Feature Attribution with Necessity and Sufficiency via Dual-stage Perturbation Test for Causal Explanation

We investigate the problem of explainability in machine learning.To address this problem, Feature Attribution Methods (FAMs) measure the contribution of each feature through a perturbation test, where the difference in prediction is compared under different perturbations.However, such perturbation tests may not accurately distinguish the contributions of different features, when their change in prediction is the same after perturbation.In order to enhance the ability of FAMs to distinguish different features' contributions in this challenging setting, we propose to utilize the probability (PNS) that perturbing a feature is a necessary and sufficient cause for the prediction to change as a measure of feature importance.Our approach, Feature Attribution with Necessity and Sufficiency (FANS), computes the PNS via a perturbation test involving two stages (factual and interventional).In practice, to generate counterfactual samples, we use a resampling-based approach on the observed samples to approximate the required conditional distribution.Finally, we combine FANS and gradient-based optimization to extract the subset with the largest PNS.We demonstrate that FANS outperforms existing feature attribution methods on six benchmarks.