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I have this slide from my AI class on using a Bayes network to compute a conditional probability. I don't really understand the point of converting the conditional probabilities to factors (besides the fact that it looks weird to marginalize or multiply variables in a CP). It seems kind of arbitrary. Is there some benefit I'm not noticing?

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    $\begingroup$ the benefit is that you are utilizing the distributions factorization to simplify marginalization (which on the joint is extremely expensive!) $\endgroup$ – mshlis Jun 26 at 14:17

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