Markov blanket

In a Bayesian network, the Markov blanket of node A includes its parents, children and the other parents of all of its children.

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 network, the Markov blanket of a node is its set of neighbouring nodes. A Markov blanket may also be denoted by $M B (A)$ .

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 behaviour 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.

Notes

^ Pearl, J. Probabilistic Reasoning in Intelligent Systems, Morgan Kaufmann, 1988.

Categories:

Probability theory
Bayesian networks
Markov networks

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