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Autores principales: Hodgkinson, Liam, van der Heide, Chris, Salomone, Robert, Roosta, Fred, Mahoney, Michael W.
Formato: Preprint
Publicado: 2023
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Acceso en línea:https://arxiv.org/abs/2307.07785
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author Hodgkinson, Liam
van der Heide, Chris
Salomone, Robert
Roosta, Fred
Mahoney, Michael W.
author_facet Hodgkinson, Liam
van der Heide, Chris
Salomone, Robert
Roosta, Fred
Mahoney, Michael W.
contents The problem of model selection is considered for the setting of interpolating estimators, where the number of model parameters exceeds the size of the dataset. Classical information criteria typically consider the large-data limit, penalizing model size. However, these criteria are not appropriate in modern settings where overparameterized models tend to perform well. For any overparameterized model, we show that there exists a dual underparameterized model that possesses the same marginal likelihood, thus establishing a form of Bayesian duality. This enables more classical methods to be used in the overparameterized setting, revealing the Interpolating Information Criterion, a measure of model quality that naturally incorporates the choice of prior into the model selection. Our new information criterion accounts for prior misspecification, geometric and spectral properties of the model, and is numerically consistent with known empirical and theoretical behavior in this regime.
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institution arXiv
publishDate 2023
record_format arxiv
spellingShingle The Interpolating Information Criterion for Overparameterized Models
Hodgkinson, Liam
van der Heide, Chris
Salomone, Robert
Roosta, Fred
Mahoney, Michael W.
Machine Learning
The problem of model selection is considered for the setting of interpolating estimators, where the number of model parameters exceeds the size of the dataset. Classical information criteria typically consider the large-data limit, penalizing model size. However, these criteria are not appropriate in modern settings where overparameterized models tend to perform well. For any overparameterized model, we show that there exists a dual underparameterized model that possesses the same marginal likelihood, thus establishing a form of Bayesian duality. This enables more classical methods to be used in the overparameterized setting, revealing the Interpolating Information Criterion, a measure of model quality that naturally incorporates the choice of prior into the model selection. Our new information criterion accounts for prior misspecification, geometric and spectral properties of the model, and is numerically consistent with known empirical and theoretical behavior in this regime.
title The Interpolating Information Criterion for Overparameterized Models
topic Machine Learning
url https://arxiv.org/abs/2307.07785