Related papers: The reproducing kernel Hilbert spaces underlying l…
We consider Markov Decision Problems defined over continuous state and action spaces, where an autonomous agent seeks to learn a map from its states to actions so as to maximize its long-term discounted accumulation of rewards. We address…
Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…
This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely…
We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case setting. The weights in the norm of the function space depend…
Kernel Adaptive Filtering (KAF) are mathematically principled methods which search for a function in a Reproducing Kernel Hilbert Space. While they work well for tasks such as time series prediction and system identification they are…
This manuscript presents an algorithm for obtaining an approximation of a nonlinear high order control affine dynamical system. Controlled trajectories of the system are leveraged as the central unit of information via embedding them in…
The dynamic programming approach is one of the most powerful ones in optimal control. However, when dealing with optimal control problems of stochastic Volterra integral equations (SVIEs) with completely monotone kernels, deep mathematical…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
This paper studies the probabilistic function approximation problem over reproducing kernel Hilbert spaces. We show the existence and uniqueness of the optimizer under mild assumptions. Furthermore, we generalize the celebrated representer…
The theory of positive kernels and associated reproducing kernel Hilbert spaces, especially in the setting of holomorphic functions, has been an important tool for the last several decades in a number of areas of complex analysis and…
We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on…
We consider policy evaluation in infinite-horizon discounted Markov decision problems (MDPs) with infinite spaces. We reformulate this task a compositional stochastic program with a function-valued decision variable that belongs to a…
We review definitions and properties of reproducing kernel Hilbert spaces attached to Gaussian variables and processes, with a view to applications in nonparametric Bayesian statistics using Gaussian priors. The rate of contraction of…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
In this work, we investigate Gaussian Processes indexed by multidimensional distributions. While directly constructing radial positive definite kernels based on the Wasserstein distance has been proven to be possible in the unidimensional…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish that testing for the \emph{equality} of two non-atomic…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
We develop a comprehensive framework for spatio-temporal prediction of time-varying vector fields using operator-valued reproducing kernel Hilbert spaces (OV RKHS). By integrating Sobolev regularity with Koopman operator theory, we…
The work of Kalman and Bucy has established a duality between filtering and optimal estimation in the context of time-continuous linear systems. This duality has recently been extended to time-continuous nonlinear systems in terms of an…