Related papers: Operator-Based Machine Intelligence: A Hilbert Spa…

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…

Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring…

We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number…

This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…

Since its introduction, the Discrete Variable Representation (DVR) basis set has become an invaluable representation of state vectors and Hermitian operators in non-relativistic quantum dynamics and spectroscopy calculations. On the other…

We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…

This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…

The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…

Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman…

This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents…

In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…

We propose a novel approach for pixel classification in hyperspectral images, leveraging on both the spatial and spectral information in the data. The introduced method relies on a recently proposed framework for learning on distributions…

This paper designs novel nonparametric Bellman mappings in reproducing kernel Hilbert spaces (RKHSs) for reinforcement learning (RL). The proposed mappings benefit from the rich approximating properties of RKHSs, adopt no assumptions on the…

Kernel methods have been among the most popular techniques in machine learning, where learning tasks are solved using the property of reproducing kernel Hilbert space (RKHS). In this paper, we propose a novel data analysis framework with…

We present a novel variation of online kernel machines in which we exploit a consensus based optimization mechanism to guide the evolution of decision functions drawn from a reproducing kernel Hilbert space, which efficiently models the…

Many machine learning algorithms can be interpreted as procedures for estimating functions defined on the data distribution. In this paper we present a conceptual framework that formulates a wide range of learning problems as variational…

Reproducing kernel Hilbert spaces (RKHSs) are key spaces for machine learning that are becoming popular also for linear system identification. In particular, the so-called stable RKHSs can be used to model absolutely summable impulse…

Koopman operator provides a general linear description of nonlinear systems, whose estimation from data (via extended dynamic mode decomposition) has been extensively studied. However, the elusiveness between the Koopman spectrum and the…

We develop a Hilbert space framework for a number of general multi-scale problems from dynamics. The aim is to identify a spectral theory for a class of systems based on iterations of a non-invertible endomorphism. We are motivated by the…

Learning in the reproducing kernel Hilbert space (RKHS) such as the support vector machine has been recognized as a promising technique. It continues to be highly effective and competitive in numerous prediction tasks, particularly in…