Distributional Counterfactual Explanations With Optimal Transport

Counterfactual explanations (CE) are the de facto method of 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 CE to a distributional context, broadening the scope from individual data points to entire input and output distributions, named distributional counterfactual explanation (DCE). In DCE, we take the stakeholder's perspective and shift focus 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 in both the 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 quantitative and qualitative experiments, highlighting its potential to provide deep insights into decision-making models.