Iteratively reweighted kernel machines efficiently learn sparse functions

Fuente: arXiv
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Main Authors: Zhu, Libin, Davis, Damek, Drusvyatskiy, Dmitriy, Fazel, Maryam
Format: Preprint
Published: 2025
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author Zhu, Libin
Davis, Damek
Drusvyatskiy, Dmitriy
Fazel, Maryam
author_facet Zhu, Libin
Davis, Damek
Drusvyatskiy, Dmitriy
Fazel, Maryam
contents The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are not unique to neural networks, and can be elicited from classical kernel methods. Namely, we show that the derivative of the kernel predictor can detect the influential coordinates with low sample complexity. Moreover, by iteratively using the derivatives to reweight the data and retrain kernel machines, one is able to efficiently learn hierarchical polynomials with finite leap complexity. Numerical experiments illustrate the developed theory.
format Preprint
id arxiv_https___arxiv_org_abs_2505_08277
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Iteratively reweighted kernel machines efficiently learn sparse functions
Zhu, Libin
Davis, Damek
Drusvyatskiy, Dmitriy
Fazel, Maryam
Machine Learning
Optimization and Control
Statistics Theory
The impressive practical performance of neural networks is often attributed to their ability to learn low-dimensional data representations and hierarchical structure directly from data. In this work, we argue that these two phenomena are not unique to neural networks, and can be elicited from classical kernel methods. Namely, we show that the derivative of the kernel predictor can detect the influential coordinates with low sample complexity. Moreover, by iteratively using the derivatives to reweight the data and retrain kernel machines, one is able to efficiently learn hierarchical polynomials with finite leap complexity. Numerical experiments illustrate the developed theory.
title Iteratively reweighted kernel machines efficiently learn sparse functions
topic Machine Learning
Optimization and Control
Statistics Theory
url https://arxiv.org/abs/2505.08277