A globally convergent algorithm for a lasso-penalized mixture of linear regression models

Lloyd-Jones, Luke R., Nguyen, Hien D. and McLachlan, Geoffrey J. (2017) A globally convergent algorithm for a lasso-penalized mixture of linear regression models. Computational Statistics and Data Analysis, 119 19-38. doi:10.1016/j.csda.2017.09.003

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Author Lloyd-Jones, Luke R.
Nguyen, Hien D.
McLachlan, Geoffrey J.
Title A globally convergent algorithm for a lasso-penalized mixture of linear regression models
Journal name Computational Statistics and Data Analysis   Check publisher's open access policy
ISSN 0167-9473
Publication date 2017-09-20
Year available 2017
Sub-type Article (original research)
DOI 10.1016/j.csda.2017.09.003
Open Access Status File (Author Post-print)
Volume 119
Start page 19
End page 38
Total pages 20
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Language eng
Subject 2613 Statistics and Probability
2605 Computational Mathematics
1703 Computational Theory and Mathematics
2604 Applied Mathematics
Abstract Variable selection is an old and pervasive problem in regression analysis. One solution is to impose a lasso penalty to shrink parameter estimates toward zero and perform continuous model selection. The lasso-penalized mixture of linear regressions model (L-MLR) is a class of regularization methods for the model selection problem in the fixed number of variables setting. A new algorithm is proposed for the maximum penalized-likelihood estimation of the L-MLR model. This algorithm is constructed via the minorization–maximization algorithm paradigm. Such a construction allows for coordinate-wise updates of the parameter components, and produces globally convergent sequences of estimates that generate monotonic sequences of penalized log-likelihood values. These three features are missing in the previously presented approximate expectation–maximization algorithms. The previous difficulty in producing a globally convergent algorithm for the maximum penalized-likelihood estimation of the L-MLR model is due to the intractability of finding exact updates for the mixture model mixing proportions in the maximization-step. This issue is resolved by showing that it can be converted into a simple numerical root finding problem that is proven to have a unique solution. The method is tested in simulation and with an application to Major League Baseball salary data from the 1990s and the present day, where the concept of whether player salaries are associated with batting performance is investigated.
Keyword Lasso
Mixture of linear regressions model
MM algorithm
Major League Baseball
Q-Index Code C1
Q-Index Status Provisional Code
Grant ID DE170101134
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Wed, 25 Oct 2017, 15:04:08 EST by Professor Geoff Mclachlan on behalf of Mathematics