Network estimation in State Space Model with L1-regularization constraint

Biological networks have arisen as an attractive paradigm of genomic science ever since the introduction of large scale genomic technologies which carried the promise of elucidating the relationship in functional genomics. Microarray technologies coupled with appropriate mathematical or statistical models have made it possible to identify dynamic regulatory networks or to measure time course of the expression level of many genes simultaneously. However one of the few limitations fall on the high-dimensional nature of such data coupled with the fact that these gene expression data are known to include some hidden process. In that regards, we are concerned with deriving a method for inferring a sparse dynamic network in a high dimensional data setting. We assume that the observations are noisy measurements of gene expression in the form of mRNAs, whose dynamics can be described by some unknown or hidden process. We build an input-dependent linear state space model from these hidden states and demonstrate how an incorporated $L_{1}$ regularization constraint in an Expectation-Maximization (EM) algorithm can be used to reverse engineer transcriptional networks from gene expression profiling data. This corresponds to estimating the model interaction parameters. The proposed method is illustrated on time-course microarray data obtained from a well established T-cell data. At the optimum tuning parameters we found genes TRAF5, JUND, CDK4, CASP4, CD69, and C3X1 to have higher number of inwards directed connections and FYB, CCNA2, AKT1 and CASP8 to be genes with higher number of outwards directed connections. We recommend these genes to be object for further investigation. Caspase 4 is also found to activate the expression of JunD which in turn represses the cell cycle regulator CDC2.Comment: arXiv admin note: substantial text overlap with arXiv:1308.359

Penalized EM algorithm and copula skeptic graphical models for inferring networks for mixed variables

In this article, we consider the problem of reconstructing networks for continuous, binary, count and discrete ordinal variables by estimating sparse precision matrix in Gaussian copula graphical models. We propose two approaches: $\ell_1$ penalized extended rank likelihood with Monte Carlo Expectation-Maximization algorithm (copula EM glasso) and copula skeptic with pair-wise copula estimation for copula Gaussian graphical models. The proposed approaches help to infer networks arising from nonnormal and mixed variables. We demonstrate the performance of our methods through simulation studies and analysis of breast cancer genomic and clinical data and maize genetics data

Model-based clustering for populations of networks

Until recently obtaining data on populations of networks was typically rare. However, with the advancement of automatic monitoring devices and the growing social and scientific interest in networks, such data has become more widely available. From sociological experiments involving cognitive social structures to fMRI scans revealing large-scale brain networks of groups of patients, there is a growing awareness that we urgently need tools to analyse populations of networks and particularly to model the variation between networks due to covariates. We propose a model-based clustering method based on mixtures of generalized linear (mixed) models that can be employed to describe the joint distribution of a populations of networks in a parsimonious manner and to identify subpopulations of networks that share certain topological properties of interest (degree distribution, community structure, effect of covariates on the presence of an edge, etc.). Maximum likelihood estimation for the proposed model can be efficiently carried out with an implementation of the EM algorithm. We assess the performance of this method on simulated data and conclude with an example application on advice networks in a small business.Comment: The final (published) version of the article can be downloaded for free (Open Access) from the editor's website (click on the DOI link below

Estimating Network Kinetics of the MAPK/ERK Pathway Using Biochemical Data

The MAPK/ERK pathway is a major signal transduction system which regulates many fundamental cellular processes including the growth control and the cell death. As a result of these roles, it has a crucial importance in cancer as well as normal developmental processes. Therefore, it has been intensively studied resulting in a wealth of knowledge about its activation. It is also well documented that the activation kinetics of the pathway is crucial to determine the nature of the biological response. However, while individual biochemical steps are well characterized, it is still difficult to predict or even understand how the activation kinetics works. The aim of this paper is to estimate the stochastic rate constants of the MAPK/ERK network dynamics. Accordingly, taking a Bayesian approach, we combined underlying qualitative biological knowledge in several competing dynamic models via sets of quasireactions and estimated the stochastic rate constants of these reactions. Comparing the resulting estimates via the BIC and DIC criteria, we chose a biological model which includes EGFR degradation—Raf-MEK-ERK cascade without the involvement of RKIPs.

De novo construction of polyploid linkage maps using discrete graphical models

Linkage maps are used to identify the location of genes responsible for traits and diseases. New sequencing techniques have created opportunities to substantially increase the density of genetic markers. Such revolutionary advances in technology have given rise to new challenges, such as creating high-density linkage maps. Current multiple testing approaches based on pairwise recombination fractions are underpowered in the high-dimensional setting and do not extend easily to polyploid species. We propose to construct linkage maps using graphical models either via a sparse Gaussian copula or a nonparanormal skeptic approach. Linkage groups (LGs), typically chromosomes, and the order of markers in each LG are determined by inferring the conditional independence relationships among large numbers of markers in the genome. Through simulations, we illustrate the utility of our map construction method and compare its performance with other available methods, both when the data are clean and contain no missing observations and when data contain genotyping errors and are incomplete. We apply the proposed method to two genotype datasets: barley and potato from diploid and polypoid populations, respectively. Our comprehensive map construction method makes full use of the dosage SNP data to reconstruct linkage map for any bi-parental diploid and polyploid species. We have implemented the method in the R package netgwas.Comment: 25 pages, 7 figure

Reproducing kernel Hilbert space based estimation of systems of ordinary differential equations

Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models in many branches of science they have not been the focus of systematic statistical analysis until recently. In this work we propose a general approach to estimate the parameters of systems of differential equations measured with noise. Our methodology is based on the maximization of the penalized likelihood where the system of differential equations is used as a penalty. To do so, we use a Reproducing Kernel Hilbert Space approach that allows to formulate the estimation problem as an unconstrained numeric maximization problem easy to solve. The proposed method is tested with synthetically simulated data and it is used to estimate the unobserved transcription factor CdaR in Steptomyes coelicolor using gene expression data of the genes it regulates.Comment: 16 pages, 6 figure

Identifying overlapping terrorist cells from the Noordin Top actor-event network

Actor-event data are common in sociological settings, whereby one registers the pattern of attendance of a group of social actors to a number of events. We focus on 79 members of the Noordin Top terrorist network, who were monitored attending 45 events. The attendance or non-attendance of the terrorist to events defines the social fabric, such as group coherence and social communities. The aim of the analysis of such data is to learn about the affiliation structure. Actor-event data is often transformed to actor-actor data in order to be further analysed by network models, such as stochastic block models. This transformation and such analyses lead to a natural loss of information, particularly when one is interested in identifying, possibly overlapping, subgroups or communities of actors on the basis of their attendances to events. In this paper we propose an actor-event model for overlapping communities of terrorists, which simplifies interpretation of the network. We propose a mixture model with overlapping clusters for the analysis of the binary actor-event network data, called {\tt manet}, and develop a Bayesian procedure for inference. After a simulation study, we show how this analysis of the terrorist network has clear interpretative advantages over the more traditional approaches of affiliation network analysis.Comment: 24 pages, 5 figures; related R package (manet) available on CRA

A penalized inference approach to stochastic block modelling of community structure in the Italian Parliament

We analyse bill cosponsorship networks in the Italian Chamber of Deputies. In comparison with other parliaments, a distinguishing feature of the Chamber is the large number of political groups. Our analysis aims to infer the pattern of collaborations between these groups from data on bill cosponsorships. We propose an extension of stochastic block models for edge-valued graphs and derive measures of group productivity and of collaboration between political parties. As the model proposed encloses a large number of parameters, we pursue a penalized likelihood approach that enables us to infer a sparse reduced graph displaying collaborations between political parties

Generalized information criterion for model selection in penalized graphical models

This paper introduces an estimator of the relative directed distance between an estimated model and the true model, based on the Kulback-Leibler divergence and is motivated by the generalized information criterion proposed by Konishi and Kitagawa. This estimator can be used to select model in penalized Gaussian copula graphical models. The use of this estimator is not feasible for high-dimensional cases. However, we derive an efficient way to compute this estimator which is feasible for the latter class of problems. Moreover, this estimator is, generally, appropriate for several penalties such as lasso, adaptive lasso and smoothly clipped absolute deviation penalty. Simulations show that the method performs similarly to KL oracle estimator and it also improves BIC performance in terms of support recovery of the graph. Specifically, we compare our method with Akaike information criterion, Bayesian information criterion and cross validation for band, sparse and dense network structures