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Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of…

Optimization and Control · Mathematics 2021-03-25 Adam J. Thorpe , Meeko M. K. Oishi

We implement an algorithm which is aimed to reduce the dimensions of the Hilbert space of quantum many-body systems by means of a renormalization procedure. We test the role and importance of different representations on the reduction…

Quantum Physics · Physics 2015-05-27 Tarek Khalil , Jean Richert

Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…

Optimization and Control · Mathematics 2023-08-23 Pierre-Cyril Aubin-Frankowski , Alain Bensoussan

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…

Machine Learning · Computer Science 2015-04-14 Carlo Ciliberto , Lorenzo Rosasco , Silvia Villa

We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…

Numerical Analysis · Mathematics 2022-10-12 Satoshi Hayakawa , Harald Oberhauser , Terry Lyons

In this paper, we propose a random gradient-free method for optimization in infinite dimensional Hilbert spaces, applicable to functional optimization in diverse settings. Though such problems are often solved through finite-dimensional…

Optimization and Control · Mathematics 2025-12-25 Caio Lins Peixoto , Daniel Csillag , Bernardo F. P. da Costa , Yuri F. Saporito

Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm…

Statistics Theory · Mathematics 2020-01-03 Rui Tuo , Yan Wang , C. F. Jeff Wu

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…

Functional Analysis · Mathematics 2017-08-22 Palle Jorgensen , Feng Tian

Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high…

Machine Learning · Statistics 2018-04-17 Bharath Bhushan Damodaran

Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces. In the context of interpolation, the…

Numerical Analysis · Mathematics 2025-01-09 Gabriele Santin , Tizian Wenzel , Bernard Haasdonk

We study the hermitian one matrix model with semi-classical potential. This is a general unitary invariant random matrix ensemble in which the potential has a derivative that is a rational function and the measure is supported on some…

Mathematical Physics · Physics 2015-04-20 Max R. Atkin

Large kernel convolutions offer a scalable alternative to vision transformers for high-resolution 3D volumetric analysis, yet naively increasing kernel size often leads to optimization instability. Motivated by the spatial bias inherent in…

Computer Vision and Pattern Recognition · Computer Science 2026-02-02 Ho Hin Lee , Quan Liu , Shunxing Bao , Yuankai Huo , Bennett A. Landman

This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and…

Machine Learning · Statistics 2025-05-21 Andrea Della Vecchia , Arnaud Mavakala Watusadisi , Ernesto De Vito , Lorenzo Rosasco

This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…

Optimization and Control · Mathematics 2018-10-26 Sören Bartels , Gerd Wachsmuth

This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…

Machine Learning · Computer Science 2015-09-16 Corinna Cortes , Prasoon Goyal , Vitaly Kuznetsov , Mehryar Mohri

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…

Statistics Theory · Mathematics 2010-09-30 Gilles Blanchard , Nicole Kraemer

We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…

Optimization and Control · Mathematics 2020-11-20 Adam J. Thorpe , Kendric R. Ortiz , Meeko M. K. Oishi

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…

Classical Analysis and ODEs · Mathematics 2007-05-23 Palle E. T. Jorgensen

Motivation: A branching processes model yields an unevenly stochastically distributed dataset that consists of sparse and dense regions. This work addresses the problem of precisely evaluating parameters for such a model. Applying a…

Machine Learning · Statistics 2023-05-09 Iurii S. Nagornov

This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…

Computational Engineering, Finance, and Science · Computer Science 2024-11-26 Julien Bect , Niklas Georg , Ulrich Römer , Sebastian Schöps