Consider a classification problem where we are trying to predict the binary class labely{0,1} given the input x.

Assume x has two parts e.g. x=(x1,x2)Twherex2{0,1} and we already know the distribution p(x2y).

derive a classifierp(yx) which explicitly takes advantage of this known distribution but makes no other assumption about the date. Explicitly define what other distributions we need to estimate from the data. Ifx1 is a discrete variable with Kchoices(x1{1,2,...K}) and we want to avoid making more assumptions about the data, what are the forms of the distributions and how many parameters do we need to estimate?