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If we use Maximum Likelihood in a binary Graphical Model, the probability of a child given multiple parents is (without any smoothing): For a value of a child=1 P(Child=1|Parents=some combination)=Number of times (Child=1&Parents=some combination)/Number of times(Parents=some combination) My questions are 2 Is it valid to say?: P(child=1|parent_1=1)=NoT(Child=1&Parent=1)/Not(Parent=1) That is, the marginal probability of a single parent over the child? If this is true (which I believe it is), how can we relate this marginal to: P(child=1|Parents=some combination) I think is not that direct, since the parents are not independent. Thus, we can't simply multiply the marginals. I hope the question is well stated. Thanks |
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The thing you actually want, using the definition of conditional probability, is P(child=1|Parents=some combination) = P(child=1&Parents=some combination)/P(parents=some combination). You can't write these in terms of pairwise counts unless you have strong independence assumptions in your model, so you should really want NoT(child=1&Parents=some combination)/NoT(Parents=some combination) Ok, yes, I was doing some experiments over multiple parents and I did managed to get something, but definitively the multiplication was not the answer. Thanks
(Aug 24 '11 at 08:56)
Leon Palafox
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