A quasi-Newton acceleration for high-dimensional optimization algorithms

Authors:
Hua Zhou;David Alexander;Kenneth Lange
Affiliations:
Department of Human Genetics, University of California, Los Angeles, USA 90095;Department of Biomathematics, University of California, Los Angeles, USA;Departments of Biomathematics, Human Genetics, and Statistics, University of California, Los Angeles, USA
Venue:
Statistics and Computing
Year:
2011

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Abstract

In many statistical problems, maximum likelihood estimation by an EM or MM algorithm suffers from excruciatingly slow convergence. This tendency limits the application of these algorithms to modern high-dimensional problems in data mining, genomics, and imaging. Unfortunately, most existing acceleration techniques are ill-suited to complicated models involving large numbers of parameters. The squared iterative methods (SQUAREM) recently proposed by Varadhan and Roland constitute one notable exception. This paper presents a new quasi-Newton acceleration scheme that requires only modest increments in computation per iteration and overall storage and rivals or surpasses the performance of SQUAREM on several representative test problems.