Bayesian Hierarchical Models for Counterfactual Estimation

TL;DR

This paper introduces a Bayesian hierarchical framework for generating diverse, valid, and feasible counterfactual explanations, incorporating uncertainty quantification and fairness considerations across subgroups.

Contribution

It proposes a probabilistic, hierarchical approach to counterfactual estimation that improves diversity, robustness, and fairness over existing methods.

Findings

Counterfactuals are valid, sparse, and diverse.

The Bayesian approach quantifies uncertainty effectively.

Sharing information across subgroups enhances robustness and fairness.

Abstract

Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single point solution and propose a probabilistic paradigm to estimate a diverse set of counterfactuals. Specifically, we treat the perturbations as random variables endowed with prior distribution functions. This allows sampling multiple counterfactuals from the posterior density, with the added benefit of incorporating inductive biases, preserving domain specific constraints and quantifying uncertainty in estimates. More importantly, we leverage Bayesian hierarchical modeling to share information across different subgroups of a population, which can both improve robustness and measure fairness. A gradient based sampler with superior convergence characteristics efficiently computes the posterior samples. Experiments across several datasets demonstrate that the counterfactuals estimated using our approach are valid, sparse, diverse and feasible.