Accession Number:

ADA621745

Title:

Mechanism of UV-Induced Damage to Mammalian Collagen

Descriptive Note:

Final rept. 13 Sep 2010-12 Sep 2014

Corporate Author:

MOREHOUSE SCHOOL OF MEDICINE ATLANTA GA

Personal Author(s):

Report Date:

2014-12-12

Pagination or Media Count:

50.0

Abstract:

We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts a treatment of these algorithms at the population level in the limit of infinite data, followed by results that apply to updates based on a finite set of samples. First, we characterize the domain of attraction of any global maximizer of the population likelihood. This characterization is based on a novel view of the EM updates as a perturbed form of likelihood ascent, or in parallel, of the gradient EM updates as a perturbed form of standard gradient ascent. Leveraging this characterization, we then provide non-asymptotic guarantees on the EM and gradient EM algorithms when applied to a finite set of samples. We develop consequences of our general theory for three canonical examples of incomplete-data problems mixture of Gaussians, mixture of regressions, and linear regression with covariates missing completely at random. In each case, our theory guarantees that with a suitable initialization, a relatively small number of EM or gradient EM steps will yield with high probability an estimate that is within statistical error of the MLE. We provide simulations to confirm this theoretically predicted behavior.

Subject Categories:

  • Biochemistry
  • Anatomy and Physiology
  • Physical Chemistry

Distribution Statement:

APPROVED FOR PUBLIC RELEASE