Related papers: Ensemble forecasts in reproducing kernel Hilbert s…
This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…
Learning from examples is one of the key problems in science and engineering. It deals with function reconstruction from a finite set of direct and noisy samples. Regularization in reproducing kernel Hilbert spaces (RKHSs) is widely used to…
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…
Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance…
We introduce a functional gradient descent trajectory optimization algorithm for robot motion planning in Reproducing Kernel Hilbert Spaces (RKHSs). Functional gradient algorithms are a popular choice for motion planning in complex…
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…
Every invertible, measure-preserving dynamical system induces a Koopman operator, which is a linear, unitary evolution operator acting on the $L^2$ space of observables associated with the invariant measure. Koopman eigenfunctions represent…
We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…
Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…
For three applications of central interest in finance, we demonstrate the relevance of numerical algorithms based on reproducing kernel Hilbert space (RKHS) techniques. Three use cases are investigated. First, we show that extrapolating…
We study the estimation and prediction of functional autoregressive~(FAR) processes, a statistical tool for modeling functional time series data. Due to the infinite-dimensional nature of FAR processes, the existing literature addresses its…
In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…
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…
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with…
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…
Probabilistic predictions are probability distributions over the set of possible outcomes. Such predictions quantify the uncertainty in the outcome, making them essential for effective decision making. By combining multiple predictions, the…
Spatial temporal reconstruction of dynamical system is indeed a crucial problem with diverse applications ranging from climate modeling to numerous chaotic and physical processes. These reconstructions are based on the harmonious…
Development of metrics for structural data-generating mechanisms is fundamental in machine learning and the related fields. In this paper, we give a general framework to construct metrics on random nonlinear dynamical systems, defined with…
Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system…