How to induce regularization in linear models: A guide to reparametrizing gradient flow

Fuente: arXiv
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Main Authors: Chou, Hung-Hsu, Maly, Johannes, Stöger, Dominik
Format: Preprint
Published: 2023
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author Chou, Hung-Hsu
Maly, Johannes
Stöger, Dominik
author_facet Chou, Hung-Hsu
Maly, Johannes
Stöger, Dominik
contents In this work, we analyze the relation between reparametrizations of gradient flow and the induced implicit bias in linear models, which encompass various basic regression tasks. In particular, we aim at understanding the influence of the model parameters - reparametrization, loss, and link function - on the convergence behavior of gradient flow. Our results provide conditions under which the implicit bias can be well-described and convergence of the flow is guaranteed. We furthermore show how to use these insights for designing reparametrization functions that lead to specific implicit biases which are closely connected to $\ell_p$- or trigonometric regularizers.
format Preprint
id arxiv_https___arxiv_org_abs_2308_04921
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle How to induce regularization in linear models: A guide to reparametrizing gradient flow
Chou, Hung-Hsu
Maly, Johannes
Stöger, Dominik
Optimization and Control
Numerical Analysis
In this work, we analyze the relation between reparametrizations of gradient flow and the induced implicit bias in linear models, which encompass various basic regression tasks. In particular, we aim at understanding the influence of the model parameters - reparametrization, loss, and link function - on the convergence behavior of gradient flow. Our results provide conditions under which the implicit bias can be well-described and convergence of the flow is guaranteed. We furthermore show how to use these insights for designing reparametrization functions that lead to specific implicit biases which are closely connected to $\ell_p$- or trigonometric regularizers.
title How to induce regularization in linear models: A guide to reparametrizing gradient flow
topic Optimization and Control
Numerical Analysis
url https://arxiv.org/abs/2308.04921