DBNScoreStep1: First order dependence graph G(1) inference

Description

Given a time series dataset for $p$ genes, this function infers a 1st order dependence score matrix S1 ($p \times p$) which contains the score of each edge of a Dynamic Bayesian Network (DAG G(1)) describing first order dependencies between successives variables. The smallest score points out the most significant edge for the 1st order dependence DAG G(1). The sets of both predictor and target genes can be reduced to different subsets of the $p$ genes. DBNScoreStep1 is the first step of the estimation procedure described in the references. See function DBNScoreStep2 to perform the second step selection and infer a score matrix describing full order dependencies.

Usage

DBNScoreStep1(data,method='ls',predPosition=NULL,targetPosition=NULL)

Arguments

data

a matrix with $n$ rows (=time points) and $p$ columns (=genes) containing the gene expression time series.

method

currently M estimation with either LS, Tukey bisquare or Huber estimator: c('ls','tukey','huber'), default='ls'.

predPosition

To be specified to reduce the set of possible predictor genes to a subset of $d

targetPosition

To be specified to reduce the set of possible target genes to a subset of $r

Value

$\mathrm{min}(r,p)$ rows (=target genes) and $\mathrm{min}(d,p)$ columns (=predictor genes) containing the scores S1 obtained with least square estimator, out$S1huber a matrix containing scores S1 obtained with Huber estimator, out$S1tukey a matrix containing scores S1 obtained with Tukey bisquare (or biweight) estimator.(out$S1ls[i,j] is the score for the edge $j \leftarrow i$ pointing out from predictor $j$ toward target $i$.)

References

Lebre, S. 2009. Inferring dynamic bayesian network with low order independencies, Statistical Applications in Genetics and Molecular Biology, 2009: Vol. 8: Iss. 1, Article 9.

Examples

Run this code

## load G1DBN Library
library(G1DBN)

data(arth800line)
data<-as.matrix(arth800line)
id<-c(60, 141, 260, 333, 365, 424, 441, 512, 521, 578, 789, 799)
names<-c("carbohydrate/sugar transporter","ATGPX2","putative integral
membrane prot" ,
"AT3G05900", "At3g27350", "At1g16720","ATISA3/ISA3","AT4G32190",
"catalase", "plasma membrane intrinsic prot", "At4g16146", "DPE2")

## compute score S1 
out<-DBNScoreStep1(data,method='ls', targetPosition=id,predPosition=id)
round(out$S1ls,2)


## Threshold for the selection of the edges after Step 1
alpha1=0.5
## Build the edges with id as label
edgesG1id<-BuildEdges(score=out$S1ls,threshold=alpha1,
                       targetNames=id,predNames=id,prec=6)
## Build the edges with names as label
edgesG1names<-BuildEdges(score=out$S1ls,threshold=alpha1,
                         targetNames=names,predNames=names,prec=6)
edgesG1id[1:15,]
edgesG1names[1:15,]


## compute score S2 from S1 
S2<-DBNScoreStep2(out$S1ls,data,method='ls',alpha1=alpha1,
                  predPosition=id,targetPosition=id)
S2

## Threshold for the selection of the edges after Step 2
alpha2=0.05
## Build the edges with id as label
edgesG2id<-BuildEdges(score=S2,threshold=alpha2,
                      targetNames=id,predNames=id,prec=6)
## Build the edges with names as label
edgesG2names<-BuildEdges(score=S2,threshold=alpha2,
                         targetNames=names,predNames=names,prec=6)
edgesG2id
edgesG2names


## As the number of genes is reduced to 10 here, this results slightly differ
## from the results obtained in the paper (Lebre, 2009) cited in References.


## ======================================
## PLOTTING THE RESULTS...
## ______________________________________
## Not run: 
# ## The Inferred Nets
# ## -----------------
# 
# ## Nodes coordinates are calculated according to the global structure of the graph
# all_parents=c(edgesG1id[,1], edgesG2id[,1])
# all_targets=c(edgesG1id[,2], edgesG2id[,2])
# posEdgesG1=1:dim(edgesG1id)[1]
# posEdgesG2=(dim(edgesG1id)[1]+1):length(all_targets)
# 
# ## Global network with all the edges
# netAll = graph.edgelist(cbind(as.character(all_parents),as.character(all_targets )))
# 
# ## Nodes coordinates
# nodeCoord=layout.fruchterman.reingold(netAll)
# 
# 
# split.screen(c(1,2))
# 
# # after Step 1
# screen(1)
# # set the edges list
# netG1 = graph.edgelist(cbind(as.character(edgesG1id[,1]),as.character(edgesG1id[,2])))
# # set the object for plotting the network with global coordinates of all nodes
# G1toPlot=delete.edges(netAll, E(netAll)[posEdgesG2] )
# # plot the network
# plot(G1toPlot, layout=nodeCoord, vertex.label = 
# get.vertex.attribute(G1toPlot , name="name"), edge.arrow.size = 0.2,
# main="G1DBN Inferred network:\n Step 1")
# 
# # after Step 2
# screen(2)
# # set the edges list
# 
# netG2 = graph.edgelist(cbind(as.character(edgesG2id[,1]),as.character(edgesG2id[,2])))
# # set the object for plotting the network with global coordinates of all nodes
# G2toPlot=delete.edges(netAll, E(netAll)[posEdgesG1] )
# # plot the network
# plot(G2toPlot, layout=nodeCoord, vertex.label = 
# get.vertex.attribute(G2toPlot , name="name"),edge.arrow.size = 0.2,
# main="G1DBN Inferred network:\n Step 2")
# 
# close.screen(all = TRUE)
# ## End(Not run)