使用广义链接矩阵分解预测特定对决中的击球率
Predicting Batting Averages in Specific Matchups Using Generalized Linked Matrix Factorization
AI总结：
本文提出一种基于交替广义线性模型的降维方法，用于预测特定击球手对阵特定投手时的击球率，该方法能整合多个数据源，略优于现有方法且易于扩展。
摘要：
预测特定击球手对阵特定投手时的击球率是棒球中的一个具有挑战性的问题。以往用于估计这些对决中击球率的方法采用了回归模型，这些模型可以纳入投手和击球手各自的击球率。然而，由于回归中高维数据的挑战，这些方法在纳入许多额外参数的灵活性上受到限制。降维方法可以通过在预测变量中发现一组较低秩的模式来将许多预测变量纳入模型，从而提供额外的灵活性。本文表明，降维方法可用于预测击球率。为了纳入二项分布数据（击球率）以及关于每位击球手和投手的额外数据，本文提出了一种新颖的降维方法，该方法使用交替广义线性模型来估计与击球率相关的三个数据源之间的共享模式。虽然这种新方法在基于模拟和交叉验证研究的击球率插补上略优于现有方法，但其最大的优势在于可以轻松纳入其他数据源。随着数据收集技术的不断改进，未来将有更多变量可用，该方法将随着更多信息性数据而变得更加准确。
英文摘要：
Predicting batting averages for specific batters against specific pitchers is a challenging problem in baseball. Previous methods for estimating batting averages in these matchups have used regression models that can incorporate the pitcher's and batter's individual batting averages. However, these methods are limited in their flexibility to include many additional parameters because of the challenges of high-dimensional data in regression. Dimension reduction methods can be used to incorporate many predictors into the model by finding a lower rank set of patterns among them, providing added flexibility. This paper illustrates that dimension reduction methods can be useful for predicting batting averages. To incorporate binomial data (batting averages) as well as additional data about each batter and pitcher, this paper proposes a novel dimension reduction method that uses alternating generalized linear models to estimate shared patterns across three data sources related to batting averages. While the novel method slightly outperforms existing methods for imputing batting averages based on simulations and a cross-validation study, the biggest advantage is that it can easily incorporate other sources of data. As data-collection technology continues to improve, more variables will be available, and this method will be more accurate with more informative data in the future.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
