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Title: Component contribution maximization: An estimation approach for stochastic expectation-maximization Authors:  Alexander Sharp - University of Waterloo (Canada) [presenting]
Ryan Browne - University of Waterloo (Canada)
Abstract: The Stochastic EM algorithm replaces the E-step with a Monte Carlo approximation, trading monotonicity for the potential to escape local maxima. A consequence is that the final parameter value returned by the algorithm is no longer guaranteed to be the best estimate. Common solutions include averaging the tail of the chain, or choosing the value associated with the largest likelihood value. We prove that when the model parameter is a scalar, this second estimator is asymptotically Laplace distributed and consistent for the maximum likelihood estimate (mle), with a convergence rate that is square the convergence rate of the average. We further show, however, that as the parameter dimension increases, this estimator becomes bounded arbitrarily far from the mle. In light of this shortcoming, a new estimator for the high dimensional parameter case is proposed, which we show is consistent and successfully achieves the faster convergence rate previously observed only in the single-dimensional case. We demonstrate through multiple simulation studies the increased performance this estimator provides over topical approaches.