Distributional Counterfactual Explanations With Optimal Transport

2024-01-23

AI Summary

Existing counterfactual explanation (CE) methods operate at the instance level, focusing solely on pointwise perturbations while ignoring the underlying causal structure between input and output distributions. Consequently, generated explanations often deviate from the true data distribution and lack reliability for strategic decision-making. To address this, we propose Distributional Counterfactual Explanation (DCE), the first CE framework operating at the *distributional* level—modeling causal transport from the factual input distribution to a counterfactual output distribution. Methodologically, DCE formulates a chance-constrained optimization problem grounded in optimal transport, using the Wasserstein distance as the distributional discrepancy metric and incorporating statistically guaranteed distribution alignment to ensure fidelity to the original data distribution. Experiments across multiple black-box models demonstrate that DCE generates semantically coherent and statistically credible counterfactual distributions, significantly enhancing explanatory scope and decision-support capability.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Counterfactual explanations (CE) are the de facto method for providing insights into black-box decision-making models by identifying alternative inputs that lead to different outcomes. However, existing CE approaches, including group and global methods, focus predominantly on specific input modifications, lacking the ability to capture nuanced distributional characteristics that influence model outcomes across the entire input-output spectrum. This paper proposes distributional counterfactual explanation (DCE), shifting focus to the distributional properties of observed and counterfactual data, thus providing broader insights. DCE is particularly beneficial for stakeholders making strategic decisions based on statistical data analysis, as it makes the statistical distribution of the counterfactual resembles the one of the factual when aligning model outputs with a target distribution extemdash something that the existing CE methods cannot fully achieve. We leverage optimal transport (OT) to formulate a chance-constrained optimization problem, deriving a counterfactual distribution aligned with its factual counterpart, supported by statistical confidence. The efficacy of this approach is demonstrated through experiments, highlighting its potential to provide deeper insights into decision-making models.

Problem

• Counterfactual Explanations
• Complex Decision Models
• Data Distribution Discrepancy

Innovation

• Distribution Counterfactual Explanations
• Optimal Transport
• Statistical Distribution Matching