Information-theoretic causal power

Abstract

The causal power of C over E is (roughly) the degree to which changes in C cause changes in E. A formal measure of causal power would be very useful, as an aid to understanding and modeling complex stochastic systems. Previous attempts to measure causal power, such as those of Good [16], Cheng [3], and Glymour [15], while useful, suffer from one fundamental flaw: they only give sensible results when applied to very restricted types of causal system, all of which exhibit causal transitivity. Causal Bayesian networks, however, are not in general transitive. We develop an information-theoretic alternative, causal information, which applies to any kind of causal Bayesian network. Causal information is based upon three ideas. First, we assume that the system can be represented causally as a Bayesian network. Second, we use hypothetical interventions to select the causal from the non-causal paths connecting C to E. Third, we use a variation on the information-theoretic measure mutual information to summarize the total causal influence of C on E. Our measure gives sensible results for a much wider variety of complex stochastic systems than previous attempts and promises to simplify the interpretation and application of Bayesian networks. © 2009 Springer US.