Maximum Entropy modelling - likelihood equation
I'd merely add a comment if I could ...

What is your interpretation of p(y|x)? The usual expression is "the probability of y given x", i.e. the dependent variable corresponding to the independent variable in the probability distribution. This is the function you want to maximize, not the inverse function.

As a side note, there are two ways that the entropy form of the equation on the right can be used. This can be added to a cost function as a regularization kernel, with a modulating coefficient; or it can be the primary term in the cost function -- the entropy to be maximized -- with constraints from the physical system introduced with Lagrange multipliers.