Using Mutual Information to Measure the Predictive Power of Principal Components

Andreas Artemiou ()
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Andreas Artemiou: Cardiff University, School of Mathematics

A chapter in Festschrift in Honor of R. Dennis Cook, 2021, pp 1-16 from Springer

Abstract: Abstract In this work we propose the use of mutual information to measure the predictive potential of principal components in regression. We show that this criterion produces the same results as previous works which used the correlation to measure the strength of the relationship between the response variable with the extracted principal components in Gaussian settings. We demonstrate this in the linear regression model and also beyond that, in the conditional mean model and the conditional independence model, two common choices in sufficient dimension reduction, achieving a connection between unsupervised and supervised dimension reduction methods.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-69009-0_1

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DOI: 10.1007/978-3-030-69009-0_1

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