Regularization theory and neural networks architectures
Neural Computation
Expected classification error of the Fisher linear classifier with pseudo-inverse covariance matrix
Pattern Recognition Letters
Sparse graphical models for exploring gene expression data
Journal of Multivariate Analysis
An introduction to ROC analysis
Pattern Recognition Letters - Special issue: ROC analysis in pattern recognition
A Robust Procedure For Gaussian Graphical Model Search From Microarray Data With p Larger Than n
The Journal of Machine Learning Research
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Motivation: The inference, or 'reverse-engineering', of gene regulatory networks from expression data and the description of the complex dependency structures among genes are open issues in modern molecular biology. Results: In this paper we compared three regularized methods of covariance selection for the inference of gene regulatory networks, developed to circumvent the problems raising when the number of observations n is smaller than the number of genes p. The examined approaches provided three alternative estimates of the inverse covariance matrix: (a) the 'PINV' method is based on the Moore-Penrose pseudoinverse, (b) the 'RCM' method performs correlation between regression residuals and (c) '@?"2"C' method maximizes a properly regularized log-likelihood function. Our extensive simulation studies showed that @?"2"C outperformed the other two methods having the most predictive partial correlation estimates and the highest values of sensitivity to infer conditional dependencies between genes even when a few number of observations was available. The application of this method for inferring gene networks of the isoprenoid biosynthesis pathways in Arabidopsis thaliana allowed to enlighten a negative partial correlation coefficient between the two hubs in the two isoprenoid pathways and, more importantly, provided an evidence of cross-talk between genes in the plastidial and the cytosolic pathways. When applied to gene expression data relative to a signature of HRAS oncogene in human cell cultures, the method revealed 9 genes (p-value