Abstract¶
Probabilistic graphical models are useful tools for modeling systems governed by probabilistic structure. Bayesian networks are one class of probabilistic graphical model that have proven useful for characterizing both formal systems and for reasoning with those systems. Probabilistic dependencies in Bayesian networks are graphically expressed in terms of directed links from parents to their children. Casual Bayesian networks are a generalization of Bayesian networks that allow one to “intervene” and perform “graph surgery” — cutting nodes off from their parents. Causal theories are a formal framework for generating causal Bayesian networks.
This report provides a brief introduction to the formal tools needed to comprehend Bayesian networks, including probability theory and graph theory. Then, it describes Bayesian networks and causal Bayesian networks. It introduces some of the most basic functionality of the extensive NetworkX python package for working with complex graphs and networks networkx. I introduce some utilities I have build on top of NetworkX including conditional graph enumeration and sampling from discrete valued Bayesian networks encoded in NetworkX graphs pacer2015cbnx. I call this Causal Bayesian NetworkX, or cbnx. I conclude by introducing a formal framework for generating causal Bayesian networks called theory based causal induction griffithst09, out of which these utilities emerged. I discuss the background motivations for frameworks of this sort, their use in computational cognitive science, and the use of computational cognitive science for the machine learning community at large.
