Joint structure learning and causal effect estimation for categorical graphical models

TL;DR

This paper introduces a Bayesian framework for joint structure learning and causal effect estimation in categorical graphical models, utilizing reversible jump MCMC to handle model uncertainty and improve estimation accuracy.

Contribution

It develops a novel Bayesian approach combining DAG structure learning with causal effect estimation for categorical data, incorporating model uncertainty via reversible jump MCMC.

Findings

Outperforms existing methods in simulation studies

Provides full posterior distributions of causal effects

Successfully applied to real depression and anxiety dataset

Abstract

We consider a a collection of categorical random variables. Of special interest is the causal effect on an outcome variable following an intervention on another variable. Conditionally on a Directed Acyclic Graph (DAG), we assume that the joint law of the random variables can be factorized according to the DAG, where each term is a categorical distribution for the node-variable given a configuration of its parents. The graph is equipped with a causal interpretation through the notion of interventional distribution and the allied "do-calculus". From a modeling perspective, the likelihood is decomposed into a product over nodes and parents of DAG-parameters, on which a suitably specified collection of Dirichlet priors is assigned. The overall joint distribution on the ensemble of DAG-parameters is then constructed using global and local independence. We account for DAG-model uncertainty and propose a reversible jump Markov Chain Monte Carlo (MCMC) algorithm which targets the joint posterior over DAGs and DAG-parameters; from the output we are able to recover a full posterior distribution of any causal effect coefficient of interest, possibly summarized by a Bayesian Model Averaging (BMA) point estimate. We validate our method through extensive simulation studies, wherein comparisons with alternative state-of-the-art procedures reveal an outperformance in terms of estimation accuracy. Finally, we analyze a dataset relative to a study on depression and anxiety in undergraduate students.