Ben Van Roy

Stanford University

**Abstract**

When used to guide decisions, linear regression analysis typically involves estimation of regression coefficients via ordinary least squares and their subsequent use in an optimization problem. When features are not chosen perfectly, it can be beneficial to account for the decision objective when computing regression coefficients. Empirical optimization does so but sacrifices performance when features are well-chosen or training data are insufficient. We propose directed regression, an efficient algorithm that combines merits of ordinary least squares and empirical optimization. We demonstrate through computational studies that directed regression generates performance gains over either alternative. We also develop a theory that motivates the algorithm.

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