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A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning prob- lems with nonscalar outputs like…

Regularized kernel methods such as support vector machines (SVM) and support vector regression (SVR) constitute a broad and flexible class of methods which are theoretically well investigated and commonly used in nonparametric…

In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…

In modern robotics, effectively computing optimal control policies under dynamically varying environments poses substantial challenges to the off-the-shelf parametric policy gradient methods, such as the Deep Deterministic Policy Gradient…

Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…

Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…

Reproducing kernel Hilbert spaces (RKHSs) are special Hilbert spaces in one-to-one correspondence with positive definite maps called kernels. They are widely employed in machine learning to reconstruct unknown functions from sparse and…

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…

The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…

Motivated by the inherent heterogeneity observed in many functional or imaging datasets, this paper focuses on subgroup learning in functional or image responses. While change-plane analysis has demonstrated empirical success in practice,…

In this paper, we consider the reproducing property in Reproducing Kernel Hilbert Spaces (RKHS). We establish a reproducing property for the closure of the class of combinations of composition operators under minimal conditions. This allows…

Many recent theoretical works on \emph{meta-learning} aim to achieve guarantees in leveraging similar representational structures from related tasks towards simplifying a target task. The main aim of theoretical guarantees on the subject is…

The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. However, existing data-driven approaches to learning the Koopman operator rely on batch data. In this work, we present…

Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to…

We address data-driven learning of the infinitesimal generator of stochastic diffusion processes, essential for understanding numerical simulations of natural and physical systems. The unbounded nature of the generator poses significant…

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…

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…

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…