Iterative reconstruction of high-dimensional Gaussian Graphical Models based on a new method to estimate partial correlations under constraints.

In the context of Gaussian Graphical Models (GGMs) with high-dimensional small sample data, we present a simple procedure, called PACOSE - standing for PArtial COrrelation SElection - to estimate partial correlations under the constraint that some of them are strictly zero. This method can also be extended to covariance selection. If the goal is to estimate a GGM, our new procedure can be applied to re-estimate the partial correlations after a first graph has been estimated in the hope to improve the estimation of non-zero coefficients. This iterated version of PACOSE is called iPACOSE. In a simulation study, we compare PACOSE to existing methods and show that the re-estimated partial correlation coefficients may be closer to the real values in important cases. Plus, we show on simulated and real data that iPACOSE shows very interesting properties with regards to sensitivity, positive predictive value and stability

Sparse covariance estimation in heterogeneous samples

Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous populations where such assumption is not satisfied, leading in turn to nonlinear relationships among variables. To tackle these problems we explore mixtures of GGMs; in particular, we consider both infinite mixture models of GGMs and infinite hidden Markov models with GGM emission distributions. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. The main advantage of considering infinite mixtures is that they allow us easily to estimate the number of number of subpopulations in the sample. As an illustration, we study the trends in exchange rate fluctuations in the pre-Euro era. This example demonstrates that the models are very flexible while providing extremely interesting interesting insights into real-life applications

Inferring cellular networks – a review

In this review we give an overview of computational and statistical methods to reconstruct cellular networks. Although this area of research is vast and fast developing, we show that most currently used methods can be organized by a few key concepts. The first part of the review deals with conditional independence models including Gaussian graphical models and Bayesian networks. The second part discusses probabilistic and graph-based methods for data from experimental interventions and perturbations

A survey of models for inference of gene regulatory networks

In this article, I present the biological backgrounds of microarray, ChIP-chip and ChIPSeq technologies and the application of computational methods in reverse engineering of gene regulatory networks (GRNs). The most commonly used GRNs models based on Boolean networks, Bayesian networks, relevance networks, differential and difference equations are described. A novel model for integration of prior biological knowledge in the GRNs inference is presented, too. The advantages and disadvantages of the described models are compared. The GRNs validation criteria are depicted. Current trends and further directions for GRNs inference using prior knowledge are given at the end of the paper