Seminar by Alexander Sharp

Please Note: This seminar will be held online.

Characterizing the Asymptotic Properties of SEMmax Parameter Estimation

The Expectation-Maximization (EM) algorithm, first introduced by Dempster et al. (1977), is a well known numerical algorithm used to perform maximum likelihood estimation. Since its conception, many modifications to the EM algorithm have been proposed, including one notable modification known as the Stochastic Expectation-Maximization algorithm (SEM). First theorized by Celeux and Diebolt (1985), SEM replaces the E-step of the original EM algorithm with a Monte Carlo approximation, introducing some randomness into the algorithm’s behaviour (hence “Stochastic”). As a result, the algorithm no longer converges to a point, but instead bounces around, spending lots of time in areas of high density. The result of running SEM is therefore a sequence of parameter estimates. The task of the practitioner is to figure out how to use this sequence to generate a single, good estimate. One common method is to simply take the average of all estimates in the resulting sequence. This procedure is dubbed "SEMmean" by Biernacki et al. (2003), and its theoretical properties were studied in Nielsen (2000). Another option is to just pluck the estimate from the sequence which corresponds to the largest likelihood value and use that as the best estimate. This approach is referred to as the "SEMmax" strategy. Unlike SEMmean, the theoretical properties of SEMmax have not been formally explored. Our research aims to fill that void. In this talk I will discuss the progress and ideas we've had so far in characterizing these properties. Do note that this represents a work in progress, which means I will be discussing mostly incomplete, but nonetheless promising, research lines for solving this problem.