ROCK: A variational formulation for occupation kernel methods in Reproducing Kernel Hilbert Spaces

2025-03-18 · Victor Rielly, Kamel Lahouel, Chau Nguyen, Bruno Jedynak

We present a Representer Theorem result for a large class of weak formulation problems. We provide examples of applications of our formulation both in traditional machine learning and numerical methods as well as in new and emerging techniques. Finally we apply our formulation to generalize the multivariate occupation kernel (MOCK) method for learning dynamical systems from data proposing the more general Riesz Occupation Kernel (ROCK) method. Our generalized methods are both more computationally efficient and performant on most of the benchmarks we test against.

📄 PDF Abstract BibTeX arXiv:2503.13791

Code (0)

등록된 구현이 없습니다.

Generalized support vector regression: duality and tensor-kernel representation

2016-03-18 · Saverio Salzo, Johan A. K. Suykens

In this paper we study the variational problem associated to support vector regression in Banach function spaces. Using the Fenchel-Rockafellar duality theory, we give explicit formulation of the dual problem as well as …

regression

Occupation Kernel Hilbert Spaces for Fractional Order Liouville Operators and Dynamic Mode Decomposition

2021-02-26 · Joel A. Rosenfeld, Benjamin Russo, Xiuying Li

This manuscript gives a theoretical framework for a new Hilbert space of functions, the so called occupation kernel Hilbert space (OKHS), that operate on collections of signals rather than real or complex numbers. To sup…

MOCK: an Algorithm for Learning Nonparametric Differential Equations via Multivariate Occupation Kernel Functions

2023-06-16 · Victor Rielly, Kamel Lahouel, Ethan Lew, Nicholas Fisher 외

Learning a nonparametric system of ordinary differential equations from trajectories in a $d$-dimensional state space requires learning $d$ functions of $d$ variables. Explicit formulations often scale quadratically in $…

Trajectory Prediction

Fault Detection via Occupation Kernel Principal Component Analysis

2023-03-20 · Zachary Morrison, Benjamin P. Russo, Yingzhao Lian, Rushikesh Kamalapurkar

The reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamical system. While traditional model-based methods have been widely used for fault detection, data-d…

Fault Detection

CUROCKET: Optimizing ROCKET for GPU

2026-01-23 · Ole Stüven, Keno Moenck, Thorsten Schüppstuhl arxiv

ROCKET (RandOm Convolutional KErnel Transform) is a feature extraction algorithm created for Time Series Classification (TSC), published in 2019. It applies convolution with randomly generated kernels on a time series, p…

Time Series Classification Computational Efficiency