Markov Blanket

Given random variables \(\mathbf{X}=\{X_1,\cdots,X_n\}\), the Markov blanket of a random variable \(X_i \in \mathbf{X}\) is any subset \(\mathbf{X}_B \subset \mathbf{X}\) such that \[ X_i -||- \mathbf{X}\textbackslash \mathbf{X}_B | \mathbf{X}_B\]

That is, within the set of random variables \(\mathbf{X}\), \(\mathbf{X}_B\) has all the information relevant for \(X_i\), and the rest of the variables do not provide information about \(X_i\).

A Markov blanket where none of its subsets are Markov blankets themselves is called a Markov boundary.