Alternating Minimization for Regression with Tropical Rational Functions

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Bibliographic Details
Main Authors:	Dunbar, Alex, Ruthotto, Lars
Format:	Preprint
Published:	2023
Subjects:	Optimization and Control Machine Learning 90C24, 14T90, 62J02
Online Access:	Acceder al recurso
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_version_	1866909264689233920
author	Dunbar, Alex Ruthotto, Lars
author_facet	Dunbar, Alex Ruthotto, Lars
contents	We propose an alternating minimization heuristic for regression over the space of tropical rational functions with fixed exponents. The method alternates between fitting the numerator and denominator terms via tropical polynomial regression, which is known to admit a closed form solution. We demonstrate the behavior of the alternating minimization method experimentally. Experiments demonstrate that the heuristic provides a reasonable approximation of the input data. Our work is motivated by applications to ReLU neural networks, a popular class of network architectures in the machine learning community which are closely related to tropical rational functions.
format	Preprint
id	arxiv_https___arxiv_org_abs_2305_20072
institution	arXiv
publishDate	2023
record_format	arxiv
spellingShingle	Alternating Minimization for Regression with Tropical Rational Functions Dunbar, Alex Ruthotto, Lars Optimization and Control Machine Learning 90C24, 14T90, 62J02 We propose an alternating minimization heuristic for regression over the space of tropical rational functions with fixed exponents. The method alternates between fitting the numerator and denominator terms via tropical polynomial regression, which is known to admit a closed form solution. We demonstrate the behavior of the alternating minimization method experimentally. Experiments demonstrate that the heuristic provides a reasonable approximation of the input data. Our work is motivated by applications to ReLU neural networks, a popular class of network architectures in the machine learning community which are closely related to tropical rational functions.
title	Alternating Minimization for Regression with Tropical Rational Functions
topic	Optimization and Control Machine Learning 90C24, 14T90, 62J02
url	https://arxiv.org/abs/2305.20072

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