  Learning Markov blanket (MB) structures has proven useful in performing
feature selection, learning Bayesian networks (BNs), and discovering causal
relationships. We present a formula for efficiently determining the number of
MB structures given a target variable and a set of other variables. As
expected, the number of MB structures grows exponentially. However, we show
quantitatively that there are many fewer MB structures that contain the target
variable than there are BN structures that contain it. In particular, the ratio
of BN structures to MB structures appears to increase exponentially in the
number of variables.
