DISCOUNT: Distributional Counterfactual Explanation With Optimal Transport

Counterfactual Explanations (CE) is the de facto method for providing insight and interpretability in black-box decision-making models by identifying alternative input instances that lead to different outcomes. This paper extends the concept of CEs to a distributional context, broadening the scope from individual data points to entire input and output distributions, named Distributional Counterfactual Explanation (DCE). In DCE, our focus shifts to analyzing the distributional properties of the factual and counterfactual, drawing parallels to the classical approach of assessing individual instances and their resulting decisions. We leverage Optimal Transport (OT) to frame a chance-constrained optimization problem, aiming to derive a counterfactual distribution that closely aligns with its factual counterpart, substantiated by statistical confidence. Our proposed optimization method, DISCOUNT, strategically balances this confidence across both input and output distributions. This algorithm is accompanied by an analysis of its convergence rate. The efficacy of our proposed method is substantiated through a series of illustrative case studies, highlighting its potential in providing deep insights into decision-making models.