Learning Generalized Gumbel-max Causal Mechanisms

TL;DR

This paper introduces a generalized family of causal mechanisms for Structural Causal Models that can be trained to minimize variance in counterfactual effect estimation, improving over fixed mechanisms like Gumbel-max.

Contribution

It proposes a parameterized family of causal mechanisms that optimize counterfactual variance, extending Gumbel-max models and enabling better generalization to unseen queries.

Findings

Lower variance in counterfactual effect estimates.

Effective training of causal mechanisms on query distributions.

Generalization to unseen counterfactual queries.

Abstract

To perform counterfactual reasoning in Structural Causal Models (SCMs), one needs to know the causal mechanisms, which provide factorizations of conditional distributions into noise sources and deterministic functions mapping realizations of noise to samples. Unfortunately, the causal mechanism is not uniquely identified by data that can be gathered by observing and interacting with the world, so there remains the question of how to choose causal mechanisms. In recent work, Oberst & Sontag (2019) propose Gumbel-max SCMs, which use Gumbel-max reparameterizations as the causal mechanism due to an intuitively appealing counterfactual stability property. In this work, we instead argue for choosing a causal mechanism that is best under a quantitative criteria such as minimizing variance when estimating counterfactual treatment effects. We propose a parameterized family of causal mechanisms that generalize Gumbel-max. We show that they can be trained to minimize counterfactual effect variance and other losses on a distribution of queries of interest, yielding lower variance estimates of counterfactual treatment effect than fixed alternatives, also generalizing to queries not seen at training time.