A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects

03/08/2019
by   Daniel Malinsky, et al.
0

The do-calculus is a well-known deductive system for deriving connections between interventional and observed distributions, and has been proven complete for a number of important identifiability problems in causal inference. Nevertheless, as it is currently defined, the do-calculus is inapplicable to causal problems that involve complex nested counterfactuals which cannot be expressed in terms of the "do" operator. Such problems include analyses of path-specific effects and dynamic treatment regimes. In this paper we present the potential outcome calculus (po-calculus), a natural generalization of do-calculus for arbitrary potential outcomes. We thereby provide a bridge between identification approaches which have their origins in artificial intelligence and statistics, respectively. We use po-calculus to give a complete identification algorithm for conditional path-specific effects with applications to problems in mediation analysis and algorithmic fairness.

READ FULL TEXT

page 1

page 2

page 3

page 4

10/24/2021

Partially Intervenable Causal Models

Graphical causal models led to the development of complete non-parametri...
01/10/2013

A Calculus for Causal Relevance

This paper presents a sound and completecalculus for causal relevance, b...
09/21/2020

Identifying Causal Effects via Context-specific Independence Relations

Causal effect identification considers whether an interventional probabi...
10/16/2012

The Do-Calculus Revisited

The do-calculus was developed in 1995 to facilitate the identification o...
06/06/2021

Path-specific Effects Based on Information Accounts of Causality

Path-specific effects in mediation analysis provide a useful tool for fa...
07/09/2021

Algorithmic Causal Effect Identification with causaleffect

Our evolution as a species made a huge step forward when we understood t...
08/13/2020

Multivariate Counterfactual Systems And Causal Graphical Models

Among Judea Pearl's many contributions to Causality and Statistics, the ...