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Abstract
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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.
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Keywords
regression, Lasso, topology, Betti numbers, model selection
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Mathematical Subject Classification
Primary: 55U15, 62J07
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Milestones
Received: 31 August 2021
Revised: 21 October 2022
Accepted: 24 October 2022
Published: 4 May 2023
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Publishers). |
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