Sparse Approximate Solutions to Max-Plus Equations with Application to Multivariate Convex Regression

2020/11/06 by Tsilivis, Nikos, Tsiamis, Anastasios, Maragos, Petros
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2011.04468

Abstract

In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial time for any ℓ_p approximation error. Based on these results, we propose a novel method for piecewise-linear fitting of convex multivariate functions, with optimality guarantees for the model parameters and an approximately minimum number of affine regions.

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