Convergence of Expectation-Maximization Algorithm with Mixed-Integer Optimization

The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters comprise both discrete and continuous variables, making the convergence analysis nontrivial. This paper introduces a set of conditions that ensure the convergence of a specific class of EM algorithms that estimate a mixture of discrete and continuous parameters. Our results offer a new analysis technique for iterative algorithms that solve mixed-integer …

algorithm algorithms analysis continuity continuous convergence eess.sp expectation-maximization function likelihood making mixed optimization paper parameters set stat.ml variables