A Bayesian Approach to Learning Causal Networks

TL;DR

This paper explores Bayesian methods for learning both acausal and causal Bayesian networks, introducing new assumptions to extend existing techniques for causal network learning.

Contribution

It introduces two new assumptions, mechanism independence and component independence, enabling the use of acausal network learning methods for causal networks.

Findings

Additional assumptions are necessary for causal network learning.

Mechanism and component independence assumptions facilitate causal learning.

Existing acausal methods can be adapted for causal networks with new assumptions.

Abstract

Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning acausal networks are fairly well developed. These methods often employ assumptions to facilitate the construction of priors, including the assumptions of parameter independence, parameter modularity, and likelihood equivalence. We show that although these assumptions also can be appropriate for learning causal networks, we need additional assumptions in order to learn causal networks. We introduce two sufficient assumptions, called {em mechanism independence} and {em component independence}. We show that these new assumptions, when combined with parameter independence, parameter modularity, and likelihood equivalence, allow us to apply methods for learning acausal networks to learn causal networks.