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- Title
An exact approach to ridge regression for big data.
- Authors
Zhang, Tonglin; Yang, Baijian
- 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.
- Subjects
BIG data; RIDGE regression (Statistics); MATRICES (Mathematics); SUFFICIENT statistics; LIKELIHOOD ratio tests
- Publication
Computational Statistics, 2017, Vol 32, Issue 3, p909
- ISSN
0943-4062
- Publication type
Article
- DOI
10.1007/s00180-017-0731-5