Related papers: Mathematical foundations of stable RKHSs

For a Reproducing Kernel Hilbert Space on a complex domain we give a formula that describes the Hermitean metrics on the domain which are pull-backs of some metric on the (dual of) the RKHS via the evaluation map. Then we consider the…

Current methods for stochastic hyperparameter learning in Gaussian Processes (GPs) rely on approximations, such as computing biased stochastic gradients or using inducing points in stochastic variational inference. However, when using such…

This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…

This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new "kernel" function that represents an integration functional over a reproducing kernel Hilbert space (RKHS)…

We present accurate upper and lower bounds for the covering numbers, with explicit constants, of the unit ball for two general classes of Reproducing Kernel Hilbert Space (RKHS) on the unit sphere of $\mathbb{R}^{d+1}$. In both classes, the…

We study classes of reproducing kernels $K$ on general domains; these are kernels which arise commonly in machine learning models; models based on certain families of reproducing kernel Hilbert spaces. They are the positive definite kernels…

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

We present estimates for the covering numbers of the unit ball of Reproducing Kernel Hilbert Spaces (RKHSs) of functions on $M^d$ a d-dimensional compact two-point homogeneous space. The RKHS is generated by a continuous zonal/isotropic…

We study the problem of estimating linear response statistics under external perturbations using time series of unperturbed dynamics. Based on the fluctuation-dissipation theory, this problem is reformulated as an unsupervised learning task…

Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…

We investigate statistical properties for a broad class of modern kernel-based regression (KBR) methods. These kernel methods were developed during the last decade and are inspired by convex risk minimization in infinite-dimensional Hilbert…

Smoothing Spline ANOVA (SS-ANOVA) models in reproducing kernel Hilbert spaces (RKHS) provide a very general framework for data analysis, modeling and learning in a variety of fields. Discrete, noisy scattered, direct and indirect…

It has been hypothesized that quantum computers may lend themselves well to applications in machine learning. In the present work, we analyze function classes defined via quantum kernels. Quantum computers offer the possibility to…

Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…

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…

The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We…

This paper studies the relationship between the positive limit sets of continuous semiflows and the newly introduced definition of persistently excited (PE) sets and associated subspaces of reproducing kernel Hilbert (RKH) spaces. It is…

This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models} for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees…

This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case.…

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…