Assignment 2 - Problem 1 - Markov Blanket

[lustiz]

Hey guys, does the Markov blanket for a variable include the variable itself? Wiki says it doesn't. However, I found a definition in the ML2 slides of Prof. Roth that includes the variable which we want to compute the blanket for.

[robert.n]

Hey guys, does the Markov blanket for a variable include the variable itself? Wiki says it doesn't. However, I found a definition in the ML2 slides of Prof. Roth that includes the variable which we want to compute the blanket for.

No, it doesn't. If it could include the variable itself, then why include other variables at all? If you already know the value of a variable, then obviously the value of this variable is already independent of all other variables. Example: x1 is independent of all other variables, given x1.

This is also why it says "and all the other parents of its children".

Conclusion:
Many illustrations for the Markov blanket are wrong, including the illustration on wikipedia and in the Computer Vision book by Prince. However, there are also many correct illustrations. See Google Image search.

This illustration is correct: http://lecture.ecc.u-tokyo.ac.jp/~yamag ... lanket.png
This is not: https://origin-ars.els-cdn.com/content/ ... 5X-gr2.jpg

[franzel]

Robert is right regarding the definition.

The formal definitions from both books ("Probabilistic Graphical Models: Principles and Techniques", "Computer vision:models, learning and inference") suggest that the markov blanket of variable X does not include X itself.

However, it is convention (c.f. "Computer vision:models, learning and inference") to include the the node into the the shaded area when depicting the markov blanket.