Classification based on several marginal probability

In my data, each instance has several attributes as "TRUE" or "FALSE".

For example:

Instance1: X1=TRUE, X2=TRUE, X3=FALSE, ...
Instance2: X1=FALSE, X2=TRUE, X3=FALSE, ...


I need to classify a TRUE/FALSE attribute, named Y, of each instance. So far, what I know is the conditional probability P(Y|X1), P(Y|X2), ..., and the marginal probability P(X1), P(X2), ...

Is there an existed model to do the inference? Thanks.

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Are you saying you don't have the original data - you ONLY have the conditional probabilities and the marginals? –  Corone Feb 27 at 10:37
The more common kinds of analysis would be some form of logistic or loglinear model, but it kind of sounds like you don't have the Y's to go with each full instance, which you'd need for that. –  Glen_b Feb 27 at 11:05

Only P(Y|Xn) and P(Xn) are available in practice.

For example, the Xn are "whether a user has visited a specific website", and Y is the gender. We have data of Xn, and we can buy the distribution of gender for some specific websites.

Now I'll try the following approach:

1. Assume that P(X1, X2, ..., Xn|Y) = P(X1|Y) P(X2|Y) ... P(Xn|Y), i.e. X1, X2, ..., Xn are independent given Y
2. Evaluate P(Xn|Y) according to P(Y|Xn) and P(Xn)

The following steps are straightforward.

Maybe there are better assumptions for this case.

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