Partially Intervenable Causal Models

TL;DR

This paper introduces a new class of graphical causal models that allow for limited interventions, bridging the gap between graphical and potential outcomes approaches, and provides a complete identification theory for these models.

Contribution

It develops a unified framework for partially intervenable causal models, extending do-calculus and identification theory to models with restricted interventions.

Findings

Complete identification theory for partially intervenable models

Generalized do-calculus for restricted interventions

Unified approach connecting graphical and potential outcomes methods

Abstract

Graphical causal models led to the development of complete non-parametric identification theory in arbitrary structured systems, and general approaches to efficient inference. Nevertheless, graphical approaches to causal inference have not been embraced by the statistics and public health communities. In those communities causal assumptions are instead expressed in terms of potential outcomes, or responses to hypothetical interventions. Such interventions are generally conceptualized only on a limited set of variables, where the corresponding experiment could, in principle, be performed. By contrast, graphical approaches to causal inference generally assume interventions on all variables are well defined - an overly restrictive and unrealistic assumption that may have limited the adoption of these approaches in applied work in statistics and public health. In this paper, we build on a unification of graphical and potential outcomes approaches to causality exemplified by Single World Intervention Graphs (SWIGs) to define graphical models with a restricted set of allowed interventions. We give a complete identification theory for such models, and develop a complete calculus of interventions based on a generalization of the do-calculus, and axioms that govern probabilistic operations on Markov kernels. A corollary of our results is a complete identification theory for causal effects in another graphical framework with a restricted set of interventions, the decision theoretic graphical formulation of causality.