S-CFE: Simple Counterfactual Explanations

TL;DR

This paper introduces S-CFE, a simple and efficient method for generating sparse, manifold-aligned counterfactual explanations for classifiers, capable of handling various models and plausibility measures.

Contribution

It applies the accelerated proximal gradient method to produce sparse, plausible counterfactuals with a flexible framework that supports different classifiers and regularizers.

Findings

Produces sparser counterfactuals compared to existing methods

Maintains proximity and plausibility in explanations

Demonstrates computational efficiency on real datasets

Abstract

We study the problem of finding optimal sparse, manifold-aligned counterfactual explanations for classifiers. Canonically, this can be formulated as an optimization problem with multiple non-convex components, including classifier loss functions and manifold alignment (or \emph{plausibility}) metrics. The added complexity of enforcing \emph{sparsity}, or shorter explanations, complicates the problem further. Existing methods often focus on specific models and plausibility measures, relying on convex $\ell_1$ regularizers to enforce sparsity. In this paper, we tackle the canonical formulation using the accelerated proximal gradient (APG) method, a simple yet efficient first-order procedure capable of handling smooth non-convex objectives and non-smooth $\ell_p$ (where $0 \leq p < 1$) regularizers. This enables our approach to seamlessly incorporate various classifiers and plausibility measures while producing sparser solutions. Our algorithm only requires differentiable data-manifold regularizers and supports box constraints for bounded feature ranges, ensuring the generated counterfactuals remain \emph{actionable}. Finally, experiments on real-world datasets demonstrate that our approach effectively produces sparse, manifold-aligned counterfactual explanations while maintaining proximity to the factual data and computational efficiency.