Estimation of Counterfactual Interventions under Uncertainties
This work addresses uncertainty in counterfactual analysis for industrial applications, but it is incremental as it builds on existing Bayesian methods.
The paper tackles the problem of ambiguous counterfactual distributions in continuous settings by proposing a hierarchical Bayesian approach using a Warped Gaussian Process to model uncertainty, and demonstrates its performance in a synthetic example and an algorithmic recourse task.
Counterfactual analysis is intuitively performed by humans on a daily basis eg. "What should I have done differently to get the loan approved?". Such counterfactual questions also steer the formulation of scientific hypotheses. More formally it provides insights about potential improvements of a system by inferring the effects of hypothetical interventions into a past observation of the system's behaviour which plays a prominent role in a variety of industrial applications. Due to the hypothetical nature of such analysis, counterfactual distributions are inherently ambiguous. This ambiguity is particularly challenging in continuous settings in which a continuum of explanations exist for the same observation. In this paper, we address this problem by following a hierarchical Bayesian approach which explicitly models such uncertainty. In particular, we derive counterfactual distributions for a Bayesian Warped Gaussian Process thereby allowing for non-Gaussian distributions and non-additive noise. We illustrate the properties our approach on a synthetic and on a semi-synthetic example and show its performance when used within an algorithmic recourse downstream task.