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

• URL: http://arxiv.org/abs/2011.04468v2
• Date: Mon, 21 Dec 2020 17:54:22 GMT
• Title: Sparse Approximate Solutions to Max-Plus Equations with Application to Multivariate Convex Regression
• Authors: Nikos Tsilivis, Anastasios Tsiamis, Petros Maragos
• Abstract summary: We show how one can obtain such solutions efficiently and in minimum time for any $ell_p$ approximation error. We propose a novel method for piecewise fitting of convex functions, with optimality guarantees and an approximately sparse affine regions.
• Score: 34.99564569478268
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\ell_p$ 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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