Abstract Multivariate regression has many applications, ranging from time series prediction to genomics. Borrowing information across the outcomes can improve prediction error, even when outcomes are statistically independent. Many methods exist to implement this strategy, for example the multiresponse lasso, but choosing the optimal method for a given dataset is difficult. These issues are addressed by establishing a connection between multivariate linear regression and compound decision problems. A nonparametric empirical Bayes procedure that can learn the optimal regression method from the data itself is proposed. Furthermore, the proposed procedure is free of tuning parameters and performs well in simulations and in a multiple stock price prediction problem.

中文翻译：

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大规模多元回归的非参数经验贝叶斯方法

摘要 多元回归有很多应用，从时间序列预测到基因组学。跨结果借用信息可以改善预测误差，即使结果在统计上是独立的。有许多方法可以实现此策略，例如多响应套索，但很难为给定的数据集选择最佳方法。通过在多元线性回归和复合决策问题之间建立联系来解决这些问题。提出了一种可以从数据本身学习最优回归方法的非参数经验贝叶斯过程。此外，所提出的程序无需调整参数，并且在模拟和多股票价格预测问题中表现良好。