In This Exercise We Consider Inference In Two Layered Bayesian Networks With Logisti 2528136
In this exercise we consider inference in two-layered Bayesian networks with logistic CPDs. In these networks, all variables are binary. The variables X1, . . . , Xn in the top layer are all independent of each other. The variables Y1, . . . , Ym in the bottom layer depend on the variables in the top layer using a logistic CPD:
Suppose we observe some of the variables on the bottom layer, and we want to estimate the probability of the evidence.
a. Show that when computing the probability of evidence, we can remove variables Yi that are not observed.
b. Given evidence y, use the bound of equation (11.68) to write a variational upper bound of P(y).
c. Develop a mean field approximation to lower-bound the probability of the same evidence