Monday, July 26, 2010

Causality

Why causality is not completely captured by Bayesian networks

As [Koller & Friedman 2009], Probabilistic Graphical Models, Ch 21, explains:  We know that a Bayesian network is directed, but the direction of the arrows do not have to be meaningful.  They can even be anti-temporal.  On the other hand, it is common wisdom that a "good" BN structure should correspond to causality, in that an edge X -> Y often suggests that X "causes" Y, either directly or indirectly.  Bayesian networks with a causal structure tends to be sparser and more natural.  However, as long as the network structure is capable of representing the underlying joint distribution correctly, the answers that we obtain to probabilistic queries are the same, regardless of whether the network structure is causal or not.

It seems that causal relations cannot be captured simply by probabilistic relations but require some form of inductive algorithm to obtain, such as the IC (for "inductive causality") algorithm proposed by [Pearl 2000].

Aug 2010 Update:  a new set of slides on causality.