Algorithmic recourse under imperfect causal knowledge: a probabilistic approach (2006.06831v3)

Abstract: Recent work has discussed the limitations of counterfactual explanations to recommend actions for algorithmic recourse, and argued for the need of taking causal relationships between features into consideration. Unfortunately, in practice, the true underlying structural causal model is generally unknown. In this work, we first show that it is impossible to guarantee recourse without access to the true structural equations. To address this limitation, we propose two probabilistic approaches to select optimal actions that achieve recourse with high probability given limited causal knowledge (e.g., only the causal graph). The first captures uncertainty over structural equations under additive Gaussian noise, and uses Bayesian model averaging to estimate the counterfactual distribution. The second removes any assumptions on the structural equations by instead computing the average effect of recourse actions on individuals similar to the person who seeks recourse, leading to a novel subpopulation-based interventional notion of recourse. We then derive a gradient-based procedure for selecting optimal recourse actions, and empirically show that the proposed approaches lead to more reliable recommendations under imperfect causal knowledge than non-probabilistic baselines.

Algorithmic Recourse Under Imperfect Causal Knowledge: A Probabilistic Approach

The paper explores the vital issue of algorithmic recourse in machine learning systems where causal relationships between features are present but imperfectly understood. In typical decision-making scenarios, black-box models may reject an individual's request, such as a bank loan, and the individual seeks to understand what changes they can make to improve the decision outcome. This is the focus of "algorithmic recourse."

The critical issue addressed by this work is the limited causal knowledge available in practice. While prior approaches have often relied on detailed causal models, the availability of true structural causal models in real-world scenarios is scarce. Given this challenge, the authors provide evidence of the inherent impossibility of ensuring recourse without complete structural equations. This finding underscores the need for innovative approaches that operate under uncertainty.

The proposed methods revolve around leveraging limited causal knowledge to give probable recourse recommendations. Two primary probabilistic approaches are presented:

1. Probabilistic Counterfactual Estimation using Gaussian Processes: The authors develop a model that assumes the existing causal model belongs to the class of additive Gaussian noise models. By adopting a Bayesian approach, they employ Gaussian processes to average predictions over multiple candidate causal models, offering a distribution over possible outcomes. This approach is significant in that it accounts for structural uncertainty by leveraging model averaging to predict counterfactuals. They define a gradient-based optimization to select optimal actions maximizing the probability of a favorable outcome within this probabilistic framework.
2. Subpopulation-Based Recourse Using Conditional Average Treatment Effect (CATE): This method takes a more conservative stance by relaxing assumptions about structural equations and focusing on the average effect of interventions within subpopulations that are similar to the individual seeking recourse. By deploying conditional variational autoencoders (CVAE) for this estimation, the approach moves away from individual outcomes and instead estimates aggregated interventional effects, which can provide a robust frame for causal reasoning.

An interesting finding from the experiments conducted is the nuanced performance between the individual-focused and population-focused approaches. The authors report that while individual-based methods are prone to discrepancies from true underlying causal models, the population-based approaches are more robust to unseen variance and misspecification in structural equations, albeit at possibly higher cost.

The implications of this research are multifold. Practically, it provides a framework for deploying algorithmic decision systems where causal understanding is limited, yet some causal information is accessible. Theoretically, it pushes the boundary of work in probabilistic modelling within causally structured data, raising potential for application in systems where fairness and transparency are required, such as finance and healthcare.

Future work could focus on extending these methods to more complex causal networks, integrating them into adaptive systems where causal structures might evolve over time, or examining their suitability in particular sectors previously hindered by counterfactual infeasibility due to data constraints. This progression will invariably enhance the fidelity and efficacy of machine learning models in decision-making roles, marking a significant advance in both AI ethics and efficacy.