Networks.Fast: Fast Algorithm for Bayesian Network Discovery
In BANFF: Bayesian Network Feature Finder

Description Usage Arguments Details Value Examples

Fast Algorithm for Bayesian Network Discovery

Networks.Fast(pvalue, net, iter = 5000, nburns = 2000,
  algorithms = c("EM", "DPM"), v = 20, DPM.mcmc = list(nburn = 2000, nsave
  = 1, nskip = 0, ndisplay = 10), DPM.prior = list(a0 = 2, b0 = 1, m2 = rep(0,
  1), s2 = diag(1e+05, 1), psiinv2 = solve(diag(0.5, 1)), nu1 = 4, nu2 = 4, tau1
  = 1, tau2 = 100), DPparallel = FALSE, n.cores = 1, piall = c(0.8, 0.85,
  0.9, 0.95), rhoall = c(1, 2, 5, 10, 15), show.steps = 10,
  showlikelihood = FALSE, likelihood.frequency = 100)

`pvalue`	a vector of p-values obtained from large scale statistical hypothesis testing
`net`	a n by n network configuration, n is the length of pvalue
`iter`	number of iterations. The default is 5000
`nburns`	number of burn-in. The default is 2000
`algorithms`	vector, either "EM" or "DPM"
`v`	number of iterations set for DPM fitting by "DPdensity". v is only valid when you choose initals as "DPdensity"
`DPM.mcmc`	a list
`DPM.prior`	a list
`DPparallel`	logical.
`n.cores`	number of cores
`piall`	a vector of selections of pi0. The default vector is 0.75, 0.8, 0.85, 0.9. The selections of pi0 should be placed in sequence, from smaller to larger.
`rhoall`	a vector of selections of rho0 and rho1. The default vector is 1, 2, 5, 10, 15. The selections of rho0 and rho1 should be placed in sequence, from smaller to larger.
`show.steps`	number, default=10
`showlikelihood`	logical, default=FALSE
`likelihood.frequency`	number, default=100

This generic function fits a Bayesian Nonparametric Mixture Model for gene selection incorporating network information (Zhao et al., 2014):

r_i| g_i, theta ~ N(mu_g_i, sigma_g_i),
g_i | z_i=k, q_k ~ Discrete(a_k, q_k),
theta ~ G_0k, for g in a_k,
q_k ~ Dirichlet(tau_k 1_L_k/L_k),
theta=theta_g_g in a_0 and a_1
theta_g=(mu_g, sigma_g)

where we define

Index: a_0=(-L_0+1,-L_0+2,...,0) , a_1=(1,2,...,L_1) and the correspondent probability q_0=(q_-L_0+1, q_-L_0+2, ...,q_0), q_1=(q_1, q_2, ..., q_L_1), according to the defination of Discrete(a_k, b_k), for example, Pr(g_i=L_0+2)=q_-L_0+2.
Assumption: We have an assumption that "selected" gene or image pixel should have larger statiscs comparing to "unselected" ones without the loss of generality. In this regard, we set the restriction mu_g<mu_g+1 for g=-L_0+1, -L_0+2,...,L_1.

For this function, The NET-DPM-3, considered as Fast function is applied , and more details about the algorithm can be referred from Appnendix B.3 of Zhao et al., 2014

a list cantaining Bayesian Statistics information of the distribution of zi

trace: a n by (iter-nburns) matrix (n is the length of elements and iter-nburns is the length of the saved chain), showing the evolution of the chain for each element
mean: the mean of the distribution for each element
median: the median of the distribution for each element
var: the variance of the distribution for each element
quantile: the quantiles of the distribution for each element

## Not run: 
####Example1. For a 10X10 image with 5X5 signal for example
##Creating the network of 10X10 image
library(igraph)
library(BayesNetDiscovery)
g <- graph.lattice(length=10,dim=2)
##the input of argument \code{net}
net=as(get.adjacency(g,attr=NULL),"matrix")
## Assign the signal elements with signal intenstion as normal distribution N(1,0.2). 
## While noise is set as N(0,0.2) 
newz=rep(0,100)
for (i in 3:7)
{
 newz[(i*10+3):(i*10+7)]=1
}
testcov<-0
for(i in 1:100){
 if(newz[i]==0){
   testcov[i]<-rnorm(1,mean=0,sd=0.2)
 }else{
  testcov[i]<-rnorm(1,mean=1,sd=0.2)
 }
}
##The profile of the impage
image(matrix(testcov,10,10),col=gray(seq(0,1,length=255)))
##Transform the signals into pvalue form and begin identification
pvalue=pnorm(-testcov)
total2=Networks.Fast(pvalue,net,iter=5000,piall=c(0.8, 0.85, 0.9, 0.95),
rhoall=c(0.5,1,5,10,15))




####Example.2 Gene Network discovery
##Generating Scale free Gene Network
library(igraph)
library(BayesNetDiscovery)
g <- barabasi.game(50, power=1, zero.appeal=1.5,directed = F)
tkplot(g, layout=layout.kamada.kawai)
net=as(get.adjacency(g,attr=NULL),"matrix")
##Random assign selected genes and make the signal intension as gaussian mixture
newz=rep(c(1,0,0,1,0),10)
Simnorm=function(n){
  weight = c(0.4, 0.6)
  mu = c(5,4)
  sigma = c(1,0.5)
  z = sample(c(1,2),size=n, prob=weight,replace=TRUE)
  r = rnorm(n,mean=mu[z],sd=sigma[z])
  return(r)
}
testcov<-0
for(i in 1:50){
  if(newz[i]==0){
    testcov[i]<-rnorm(1,mean=0,sd=1)
   }else{
  testcov[i]<-Simnorm(1)
  }
}
pvalue=pnorm(-testcov)
total1=Networks.Fast(pvalue,net,iter=5000,v=20,piall=c(0.8, 0.85, 0.9, 0.95),
rhoall=c(1, 2, 5, 10, 15))

## End(Not run)