INTERDISCIPLINARY STOCHASTIC PROCESSES COLLOQUIUM

Tuesday April 17, room 60 Evans, 4.10 - 5.00pm

Speaker: Kenneth Lange
(Biomathematics and Human Genetics, UCLA) 

Title: An Overview of the MM Algorithm

Abstract: 
Most problems in frequentist statistics involve optimization of a
function such as a likelihood or a sum of squares.  EM algorithms are
among the most effective algorithms for maximum likelihood estimation
because they consistently drive the likelihood uphill by maximizing a
simple surrogate function for the loglikelihood. Iterative
optimization of a surrogate function as exemplified by an EM
algorithm does not necessarily require missing data.  Indeed, every
EM algorithm is a special case of the more general class of MM
optimization algorithms, which typically exploit convexity rather
than missing data in majorizing or minorizing an objective
function.  MM algorithms deserve to be part of the standard toolkit
of every statistician. The current talk explains the principle behind
MM algorithms, suggests some methods for constructing them, and
discusses some of their attractive features. As time permits, I
discuss specific applications to quantile finding, Bradley-Terry
ranking, random graphs, transmission tomography, discriminant
analysis, and convex programming.