Markov Blanket

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A Markov Blanket of a Directed Graph Graph Node are its Parent Nodes, Children Nodes, and the Parent Node of the Children Nodes.



References

2018

  • (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Markov_blanket Retrieved:2018-11-14.
    • 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.

      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 [math]\displaystyle{ A }[/math] in a Bayesian network is the set of nodes [math]\displaystyle{ \partial A }[/math] composed of [math]\displaystyle{ A }[/math] '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 [math]\displaystyle{ \operatorname{MB}(A) }[/math] .

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

      [math]\displaystyle{ \Pr(A \mid \partial A , B) = \Pr(A \mid \partial A). \! }[/math]

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2023

  • (Wikipedia, 2023) ⇒ https://en.wikipedia.org/wiki/Markov_blanket Retrieved:2023-10-9.
    • In statistics and machine learning, when one wants to infer a random variable with a set of variables, usually a subset is enough, and other variables are useless. Such a subset that contains all the useful information is called a Markov blanket. If a Markov blanket is minimal, meaning that it cannot drop any variable without losing information, it is called a Markov boundary. Identifying a Markov blanket or a Markov boundary helps to extract useful features. The terms of Markov blanket and Markov boundary were coined by Judea Pearl in 1988. A Markov blanket can be constituted by a set of Markov chains.