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Inferring large-scale covariance matrices from sparse genomic data  is an ubiquitous problem in bioinformatics. Clearly, the widely used  standard covariance and correlation estimators are  ill-suited for this purpose. As statistically efficient and computationally fast alternative we propose a novel shrinkage  covariance estimator that exploits the Ledoit-Wolf (2003) lemma  for analytic calculation of the optimal shrinkage intensity.Subsequently, we apply this improved covariance estimator (which has guaranteed minimum mean squared error, is well-conditioned, and is always positive definite even for small sample sizes) to the problem of inferring large-scale gene association networks.  We show that it performs very favorably compared to competing approaches both in simulations as well as in application to real expression data.

A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics