English
Related papers

Related papers: Learning nonparametric differential equations with…

200 papers

The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under…

Machine Learning · Statistics 2025-02-06 Boya Hou , Sina Sanjari , Nathan Dahlin , Alec Koppel , Subhonmesh Bose

We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its…

Econometrics · Economics 2026-01-13 Guo Yan

This paper addresses nonparametric estimation of nonlinear multivariate Hawkes processes, where the interaction functions are assumed to lie in a reproducing kernel Hilbert space (RKHS). Motivated by applications in neuroscience, the model…

Machine Learning · Statistics 2025-03-26 Anna Bonnet , Maxime Sangnier

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

Machine Learning · Computer Science 2024-06-04 Fan He , Mingzhen He , Lei Shi , Xiaolin Huang , Johan A. K. Suykens

We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) problem using operator-valued kernels. We show that some of the existing…

Machine Learning · Statistics 2015-07-16 Hachem Kadri , Mohammad Ghavamzadeh , Philippe Preux

In this paper, we introduce a new distribution regression model for probability distributions. This model is based on a Reproducing Kernel Hilbert Space (RKHS) regression framework, where universal kernels are built using Wasserstein…

Statistics Theory · Mathematics 2019-10-07 Thi Thien Trang Bui , J-M Loubes , Laurent Risser , Patricia Balaresque

We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors.…

Machine Learning · Computer Science 2013-10-21 Marco Signoretto , Lieven De Lathauwer , Johan A. K. Suykens

We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function…

Statistics Theory · Mathematics 2016-03-30 Aymeric Dieuleveut , Francis Bach

In this work, we address optimization problems where the objective function is a nonlinear function of an expected value, i.e., compositional stochastic {strongly convex programs}. We consider the case where the decision variable is not…

Optimization and Control · Mathematics 2020-11-30 Amrit Singh Bedi , Alec Koppel , Ketan Rajawat , Panchajanya Sanyal

We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical…

Machine Learning · Statistics 2011-09-07 JooSeuk Kim , Clayton D. Scott

Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…

Machine Learning · Statistics 2022-06-20 Parnian Kassraie , Jonas Rothfuss , Andreas Krause

Temporal-difference learning is a popular algorithm for policy evaluation. In this paper, we study the convergence of the regularized non-parametric TD(0) algorithm, in both the independent and Markovian observation settings. In particular,…

Optimization and Control · Mathematics 2022-05-25 Eloïse Berthier , Ziad Kobeissi , Francis Bach

In this paper, an adaptive non-parametric method is proposed to estimate the scalar-valued nonlinear function that appears in uncertain systems governed by ordinary differential equations (ODEs). By employing an infinite-dimensional…

Optimization and Control · Mathematics 2021-03-15 Jia Guo , Sai Tej Paruchuri , Andrew J. Kurdila

Pairwise learning usually refers to a learning task which involves a loss function depending on pairs of examples, among which most notable ones include ranking, metric learning and AUC maximization. In this paper, we study an online…

Machine Learning · Statistics 2015-02-26 Yiming Ying , Ding-Xuan Zhou

Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS). For non-Euclidean data spaces, positive-definite…

Machine Learning · Computer Science 2024-07-31 Nathael Da Costa , Cyrus Mostajeran , Juan-Pablo Ortega , Salem Said

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…

Optimization and Control · Mathematics 2024-12-25 Mircea Lazar

An open challenge in supervised learning is \emph{conceptual drift}: a data point begins as classified according to one label, but over time the notion of that label changes. Beyond linear autoregressive models, transfer and meta learning…

Optimization and Control · Mathematics 2019-09-13 Amrit Singh Bedi , Alec Koppel , Ketan Rajawat , Brian M. Sadler

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

Machine Learning · Statistics 2025-08-25 Patrick J. F. Groenen , Michael Greenacre

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

Machine Learning · Computer Science 2020-02-23 Patrick Heas , Cedric Herzet , Benoit Combes

We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches…

Machine Learning · Statistics 2018-11-06 Junhong Lin , Volkan Cevher