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Biostatistics (2004), 5, 3, pp. 329-340
Biostatistics Vol. 5 No. 3 © Oxford University Press 2004; all rights reserved.

Efficient quadratic regularization for expression arrays

Trevor Hastie* and Robert Tibshirani

Departments of Statistics, and Health Research & Policy, Stanford University, Sequoia Hall, CA 94305, USA
hastie{at}stanford.edu

* To whom correspondence should be addressed.

Gene expression arrays typically have 50 to 100 samples and 1000 to 20 000 variables (genes). There have been many attempts to adapt statistical models for regression and classification to these data, and in many cases these attempts have challenged the computational resources. In this article we expose a class of techniques based on quadratic regularization of linear models, including regularized (ridge) regression, logistic and multinomial regression, linear and mixture discriminant analysis, the Cox model and neural networks. For all of these models, we show that dramatic computational savings are possible over naive implementations, using standard transformations in numerical linear algebra.

Keywords: Eigengenes; Euclidean methods; Quadratic regularization; SVD


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