The Causal Interpretation of Bayesian Networks

Abstract

The common interpretation of Bayesian networks is that they are vehicles for representing probability distributions, in a graphical form supportive of human understanding and with computational mechanisms supportive of probabilistic reasoning (updating). But the interpretation of Bayesian networks assumed by causal discovery algorithms is causal: the links in the graphs specifically represent direct causal connections between variables. However, there is some tension between these two interpretations. The philosophy of probabilistic causation posits a particular connection between the two, namely that causal relations of certain kinds give rise to probabilistic relations of certain kinds. Causal discovery algorithms take advantage of this kind of connection by ruling out some Bayesian networks given observational data not supported by the posited probability-causality relation. But the discovered (remaining) Bayesian networks are then specifically causal, and not simply arbitrary representations of probability.There are multiple contentious issues underlying any causal interpretation of Bayesian networks. We will address the following questions: Since Bayesian net construction rules allow the construction of multiple distinct networks to represent the very same probability distribution, how can we come to prefer any specific one as “the” causal network? Since Bayesian nets within a Verma-Pearl pattern are strongly indistinguishable, how can causal discovery ever come to select exactly one network as “the” causal network? Causal discovery assumes faithfulness (that d-connections in the model are accompanied by probabilistic dependency in the system modeled). However, some physical systems cannot be modeled faithfully under a causal interpretation. How can causal discovery cope with that? Here we introduce a causal interpretation of Bayesian networks by way of answering these questions and then apply this interpretation to answering further questions about causal power, explanation and responsibility.Keywordscausal discoveryfaithfulnessBayesian networksprobabilistic causalityinterventioncausal powercausal responsibility