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An exact approach to ridge regression for big data

Author

Listed:
  • Tonglin Zhang

    (Purdue University)

  • Baijian Yang

    (Purdue University)

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.

Suggested Citation

  • Tonglin Zhang & Baijian Yang, 2017. "An exact approach to ridge regression for big data," Computational Statistics, Springer, vol. 32(3), pages 909-928, September.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-017-0731-5
    DOI: 10.1007/s00180-017-0731-5
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    References listed on IDEAS

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    1. Haimao Zhan & Shizhong Xu, 2012. "Adaptive Ridge Regression for Rare Variant Detection," PLOS ONE, Public Library of Science, vol. 7(8), pages 1-12, August.
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    Cited by:

    1. Salomi du Plessis & Mohammad Arashi & Gaonyalelwe Maribe & Salomon M. Millard, 2023. "Efficient Estimation and Validation of Shrinkage Estimators in Big Data Analytics," Mathematics, MDPI, vol. 11(22), pages 1-11, November.

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