Efficient Shapley Performance Attribution for Least-Squares Regression
Manuscript, October 2023.
We consider the performance of a least-squares regression model, as judged by
out-of-sample 
. Shapley values give a fair attribution of the performance
of a model to its input features, taking into account interdependencies between
features. Evaluating the Shapley values exactly requires solving a number of
regression problems that is exponential in the number of features, so a Monte
Carlo-type approximation is typically used. We focus on the special case of
least-squares regression models, where several tricks can be used to compute
and evaluate regression models efficiently. These tricks give a substantial
speed up, allowing many more Monte Carlo samples to be evaluated, achieving
better accuracy. We refer to our method as least-squares Shapley performance
attribution (LS-SPA), and describe our open-source implementation.