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Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…

Machine Learning · Computer Science 2017-04-26 Pantelis Bouboulis , Sergios Theodoridis

Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert…

Machine Learning · Computer Science 2024-11-01 Youyuan Long , Tolga Ok , Pedro Zattoni Scroccaro , Peyman Mohajerin Esfahani

Covariate shift occurs prevalently in practice, where the input distributions of the source and target data are substantially different. Despite its practical importance in various learning problems, most of the existing methods only focus…

Machine Learning · Statistics 2023-10-20 Xingdong Feng , Xin He , Caixing Wang , Chao Wang , Jingnan Zhang

Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on…

Functional Analysis · Mathematics 2021-04-06 Mattes Mollenhauer , Ingmar Schuster , Stefan Klus , Christof Schütte

We consider expected risk minimization problems when the range of the estimator is required to be nonnegative, motivated by the settings of maximum likelihood estimation (MLE) and trajectory optimization. To facilitate nonlinear…

Machine Learning · Statistics 2022-05-05 Abhishek Chakraborty , Ketan Rajawat , Alec Koppel

We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…

Statistics Theory · Mathematics 2009-09-29 Andrew R. Barron , Albert Cohen , Wolfgang Dahmen , Ronald A. DeVore

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…

Methodology · Statistics 2021-07-20 Rui Tuo , Shiyuan He , Arash Pourhabib , Yu Ding , Jianhua Z. Huang

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…

Methodology · Statistics 2013-05-07 Robert Hable

This paper presents reproducing kernel Hilbert spaces method to obtain the numerical solution for partial differential equation constrained optimization problem.

Optimization and Control · Mathematics 2016-11-09 Majid Darehmiraki

The probabilistic velocity obstacle (PVO) extends the concept of velocity obstacle (VO) to work in uncertain dynamic environments. In this paper, we show how a robust model predictive control (MPC) with PVO constraints under non-parametric…

Systems and Control · Electrical Eng. & Systems 2020-01-27 P. S. Naga Jyotish , Bharath Gopalakrishnan , A. V. S. Sai Bhargav Kumar , Arun Kumar Singh , K. Madhava Krishna , Dinesh Manocha

We present a novel diffusion scheme for online kernel-based learning over networks. So far, a major drawback of any online learning algorithm, operating in a reproducing kernel Hilbert space (RKHS), is the need for updating a growing number…

Machine Learning · Computer Science 2018-03-14 Pantelis Bouboulis , Symeon Chouvardas , Sergios Theodoridis

Variable selection is essential in high-dimensional data analysis. Although various variable selection methods have been developed, most rely on the linear model assumption. This article proposes a nonparametric variable selection method…

Machine Learning · Statistics 2021-09-30 Jongkyeong Kang , Seung Jun Shin

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…

Dynamical Systems · Mathematics 2022-09-09 Nathan Powell , Jia Guo , Sai Tej Parachuri , John Burns , Boone Estes , Andrew Kurdila

Learning in the reproducing kernel Hilbert space (RKHS) such as the support vector machine has been recognized as a promising technique. It continues to be highly effective and competitive in numerous prediction tasks, particularly in…

Machine Learning · Computer Science 2025-01-15 Gakuto Obi , Ayato Saito , Yuto Sasaki , Tsuyoshi Kato

The aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid. More specifically, it is demonstrated on one hand, how to…

Functional Analysis · Mathematics 2021-02-22 Monika Drewnik , Tomasz Miller , Zbigniew Pasternak-Winiarski

Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…

Functional Analysis · Mathematics 2017-07-27 Palle Jorgensen , Feng Tian

GenEO (`Generalised Eigenvalue problems on the Overlap') is a method from the family of spectral coarse spaces that can efficiently rely on local eigensolves in order to build a robust parallel domain decomposition preconditioner for…

Numerical Analysis · Mathematics 2024-06-11 Victorita Dolean , Mark Fry , Ivan G. Graham , Matthias Langer

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

Optimization and Control · Mathematics 2016-04-20 Martin Eigel , Kevin Sturm

A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert…

Machine Learning · Statistics 2014-06-16 Dino Sejdinovic , Heiko Strathmann , Maria Lomeli Garcia , Christophe Andrieu , Arthur Gretton

We propose a novel approach for pixel classification in hyperspectral images, leveraging on both the spatial and spectral information in the data. The introduced method relies on a recently proposed framework for learning on distributions…

Computer Vision and Pattern Recognition · Computer Science 2016-05-31 Gianni Franchi , Jesus Angulo , Dino Sejdinovic