Efficient Shapley Performance Attribution for Least-Squares Regression

We consider the performance of a least-squares regression model, as judged byout-of-sample $R^2$. Shapley values give a fair attribution of the performanceof a model to its input features, taking into account interdependencies betweenfeatures. Evaluating the Shapley values exactly requires solving a number ofregression problems that is exponential in the number of features, so a MonteCarlo-type approximation is typically used. We focus on the special case ofleast-squares regression models, where several tricks can be used to computeand evaluate regression models efficiently. These tricks give a substantialspeed up, allowing many more Monte Carlo samples to be evaluated, achievingbetter accuracy. We refer to our method as least-squares Shapley performanceattribution (LS-SPA), and describe our open-source implementation.