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Topological techniques in model selection

Shaoxiong Hu, Hugo Maruri-Aguilar and Zixiang Ma

Vol. 13 (2022), No. 1, 41–56

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.

regression, Lasso, topology, Betti numbers, model selection
Mathematical Subject Classification
Primary: 55U15, 62J07
Received: 31 August 2021
Revised: 21 October 2022
Accepted: 24 October 2022
Published: 4 May 2023
Shaoxiong Hu
Alibaba Group
Hangzhou, 311121
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