Related papers: ROCK: A variational formulation for occupation ker…
Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity…
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…
This paper presents reproducing kernel Hilbert spaces method to obtain the numerical solution for partial differential equation constrained optimization problem.
Given the reproducing kernel $k$ of the Hilbert space $\mathcal{H}_k$ we study spaces $\mathcal{H}_k(b)$ whose reproducing kernel has the form $k(1-bb^*)$, where $b$ is a row-contraction on $\mathcal{H}_k$. In terms of reproducing kernels…
On a compact Lie group $G$, we consider the reproducing kernel Hilbert space $\mathcal{H}_K$ associated with the integral kernel $K$ of a left-invariant, positive, symmetric, trace class integral operator on $L^2(G)$. We present lower and…
In this paper we consider the reproducing kernel thesis for boundedness and compactness for operators on $\ell^2$--valued Bergman-type spaces. This paper generalizes many well--known results about classical function spaces to their…
We present a reinforcement learning algorithm for learning sparse non-parametric controllers in a Reproducing Kernel Hilbert Space. We improve the sample complexity of this approach by imposing a structure of the state-action function…
Motivated by the need of processing functional-valued data, or more general, operatorvalued data, we introduce the notion of the operator reproducing kernel Hilbert space (ORKHS). This space admits a unique operator reproducing kernel which…
We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear dynamical systems. These eigenfunctions satisfy a…
In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…
Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the…
A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling…
A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times…
In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit…
Imitation Learning (IL) is an important paradigm within the broader reinforcement learning (RL) methodology. Unlike most of RL, it does not assume availability of reward-feedback. Reward inference and shaping are known to be difficult and…
We develop a variational framework to understand the properties of the functions learned by neural networks fit to data. We propose and study a family of continuous-domain linear inverse problems with total variation-like regularization in…
We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in ${\Bbb C}^d$ for which an analogue of the Nevanlinna-Pick theorem holds, in other words when the existence of a (possibly matrix-valued) function in…