Markov blanket

In machine learning, the Markov blanket for a node $A$ in a Bayesian network is the set of nodes $\partial A$ composed of $A$'s parents, its children, and its children's other parents. In a Markov random field, the Markov blanket of a node is its set of neighboring nodes. A Markov blanket may also be denoted by $MB(A)$.

Every set of nodes in the network is conditionally independent of $A$ when conditioned on the set $\partial A$, that is, when conditioned on the Markov blanket of the node $A$. The probability has the Markov property; formally, for distinct nodes $A$ and $B$:

$\Pr(A\mid \partial A,B)=\Pr(A\mid \partial A).\!$

The Markov blanket of a node contains all the variables that shield the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge needed to predict the behavior of that node. The term was coined by Pearl in 1988.^[1]

In a Bayesian network, the values of the parents and children of a node evidently give information about that node; however, its children's parents also have to be included, because they can be used to explain away the node in question. In a Markov random field, the Markov blanket for a node is simply its adjacent nodes.

See also

• Moral graph
• Andrey Markov

Notes

1. Pearl, Judea (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Representation and Reasoning Series. San Mateo CA: Morgan Kaufmann. ISBN 0-934613-73-7.