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Open AccessArticle

Parameter Estimation with the Ordered 2 Regularization via an Alternating Direction Method of Multipliers

by Mahammad Humayoo 1,2,* and Xueqi Cheng 1,2
1
CAS Key Laboratory of Network Data Science & Technology, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China
2
University of Chinese Academy of Sciences, Beijing 100190, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(20), 4291; https://doi.org/10.3390/app9204291
Received: 9 September 2019 / Revised: 7 October 2019 / Accepted: 8 October 2019 / Published: 12 October 2019
(This article belongs to the Section Computing and Artificial Intelligence)
Regularization is a popular technique in machine learning for model estimation and for avoiding overfitting. Prior studies have found that modern ordered regularization can be more effective in handling highly correlated, high-dimensional data than traditional regularization. The reason stems from the fact that the ordered regularization can reject irrelevant variables and yield an accurate estimation of the parameters. How to scale up the ordered regularization problems when facing large-scale training data remains an unanswered question. This paper explores the problem of parameter estimation with the ordered 2 -regularization via Alternating Direction Method of Multipliers (ADMM), called ADMM-O 2 . The advantages of ADMM-O 2 include (i) scaling up the ordered 2 to a large-scale dataset, (ii) predicting parameters correctly by excluding irrelevant variables automatically, and (iii) having a fast convergence rate. Experimental results on both synthetic data and real data indicate that ADMM-O 2 can perform better than or comparable to several state-of-the-art baselines. View Full-Text
Keywords: ADMM; big data; feature selection; optimization; ridge regression; ordered regularization; elastic net ADMM; big data; feature selection; optimization; ridge regression; ordered regularization; elastic net
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Humayoo, M.; Cheng, X. Parameter Estimation with the Ordered 2 Regularization via an Alternating Direction Method of Multipliers. Appl. Sci. 2019, 9, 4291.

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