Joint UConn/UMass
STATISTICS COLLOQUIUM
Patrick Flaherty, Assistant Professor
Department of Mathematics and Statistics
University of Massachusetts
Amherst
MAP Estimation for the Gaussian Mixture Model via Modern Optimization Methods
ABSTRACT
The Gaussian mixture model is a prototype for studying model-based clustering methods and a practical tool for real data analysis. The maximum likelihood or maximum a-posteriori (MAP) parameter estimates are typically estimated using the expectation-maximization (EM) algorithm. Viewed from the perspective of an optimization problem, we know that the EM algorithm can be viewed as a solution of a particular relaxation of a mixed-integer nonlinear optimization problem. Taking this optimization perspective further, we find that many other methods for estimating the parameters can be viewed as particular relaxations of the optimization problem. Using the optimization perspective, we develop some novel methods for MAP estimation for the Gaussian mixture model. These methods naturally handle complex prior constraints that would be difficult to formulate using standard distributions. Though this is a work in progress, we show some numerical experiments that give us confidence that the approach can be made scalable to large data sets.
DATE: Wednesday, April 10, 2019
TIME: 4:00 pm - 5:00 pm
PLACE: Philip E. Austin Bldg., Rm. 108
Coffee will be served at 3:30 pm, AUST 326
Pizza after colloquium, AUST 326
For more information, contact: Tracy Burke at tracy.burke@uconn.edu