Dynamic Selection of Tolerance Values for Iterative Likelihood Based Algorithms

Abstract

Iterative algorithms, such as the expectation-maximization (EM) algorithm and its many variants, are used for parameter estimation. Such algorithms are stopped us- ing a stopping rule that depends on the difference between two quantities. As the EM is a maximum likelihood estimation technique, the likelihood is monotonically increasing, and the parameter estimates improve at each iteration. Thus, stopping rules commonly rely on the difference between the likelihood or parameter estimates at the current and previous iteration becoming smaller than some pre-specified toler- ance value. This value is often selected as 10−c where c is a fixed number. Due to the arbitrary nature of this value, an unnecessary number of iterations or sub-optimal solutions can occur. This research will see the development of a context-specific value of epsilon, where epsilon is a dynamic likelihood-based tolerance value. The pro- posed stopping criterion is tested in the context of mixture model-based clustering and compared to other common tolerance values.