Can someone please explain what this sentence means "a Bayes net specifies a canonical factorization of a probability distribution into the product of the conditional distribution for each variable conditioned on its parents"? Thank you.
what does canonical factorization means in Bayes Net?
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probability
1 Answers
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This means that $p(x) = \prod_{v \in V} p(x_v|x_{\text{pa}(v)})$
So you can construct the joint probability function by multiplying conditional probabilities. Consider the following:
Then $P(a,b,c, e_1,e_2, e_2) = P(a) \cdot P(b) \cdot P(c) \cdot P(e_1|a,b,c) \cdot P(e_2|a,b,c) \cdot P(e_3|e_1, e_2)$
In other words, we factored the joint probability into a product of conditional probabilities based on the above graph.