Maximum Conditional Likelihood via Bound Maximization and the CEM Algorithm

Tony Jebara, Alex Pentland

Abstract: We present the CEM (Conditional Expectation Maximi::ation) al(cid:173) gorithm as an extension of the EM (Expectation M aximi::ation) algorithm to conditional density estimation under missing data. A bounding and maximization process is given to specifically optimize conditional likelihood instead of the usual joint likelihood. We ap(cid:173) ply the method to conditioned mixture models and use bounding techniques to derive the model's update rules . Monotonic conver(cid:173) gence, computational efficiency and regression results superior to EM are demonstrated.