Variable Importance Without Impossible Data

The most popular methods for measuring importance of the variables in a black-box prediction algorithm make use of synthetic inputs that combine predictor variables from multiple observations. These inputs can be unlikely, physically impossible, or even logically impossible. As a result, the predictions for such cases can be based on data very unlike any the black box was trained on. We think that users cannot trust an explanation of the decision of a prediction algorithm when the explanation uses such values. Instead, we advocate a method called cohort Shapley, which is grounded in economic game theory and uses only actually observed data to quantify variable importance. Cohort Shapley works by narrowing the cohort of observations judged to be similar to a target observation on one or more features. We illustrate it on an algorithmic fairness problem where it is essential to attribute importance to protected variables that the model was not trained on.Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 11 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.