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 statistics and machine learning, the Markov blanket for a node in a graphical model 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 and its children. The term was coined by Judea 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.


The Markov blanket for a node A{displaystyle A}A in a Bayesian network is the set of nodes ∂A{displaystyle partial A}partial A composed of A{displaystyle A}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. The Markov blanket of A may also be denoted by MB⁡(A){displaystyle operatorname {MB} (A)}{displaystyle operatorname {MB} (A)}.


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


Pr(A∣∂A,B)=Pr(A∣∂A).{displaystyle Pr(Amid partial A,B)=Pr(Amid partial A).!}Pr(Amid partial A,B)=Pr(Amid partial A).!


See also



  • Andrey Markov

  • Free energy minimisation

  • Moral graph

  • Separation of concerns



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..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"""""""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}








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