Optimal Transport Group Counterfactual Explanations

TL;DR

This paper introduces a novel optimal transport-based method for group counterfactual explanations that generalizes well, preserves group geometry, and outperforms existing approaches, especially when model linearity cannot be assumed.

Contribution

It proposes an explicit optimal transport map for group counterfactuals, enabling generalization without re-optimization and improving interpretability and efficiency.

Findings

Accurately generalizes to new group members

Preserves group geometry with minimal transport cost

Outperforms baseline methods when model linearity is absent

Abstract

Group counterfactual explanations find a set of counterfactual instances to explain a group of input instances contrastively. However, existing methods either (i) optimize counterfactuals only for a fixed group and do not generalize to new group members, (ii) strictly rely on strong model assumptions (e.g., linearity) for tractability or/and (iii) poorly control the counterfactual group geometry distortion. We instead learn an explicit optimal transport map that sends any group instance to its counterfactual without re-optimization, minimizing the group's total transport cost. This enables generalization with fewer parameters, making it easier to interpret the common actionable recourse. For linear classifiers, we prove that functions representing group counterfactuals are derived via mathematical optimization, identifying the underlying convex optimization type (QP, QCQP, ...). Experiments show that they accurately generalize, preserve group geometry and incur only negligible additional transport cost compared to baseline methods. If model linearity cannot be exploited, our approach also significantly outperforms the baselines.