An improved shrinkage estimator to infer regulatory networks with Gaussian graphical models

Authors:
Kevin Kontos;Gianluca Bontempi
Affiliations:
Université Libre de Bruxelles, Brussels, Belgium;Université Libre de Bruxelles, Brussels, Belgium
Venue:
Proceedings of the 2009 ACM symposium on Applied Computing
Year:
2009

Citing 6
Cited 0

The Sample Average Approximation Method for Stochastic Discrete Optimization

SIAM Journal on Optimization
A well-conditioned estimator for large-dimensional covariance matrices

Journal of Multivariate Analysis
Sparse graphical models for exploring gene expression data

Journal of Multivariate Analysis
An empirical Bayes approach to inferring large-scale gene association networks

Bioinformatics
Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical gaussian models and bayesian networks

Bioinformatics
A Robust Procedure For Gaussian Graphical Model Search From Microarray Data With p Larger Than n

The Journal of Machine Learning Research

Quantified Score

Hi-index	0.00

Visualization

Abstract

Gaussian graphical models (GGMs) are widely used to tackle the important and challenging problem of inferring genetic regulatory networks from expression data. These models have gained much attention as they encode full conditional relationships between variables, i.e. genes. As a consequence, structure learning of a GGM requires an invertible and well-conditioned covariance matrix. Unfortunately, the usual estimator---the sample covariance matrix---is ill-suited in the "small n, large p" setting characteristic of microarray data. As an alternative, [9] proposed a shrinkage estimator that is both statistically efficient and computationally fast. The effectiveness of this estimator in bioinformatics has been illustrated by [12] who successfully used it to infer genetic regulatory networks from microarray data. Unfortunately, this improved estimator requires the shrinkage intensity to be estimated from the data, which is problematic in the "small n, large p" setting. Indeed, we show that the optimal shrinkage intensity estimator used in [9, 12] is biased. We propose a parametric bootstrap approach to estimate this bias and derive a "bias-corrected" shrinkage estimator. The applicability and usefulness of our estimator are demonstrated on both simulated and real expression data.