Classification based on several marginal probability

Question

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.

Answer 1

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.