Editing Markov blanket (section)

== Markov blanket ==

A Markov blanket of a random variable <math>Y</math> in a random variable set <math>\mathcal{S}=\{X_1,\ldots,X_n\}</math> is any subset <math>\mathcal{S}_1</math> of <math>\mathcal{S}</math>, conditioned on which other variables are independent with <math>Y</math>:

<math display="block">Y\perp \!\!\! \perp\mathcal{S}\backslash\mathcal{S}_1 \mid \mathcal{S}_1.</math>

It means that <math>\mathcal{S}_1</math> contains at least all the information one needs to infer <math>Y</math>, where the variables in <math>\mathcal{S}\backslash\mathcal{S}_1</math> are redundant.

In general, a given Markov blanket is not unique. Any set in <math>\mathcal{S}</math> that contains a Markov blanket is also a Markov blanket itself. Specifically, <math>\mathcal{S}</math> is a Markov blanket of <math>Y</math> in <math>\mathcal{S}</math>.