensure that the set of values is dense. Our methods involve homogeneous dynamics and we will prove a orbit…

Kolmogorov decomposition for a given completely positive definite kernel is a generalization of Paschke's GNS construction for the completely positive map. Using Kolmogorov decomposition, to every quantum dynamical semigroup (QDS) for…

We consider a model for linear transient price impact for multiple assets that takes cross-asset impact into account. Our main goal is to single out properties that need to be imposed on the decay kernel so that the model admits…

In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…

We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…

This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the…

Due to its convolution nature, the Stieltjes integral equation can be diagonalized by Mellin transform. Several explicit resolvent kernels were obtained over the years, all of convolution type. The conditions on the given function under…

A fast convergence in a fixed-time of solutions of nonlinear dynamical systems, for which special requirements are satisfied on the derivative of a quadratic function calculated along the solutions of the system, is proposed. The conditions…