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Using Mutual Information to Measure the Predictive Power of Principal Components

In: Festschrift in Honor of R. Dennis Cook

Author

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  • Andreas Artemiou

    (Cardiff University, School of Mathematics)

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.

Suggested Citation

  • Andreas Artemiou, 2021. "Using Mutual Information to Measure the Predictive Power of Principal Components," Springer Books, in: Efstathia Bura & Bing Li (ed.), Festschrift in Honor of R. Dennis Cook, pages 1-16, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-69009-0_1
    DOI: 10.1007/978-3-030-69009-0_1
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