  We introduce a variable importance measure to quantify the impact of
individual input variables to a black box function. Our measure is based on the
Shapley value from cooperative game theory. Many measures of variable
importance operate by changing some predictor values with others held fixed,
potentially creating unlikely or even logically impossible combinations. Our
cohort Shapley measure uses only observed data points. Instead of changing the
value of a predictor we include or exclude subjects similar to the target
subject on that predictor to form a similarity cohort. Then we apply Shapley
value to the cohort averages. We connect variable importance measures from
explainable AI to function decompositions from global sensitivity analysis. We
introduce a squared cohort Shapley value that splits previously studied Shapley
effects over subjects, consistent with a Shapley axiom.
