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Topological techniques in model selection

Shaoxiong Hu, Hugo Maruri-Aguilar and Zixiang Ma

Vol. 13 (2022), No. 1, 41–56
Abstract

Toward enhancing the performance of Lasso for squarefree hierarchical polynomial models, we propose a compound criterion that combines validation error with a measure of model complexity consisting of a sum of Betti numbers of the model, seen as a simplicial complex. The compound criterion helps model selection in polynomial regression models containing higher-order interactions. Simulation results and a real data example show that the compound criteria produces sparser models with lower prediction errors than other statistical methods.

Keywords
regression, Lasso, topology, Betti numbers, model selection
Mathematical Subject Classification
Primary: 55U15, 62J07
Milestones
Received: 31 August 2021
Revised: 21 October 2022
Accepted: 24 October 2022
Published: 4 May 2023
Authors
Shaoxiong Hu
Alibaba Group
Hangzhou, 311121
China
Hugo Maruri-Aguilar
School of Mathematical Sciences
Queen Mary University of London
London, E1 4NS
United Kingdom
Zixiang Ma
Huawei Technologies Co., Ltd
Nanjing, 210012
China