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An exact approach to ridge regression for big data

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Abstract

Ridge regression is an important approach in linear regression when explanatory variables are highly correlated. Although expressions of estimators of ridge regression parameters have been successfully obtained via matrix operation after observed data are standardized, they cannot be used to big data since it is impossible to load the entire data set to the memory of a single computer and it is hard to standardize the original observed data. To overcome these difficulties, the present article proposes new methods and algorithms. The basic idea is to compute a matrix of sufficient statistics by rows. Once the matrix is derived, it is not necessary to use the original data again. Since the entire data set is only scanned once, the proposed methods and algorithms can be extremely efficient in the computation of estimates of ridge regression parameters. It is expected that the basic knowledge gained in this article will have a great impact on statistical approaches to big data.

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Acknowledgements

The authors appreciate comments from the editor, an associate editor, and two anonymous reviewers, which significantly improve the quality of the article.

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Authors and Affiliations

  1. Department of Statistics, Purdue University, 250 North University Street, West Lafayette, IN, 47907-2066, USA

    Tonglin Zhang

  2. Department of Computer and Information Technology, Purdue University, 401 North Grant Street, West Lafayette, IN, 47907-2086, USA

    Baijian Yang

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  1. Tonglin Zhang
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  2. Baijian Yang
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Correspondence to Tonglin Zhang.

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Zhang, T., Yang, B. An exact approach to ridge regression for big data. Comput Stat 32, 909–928 (2017). https://doi.org/10.1007/s00180-017-0731-5

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  • DOI: https://doi.org/10.1007/s00180-017-0731-5

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