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I'm trying to solve a question and it has asked for (I feel like I'm confused by everything, would apprecaite some help, thanks),

  1. the Markov blanket of {c,d}. From what I've read so far, Markov blanket is only for one element and then the blanket is its parents, children and children's parent. But what is the blanket of two elements? Is it the elements which are common to the blankets of these two elements?
  2. Also how do you determine c⊥e?

A Graphical Model

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  1. Although the common (wiki, or course notes) definition is for just one variable, one can think of a scenario where we can merge the two nodes (or think of a joint RV, e.g. $(X,Y)$) and define a blanket for them. The idea of the blanket in 1 RV is separating that random variable from the rest of the network such that given the blanket nodes the target node is conditionally independent of all others in the network. If the target node(s) is expanded to $(X,Y)$, instead of just $X$, its blanket should consist of the union of the two separate blankets since when they're given, the target nodes are conditionally independent from the rest.
  2. You can simply determine any independence query using d-separation algorithm.
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  • $\begingroup$ Thank you for clarifying it. $\endgroup$ – RinW May 5 at 19:29

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