Problem
In this exercise, we show how to learn Markov networks with shared parameters, such as a relational Markov network (RMN).
a. Consider the log-linear model of example, where we assume that the Study-Pair relationship is determined in the relational skeleton. Thus, we have a single template feature, with a single weight, which is applied to all study pairs. Derive the likelihood function for this model, and the gradient.
b. Now provide a formula for the likelihood function and the gradient for a general RMN.