A Bayesian Approach to Learning Causal Networks
This work addresses the challenge of causal inference in machine learning, providing a theoretical extension for researchers in probabilistic modeling, but it is incremental as it builds directly on established methods without broad empirical validation.
The paper tackles the problem of learning causal Bayesian networks by extending existing Bayesian methods for acausal networks, introducing two new assumptions (mechanism independence and component independence) that, when combined with prior assumptions, enable the application of acausal learning methods to causal networks.
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.