Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball

We propose the nuclear norm penalty as an alternative to the ridge penalty for regularized multinomial regression. This convex relaxation of reduced-rank multinomial regression has the advantage of leveraging underlying structure among the response categories to make better predictions. We apply our...

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Bibliographic Details
Published inStatistical modelling Vol. 18; no. 5-6; pp. 388 - 410
Main Authors Powers, Scott, Hastie, Trevor, Tibshirani, Robert
Format Journal Article
LanguageEnglish
Published New Delhi, India SAGE Publications 01.12.2018
Subjects
Reduced-rank regression
baseball
nuclear norm
proximal gradient descent
multinomial regression
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Summary:We propose the nuclear norm penalty as an alternative to the ridge penalty for regularized multinomial regression. This convex relaxation of reduced-rank multinomial regression has the advantage of leveraging underlying structure among the response categories to make better predictions. We apply our method, nuclear penalized multinomial regression (NPMR), to Major League Baseball play-by-play data to predict outcome probabilities based on batter–pitcher matchups. The interpretation of the results meshes well with subject-area expertise and also suggests a novel understanding of what differentiates players.
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ISSN:1471-082X
1477-0342
DOI:10.1177/1471082X18777669