Title: TreeGrad-Ranker: Feature Ranking via $O(L)$-Time Gradients for Decision Trees
Primary area: interpretability and explainable AI
Keywords: Shapley value, Banzhaf value, semi-values, decision trees, linear treeshap

Abstract: We revisit the use of probabilistic values, which include the well-known Shapley and Banzhaf values, to rank features for explaining the local predicted values of decision trees. The quality of feature rankings is typically assessed with the  insertion and deletion metrics. 
Empirically, we observe that co-optimizing these two metrics is closely related to a joint optimization that selects a subset of features to maximize the local predicted value while minimizing it for the complement. However, we theoretically show that probabilistic values are generally unreliable for solving this joint optimization.  To address this, we directly optimize the multilinear extension of the joint objective via gradient ascent, and develop TreeGrad to compute each gradient in $O(L)$ time for decision trees with $L$ leaves. The averaged gradient serves as feature scores returned by our TreeGrad-Ranker. Our TreeProb generalizes Linear TreeShap to support all probabilistic values, allowing us to compute them accurately as baselines in our experiments. As a byproduct, we introduce TreeGrad-Shap, an equally efficient but parallelizable and numerically stable alternative to Linear TreeShap. Empirically, our TreeGrad-Ranker performs significantly better on both insertion and deletion metrics.