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We propose the nuclear norm penalty as an alternative to the ridge penaltyfor regularized multinomial regression. This convex relaxation of reduced-rankmultinomial regression has the advantage of leveraging underlying structureamong the response categories to make better predictions. We apply our method,nuclear penalized multinomial regression (NPMR), to Major League Baseballplay-by-play data to predict outcome probabilities based on batter-pitchermatchups. The interpretation of the results meshes well with subject-areaexpertise and also suggests a novel understanding of what differentiatesplayers.

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