A Bayesian Approach to Constraint Based Causal Inference

TL;DR

This paper introduces a Bayesian constraint-based causal inference method that combines probabilistic scoring with traditional algorithms, improving accuracy, robustness, and interpretability in finite data scenarios.

Contribution

It presents the Bayesian Constraint-based Causal Discovery (BCCD) algorithm, integrating Bayesian scores with constraint-based methods to enhance reliability and decision confidence in causal inference.

Findings

BCCD outperforms FCI and Conservative PC algorithms in tests.

The method provides reliability estimates for causal decisions.

BCCD effectively balances robustness and theoretical guarantees.

Abstract

We target the problem of accuracy and robustness in causal inference from finite data sets. Some state-of-the-art algorithms produce clear output complete with solid theoretical guarantees but are susceptible to propagating erroneous decisions, while others are very adept at handling and representing uncertainty, but need to rely on undesirable assumptions. Our aim is to combine the inherent robustness of the Bayesian approach with the theoretical strength and clarity of constraint-based methods. We use a Bayesian score to obtain probability estimates on the input statements used in a constraint-based procedure. These are subsequently processed in decreasing order of reliability, letting more reliable decisions take precedence in case of con icts, until a single output model is obtained. Tests show that a basic implementation of the resulting Bayesian Constraint-based Causal Discovery (BCCD) algorithm already outperforms established procedures such as FCI and Conservative PC. It can also indicate which causal decisions in the output have high reliability and which do not.