Note that the objective function in Equation 5, if written in the additive form, leads to a cost function reminiscent of the one used in constraint-driven learning algorithm (CoDL) (Chang et al., 2007) (and similarly, posterior regularization (Ganchev et al., 2010), which we will discuss later at Section 6).
in CoDL, the following cost function is involved in its EM-like inference procedure: where Y c defines the set of y's that all satisfy a certain constraint c, and d defines a distance function from y to that set.