A Block Minorization-Maximization Algorithm for Heteroscedastic Regression

The computation of the maximum likelihood (ML) estimator for heteroscedastic regression models is considered. The traditional Newton algorithms for the problem require matrix multiplications and inversions, which are bottlenecks in modern Big Data contexts. A new Big Data-appropriate minorization-ma...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 23; no. 8; pp. 1131 - 1135
Main Authors: Nguyen, Hien D., Lloyd-Jones, Luke R., McLachlan, Geoffrey J.
Format: Journal Article
Language:English
Published: New York IEEE 01.08.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Big data
Biological system modeling
Computation
Computational modeling
Computer simulation
Convergence
Estimators
Heteroscedastic regression
Inversions
Mathematical analysis
Mathematical models
maximum likelihood (ML) estimation
Maximum likelihood estimation
minorization–maximization (MM) algorithm
parallel algorithm
Regression
Signal processing algorithms
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary:The computation of the maximum likelihood (ML) estimator for heteroscedastic regression models is considered. The traditional Newton algorithms for the problem require matrix multiplications and inversions, which are bottlenecks in modern Big Data contexts. A new Big Data-appropriate minorization-maximization (MM) algorithm is considered for the computation of the ML estimator. The MM algorithm is proved to generate monotonically increasing sequences of likelihood values and to be convergent to a stationary point of the log-likelihood function. A distributed and parallel implementation of the MM algorithm is presented, and the MM algorithm is shown to have differing time complexity to the Newton algorithm. Simulation studies demonstrate that the MM algorithm improves upon the computation time of the Newton algorithm in some practical scenarios where the number of observations is large.
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2016.2586180