CODEWITHSUNDEEP
machine-learningdirected-acyclic-graphsbayesian-networksmarkov
ThePerson
ThePerson

Reputation: 33

Is it possible to use the Markov Blanket to determine whether two nodes are conditionally independent?

A target node is independent of all other nodes in a Bayesian network given its Markov Blanket. I am confused how this can be applied. Can I for example target any node in the graph to determine its independence from another node?

Consider this example:

Example How would I determine whether J is independent of K given W?

Upvotes: 1

Views: 681

Answers (1)

Welpers
Welpers

Reputation: 21

For this query that you have chosen, J is not independent of K given W, simply because K is part of J's Markov blanket. Also, J cannot be independent of K because K is J's Parent.

In general, we can determine if 2 nodes are conditionally independent of each other (given some other nodes) based on the following scenarios:

1) Indirect "Causal" Effect

  • K is independent of W given J

2) Indirect Evidential Effect

  • W is independent of K given J

3) Common "Cause"

  • G is independent of W given C

4) Common Effect / Collider

  • B is NOT independent of T given X (i.e. X acts as a collider, and if we know information about X, B and T can be dependent) If X is NOT OBSERVED, then B and T are marginally independent.

It is not entirely necessary to use Markov Blankets to determine if 2 nodes are independent of each other.

But to give you a better understanding of how Markov blanket can be applied to determine independence, lets consider the node C

Given C's Markov Blanket, L, G, W, J, which are C's Parents, Children, and Children's Parents, C is then independent of every other node in the Bayesian Network.

Therefore, we can say that: C is independent of B, X, T, K, given L, G, W, J

Upvotes: 1

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