[Paper Review] Counterfactual Plans under Distributional Ambiguity

Ngoc Bui, Duy Nguyen+1 more|arXiv (Cornell University)|Jan 29, 2022

Explainable Artificial Intelligence (XAI)4 citations

TL;DR

This paper proposes a robust framework for generating counterfactual plans under distributional ambiguity in model parameters, using moment-based uncertainty quantification to bound validity probabilities and a corrective optimization method to enhance robustness. Experiments show the method significantly improves validity and diversity across real-world datasets under temporal, correctional, and geospatial shifts.

ABSTRACT

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model parameters is partially prescribed using only the first- and second-moment information. First, we propose an uncertainty quantification tool to compute the lower and upper bounds of the probability of validity for any given counterfactual plan. We then provide corrective methods to adjust the counterfactual plan to improve the validity measure. The numerical experiments validate our bounds and demonstrate that our correction increases the robustness of the counterfactual plans in different real-world datasets.

Motivation & Objective

• To address the fragility of counterfactual plans when predictive models are updated with new data, leading to parameter shifts.
• To quantify the probability bounds of counterfactual plan validity under uncertain model parameters using only first- and second-order moment information.
• To develop a correction mechanism that enhances the robustness of counterfactual plans against future model shifts.
• To design a comprehensive optimization framework (COPA) that jointly balances validity, proximity, and diversity under distributional ambiguity.
• To validate the approach on real-world datasets with various types of distributional shifts, including temporal, correctional, and geospatial shifts.

Proposed method

• The method models the uncertainty in classifier parameters using a distributional ambiguity set defined by empirical mean and covariance of model parameters from multiple training runs.
• It derives analytical lower and upper bounds on the probability of plan validity using the Gelbrich radius and moment-based distributional information.
• A correction procedure adjusts the counterfactual plan by minimizing a robustified objective that accounts for the worst-case parameter shift within the ambiguity set.
• The COPA framework formulates a multi-objective optimization problem that balances validity, proximity (via Mahalanobis distance), and diversity (via determinantal point process).
• The method uses empirical estimation of mean and covariance of model parameters from 1000 bootstrapped classifiers trained on 50% of the training data.
• It applies robust optimization techniques to ensure that the counterfactual plan remains valid across a range of plausible future model parameters.

Experimental results

Research questions

• RQ1 How can we quantify the robustness of a counterfactual plan under uncertainty in future model parameters?
• RQ2 What is the range of validity probability for a given counterfactual plan when model parameters are distributionally ambiguous?
• RQ3 How can we correct a counterfactual plan to improve its robustness against future model updates?
• RQ4 Can a unified optimization framework effectively balance validity, proximity, and diversity under model uncertainty?
• RQ5 How does the proposed method perform across different types of data shifts—temporal, correctional, and geospatial—compared to existing baselines?

Key findings

• The proposed method achieves 100% empirical validity on all three real-world datasets (German credit, SBA, Student performance), outperforming DiCE and MahalanobisCrr.
• With increasing diversity regularization (λ₂ = 10.0), COPA achieves the highest diversity (0.380) and maintains 100% empirical validity on the temporal shift dataset.
• On the geospatial shift dataset, COPA achieves 100% empirical validity and 0.998 in the L* diversity metric, significantly outperforming DiCE (0.549) and MahalanobisCrr (0.864).
• The lower validity bound computed via the uncertainty quantification tool closely tracks empirical validity, validating the theoretical bounds.
• The correction mechanism increases the robustness of counterfactual plans, particularly in high-shift scenarios such as temporal and geospatial shifts.
• COPA maintains high validity across all settings even when baseline methods like DiCE and MahalanobisCrr show significant drops in performance (e.g., DiCE drops to 40.8% on geospatial shift).