Estimation of Counterfactual Interventions under Uncertainties

TL;DR

This paper introduces a hierarchical Bayesian method for estimating counterfactual distributions under uncertainty, especially in continuous settings, using Bayesian Warped Gaussian Processes to handle non-Gaussian noise.

Contribution

It develops a novel hierarchical Bayesian framework that explicitly models uncertainty in counterfactual analysis, employing Bayesian Warped Gaussian Processes for flexible distribution estimation.

Findings

Effective in modeling non-Gaussian distributions

Handles non-additive noise in counterfactual estimation

Performs well in synthetic and semi-synthetic experiments

Abstract

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.