An Upper Bound on the Global Optimum in Parameter Estimation

Learning graphical model parameters from incomplete data is a non-convex optimization problem. Iterative algorithms, such as Expectation Maximization (EM), can be used to get a local optimum solution. However, little is known about the quality of the learned local optimum, compared to the unknown global optimum. We exploit variables that are always observed in the dataset to get an upper bound on the global optimum which can give insight into the quality of the parameters learned by estimation algorithms.