What major would make me most qualified to solve a problem like

You kidding me? Week one of a probability course is all you need to solve this

>>7693858
Actually, probably comp-sci with a concentration in artificial intelligence. It won't give you a very deep understanding of probability theory but it will give you an excessive amount of experience with problem solving on large Bayesian networks and stochastic processes.

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>>7693876
So you think the equation is true?

>>7693858
false

>>7693903
I agree. How would you go about proving it? Aside from stating the obvious "explaining away".

>>7693907
with a counterexample

>>7693912
Can you think of a way to prove the equation is false without using any real values? I'm finding myself struggling.

P(A,C|B) = P(A|B)P(C|B)
P(A,C,B) P(B) = P(A,B) P(C,B)


Not sure where to go from here to show that the two aren't equal.

>>7693907
By the d-seperstion theorem , given 3 subsets of nodes on a directed acyclic graph for a Bayesian network, if B separates A from C in the skeleton of the moralised graph of the ancestral graph of A, B and C , then A is independent of C given B.

In this case, the two unmarried parent nodes become married in the moralised graph and so their child does not separate them and so we can not conclude whether they are independent given information about their child.

>>7693858
Btw you learn this in a Bayesian statistics course.

>>7693926
I.e. There is at least one instance of such a Bayesian net where A and C are not independent given B

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>>7693929
I'm trying to learn about ML but I can't get past this because I can't prove the inequality even though I know it's true. I tried the work attached, stuck again down this path. How is this proven, aside from referencing axioms?

>>7693945
Is this the same question as in the OP?
I'm not going to read your working or think about your problem if you have not provided the question clearly.