B0632
Title: Tolerance values for stopping rules
Authors: Alexa Sochaniwsky - McMaster University (Canada) [presenting]
Paul McNicholas - McMaster University (Canada)
Abstract: Iterative algorithms, such as the expectation-maximization (EM) algorithm and its many variants, are used for maximum likelihood estimation. Such algorithms are stopped using a stopping rule that depends on the difference between two quantities. This research will see the development of context-specific values for epsilon, where epsilon is some pre-specified "small" number. These values are often selected to be $10^{-c}$ where $c$ is a fixed number; this choice often leads to an unnecessary number of iterations or sub-optimal solutions. Two options are proposed, one that uses the order of magnitude of the log-likelihood and the second that ties a BIC-inspired value in early iterations of the algorithm to the value of epsilon. These tolerance values are tested in several algorithms including EM's for mixture models of the multivariate and matrix-variate normal distributions, and hidden Markov models.
