Answering Causal Queries at Layer 3 with DiscoSCMs-Embracing Heterogeneity

TL;DR

This paper introduces DiscoSCM, a novel framework for Layer 3 counterfactual queries in causal inference, effectively addressing heterogeneity and degeneracy issues present in traditional PO and SCM frameworks.

Contribution

DiscoSCM integrates unit-specific variables and independent noise assumptions to improve counterfactual inference at individual levels, extending theoretical results to heterogeneous settings.

Findings

DiscoSCM resolves degeneracy issues in Layer 3 counterfactuals.

It extends theoretical bounds of causation to individual heterogeneity.

The framework effectively models personalized causal scenarios.

Abstract

In the realm of causal inference, Potential Outcomes (PO) and Structural Causal Models (SCM) are recognized as the principal frameworks.However, when it comes to Layer 3 valuations -- counterfactual queries deeply entwined with individual-level semantics -- both frameworks encounter limitations due to the degenerative issues brought forth by the consistency rule. This paper advocates for the Distribution-consistency Structural Causal Models (DiscoSCM) framework as a pioneering approach to counterfactual inference, skillfully integrating the strengths of both PO and SCM. The DiscoSCM framework distinctively incorporates a unit selection variable $U$ and embraces the concept of uncontrollable exogenous noise realization. Through personalized incentive scenarios, we demonstrate the inadequacies of PO and SCM frameworks in representing the probability of a user being a complier (a Layer 3 event) without degeneration, an issue adeptly resolved by adopting the assumption of independent counterfactual noises within DiscoSCM. This innovative assumption broadens the foundational counterfactual theory, facilitating the extension of numerous theoretical results regarding the probability of causation to an individual granularity level and leading to a comprehensive set of theories on heterogeneous counterfactual bounds. Ultimately, our paper posits that if one acknowledges and wishes to leverage the ubiquitous heterogeneity, understanding causality as invariance across heterogeneous units, then DiscoSCM stands as a significant advancement in the methodology of counterfactual inference.