SCHEME: Stochastically convergent heuristical Expectation Maximization estimation

This paper introduces a modification to the EM (Expectation Maximization) algorithm potentially allowing reliable convergence to the ML (Maximum Likelihood) parameter estimate for a set of previously intractable problems. The modification is based on the MCEM (Monte Carlo EM) algorithm, which substitutes sample averages for the explicit calculation of expectation. A problem with previous algorithms is that the number of samples required for convergence and the generally convergence behavior was uncertain. Using information geometric principles, we arrive at a new formulation that ensures convergence with probability one. Further, we begin an investigation attempting to minimize the number of samples required to obtain an acceptable approximation of the ML estimate. This algorithm is well suited to solve numerous challenging statistical problems.