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.

中文翻译：

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核惩罚多项式回归，用于预测棒球中的击球结果

我们建议将核范数惩罚作为正则化多项式回归的脊惩罚的替代方案。这种降阶多项式回归的凸松弛具有利用响应类别之间的基础结构来做出更好预测的优势。我们将我们的方法核惩罚多项式回归 (NPMR) 应用于美国职业棒球大联盟的逐场比赛数据，以根据击球手-投手对决来预测结果概率。结果的解释与学科领域的专业知识非常吻合，并且还提出了对不同玩家的新颖理解。