Causal Expectation-Maximisation

TL;DR

This paper introduces the causal EM algorithm to approximate counterfactuals in structural causal models with latent variables, addressing NP-hardness and providing bounds and credible intervals for counterfactual inference.

Contribution

It presents a novel causal EM algorithm for reconstructing latent variable uncertainty and approximating counterfactuals, even when structural equations are unknown.

Findings

The causal EM algorithm effectively approximates counterfactuals in various models.

Empirical results show credible intervals become accurate after multiple EM runs.

Highlights limitations of counterfactual bounds without structural equations.

Abstract

Structural causal models are the basic modelling unit in Pearl's causal theory; in principle they allow us to solve counterfactuals, which are at the top rung of the ladder of causation. But they often contain latent variables that limit their application to special settings. This appears to be a consequence of the fact, proven in this paper, that causal inference is NP-hard even in models characterised by polytree-shaped graphs. To deal with such a hardness, we introduce the causal EM algorithm. Its primary aim is to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. Counterfactual inference is then addressed via standard algorithms for Bayesian networks. The result is a general method to approximately compute counterfactuals, be they identifiable or not (in which case we deliver bounds). We show empirically, as well as by deriving credible intervals, that the approximation we provide becomes accurate in a fair number of EM runs. These results lead us finally to argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.