Counting Markov Blanket Structures
This work provides a theoretical foundation for feature selection and causal discovery, but it is incremental as it focuses on counting structures rather than learning them.
The authors tackled the problem of counting Markov blanket structures for a target variable, deriving a formula that shows exponential growth but significantly fewer structures than Bayesian networks, with the ratio increasing exponentially with variable count.
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.