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R/EBHMMNBfun.R
In EBSeqHMM: Bayesian analysis for identifying gene or isoform expression changes in ordered RNA-seq experiments
Defines functions
EBHMMNBfun
Documented in
EBHMMNBfun
#' @title Baum-Welch algorithm for a single hidden markov chain
#' @usage EBHMMNBfun(Data,NgVector=NULL,Conditions, sizeFactors,
#' PriorFC=1.5,homo=TRUE, maxround=5,
#' Pi0=NULL, Tran=NULL,NoTrend=FALSE, NumTranStage=3,
#' FCParam=NULL, AlphaIn=NULL,BetaIn=NULL,
#' StateNames=c("Up","NC","Down"),
#' EM=TRUE, UpdateParam=TRUE, Print=TRUE,
#' OnlyQ=FALSE,WithinCondR=TRUE,
#' PenalizeLowMed=TRUE, PenalizeLowMedQt=.2,PenalizeLowMedVal=10)
#' @param Data input data, rows are genes/isoforms and columns are samples
#' @param NgVector Ng vector; NULL for gene level data
#' @param Conditions A factor indicates the condition (time/spatial point) which each sample belongs to.
#' @param sizeFactors a vector indicates library size factors
#' @param Tran initial values for transition matrices
#' @param Pi0 initial values for starting probabilities
#' @param NumTranStage number of states
#' @param PriorFC target FC for gridient change
#' @param StateNames name of the hidden states
#' @param homo whether the chain is assumed to be homogenious
#' @param maxround max number of iteration
#' @param AlphaIn,BetaIn If the parameters are known and the user
#' doesn't want to estimate them from the data, user may
#' specify them here.
#' @param NoTrend if NoTrend=TRUE, initial transition probabilities will be set to be equal
#' @param FCParam not in use
#' @param EM Whether estimate the prior parameters of the beta distribution by EM
#' @param UpdateParam Whether update starting probabilities and transition probabilities
#' @param OnlyQ If OnlyQ=TRUE, the function will only return estimated q's.
#' @param WithinCondR By defining WithinCondR=TRUE, estimation of r's are obtained within each condition. (WithinCondR=FALSE is not suggested here)
#' @param Print Whether print the elapsed-time while running the test.
#' @param PenalizeLowMed,PenalizeLowMedQt,PenalizeLowMedVal
#' Transcripts with median quantile < = PenalizeLowMedQt will be penalized
#' @author Ning Leng
#' @examples
#' data(GeneExampleData)
#' CondVector <- rep(paste("t",1:5,sep=""),each=3)
#' Conditions <- factor(CondVector, levels=c("t1","t2","t3","t4","t5"))
#' Sizes <- MedianNorm(GeneExampleData)
#' tmp <- EBHMMNBfun(Data=GeneExampleData, sizeFactors=Sizes, Conditions=Conditions,
#' maxround=2, OnlyQ=TRUE)
#' @details EBHMMNBfun() function implements the Balm-Welch algorithm that estimates the starting probabilities and transition probabilities
#' of a single hidden Markov model. Here the emission distribution of each gene is assumed to be a
#' Beta-Negative Binomial distribution with parameters (r_g, alpha, beta)
#' , in which alpha and beta are shared by all the genes and r_g is gene specific.
#' If not specified, r_g, alpha and beta will be estimated using method of moments.
#' For isoform data, we assume isoforms from the same Ig group share the same beta^Ig. alpha is shared by all the isoforms and r_gi is isoform specific.
#' The user also needs to specify an expected FC.
#' @return MAPTerm: the most likely path of each gene/isoform. MAPTermNum: numeric version of MAPTerm.
#'
#' AllTerm: all possible expression paths considered in the model. PP: posterior probability of being each expression path.
#'
#' WhichMax: index of the most likely path. Allf: prior probability of being each path.
#'
#' Pi0Track: estimated starting probabilities of each iteration.
#'
#' TranTrack: estimated transition probabilities of each iteration.
#'
#' AlphaTrack, BetaTrack: estimated alpha and beta(s).
#'
#' LLAll=PostSumForLL.Sum: log likelihood of the model.
EBHMMNBfun <- function(
Data,NgVector=NULL,Conditions, sizeFactors,
PriorFC=1.5,homo=TRUE, maxround=5,
Pi0=NULL, Tran=NULL,NoTrend=FALSE, NumTranStage=3,
FCParam=NULL, AlphaIn=NULL,BetaIn=NULL,
StateNames=c("Up","NC","Down"),
EM=TRUE, UpdateParam=TRUE, Print=TRUE, OnlyQ=FALSE,WithinCondR=TRUE,
PenalizeLowMed=TRUE, PenalizeLowMedQt=.2,PenalizeLowMedVal=10
){
Dataraw <- Data
AllZeroNames <- which(rowMeans(Data)==0)
NotAllZeroNames <- which(rowMeans(Data)>0)
if(length(AllZeroNames)>0 & Print==TRUE) cat("Remove transcripts with all zero \n")
Data <- Data[NotAllZeroNames,]
if(!is.null(NgVector))NgVector <- NgVector[NotAllZeroNames]
if(is.null(NgVector))NgVector <- rep(1,nrow(Data))
if(!is.factor(Conditions))Conditions <- as.factor(Conditions)
#Rename Them
IsoNamesIn <- rownames(Data)
Names <- paste("I",c(1:dim(Data)[1]),sep="")
names(IsoNamesIn) <- Names
rownames(Data) <- paste("I",c(1:dim(Data)[1]),sep="")
names(NgVector) <- paste("I",c(1:dim(Data)[1]),sep="")
if(!length(sizeFactors)==ncol(Data)){
rownames(sizeFactors) <- rownames(Data)
colnames(sizeFactors) <- Conditions
}
NumOfNg <- nlevels(as.factor(NgVector))
NameList <- sapply(1:NumOfNg,function(i)Names[NgVector==i],simplify=FALSE)
names(NameList) <- paste("Ng",c(1:NumOfNg),sep="")
NotNone <- NULL
for (i in 1:NumOfNg) {
if (length(NameList[[i]])!=0)
NotNone <- c(NotNone,names(NameList)[i])
}
NameList <- NameList[NotNone]
NumCond <- nlevels(Conditions)
CondLevels <- levels(Conditions)
NoneZeroLength <- nlevels(as.factor(NgVector))
NameList <- sapply(1:NoneZeroLength,function(i)names(NgVector)[NgVector==i],simplify=FALSE)
DataList <- sapply(1:NoneZeroLength , function(i) Data[NameList[[i]],],simplify=FALSE)
names(DataList) <- names(NameList)
NumEachGroup <- sapply(1:NoneZeroLength , function(i)dim(DataList)[i])
# Unlist
DataList.unlist <- do.call(rbind, DataList)
# Divide by SampleSize factor
if(length(sizeFactors)==ncol(Data))
DataList.unlist.dvd <- t(t( DataList.unlist)/sizeFactors)
if(length(sizeFactors)!=ncol(Data))
DataList.unlist.dvd <- DataList.unlist/sizeFactors
# Calculate R for all conditions
# median for conditions
PairRList <- vector("list",NumCond-1)
MedList <- matrix(0,ncol=NumCond,nrow=nrow(DataList.unlist))
rownames(MedList) <- rownames(DataList.unlist)
for (lv in 1:(NumCond-1)){
idx1 <- which(Conditions==levels(Conditions)[lv])
idx2 <- which(Conditions==levels(Conditions)[lv+1])
t1 <- matrix(DataList.unlist[,idx1],nrow=dim(DataList.unlist)[1])
t2 <- matrix(DataList.unlist[,idx2],nrow=dim(DataList.unlist)[1])
tmpdata <- cbind(t1,t2)
rownames(tmpdata) <- rownames(DataList.unlist)
Cond.use <- as.factor(as.vector(Conditions)[c(idx1,idx2)])
PairRList[[lv]] <- EBTest_ext(Data=tmpdata,NgVector=NgVector,
Conditions=Cond.use,sizeFactors=sizeFactors[c(idx1,idx2)],
maxround=5, OnlyCalcR=TRUE,Print=FALSE)
tt1 <- matrix(DataList.unlist.dvd[,idx1],nrow=dim(DataList.unlist)[1])
tt2 <- matrix(DataList.unlist.dvd[,idx2],nrow=dim(DataList.unlist)[1])
MedList[,i] <- apply(tt1,1,median)
MedList[,i+1] <- apply(tt2,1,median)
}
# if only need Q
if(OnlyQ==TRUE)return(PairRList)
# Only use genes with R in all conditions
NamesInR <- sapply(PairRList,function(i)names(unlist(i[[1]])),simplify=FALSE)
GoodData0 <- Reduce(intersect, NamesInR)
GoodData <- rownames(DataList.unlist)# consider all
NotIn <- setdiff(rownames(DataList.unlist), GoodData)
# Only Use Data has Good q's
DataList.In <- sapply(1:NoneZeroLength, function(i)DataList[[i]][GoodData[GoodData%in%rownames(DataList[[i]])],],simplify=FALSE)
DataList.NotIn <- sapply(1:NoneZeroLength, function(i)DataList[[i]][NotIn[NotIn%in%rownames(DataList[[i]])],],simplify=FALSE)
DataListIn.unlist <- do.call(rbind, DataList.In)
DataListNotIn.unlist <- do.call(rbind, DataList.NotIn)
MedList.In <- MedList[GoodData,]
# R for good ones
# pairwise R
RPairsListIn <- vector("list",NumCond-1)
for(lv in 1:(NumCond-1)){
RPairsListIn[[lv]] <- sapply(1:NoneZeroLength,
function(i){
tmpname <- GoodData0[GoodData0%in%rownames(DataList[[i]])]
tmp1 <- PairRList[[lv]][[1]][[i]][tmpname]
tmpMean <- PairRList[[lv]][[2]][[i]][tmpname]
tmpVar <- PairRList[[lv]][[3]][[i]][tmpname]
NAOnes <- which(is.na(tmp1)|tmp1<0)
#print(length(NAOnes))
PNotIn <- 1-10^-6
R.NotIn <- tmpMean[NAOnes]*PNotIn/(1-PNotIn)
R.out <- tmp1
R.out[NAOnes] <- R.NotIn
R.out
R.norm <- rep(100, nrow(DataList[[i]]))
names(R.norm) <- rownames(DataList[[i]])
R.norm[names(R.out)] <- R.out
R.norm
})
# not pairwise
if(WithinCondR==TRUE){
# If calculate R from t-1 but not jointly
RPairsListIn[[lv]] <- sapply(1:NoneZeroLength,
function(i){
tmpname <- GoodData0[GoodData0%in%rownames(DataList[[i]])]
tmpMean <- PairRList[[lv]]$C1Mean[[i]][tmpname]
tmpVar <- PairRList[[lv]]$C1EstVar[[i]][tmpname]
tmpQ <- PairRList[[lv]]$QList1[[i]][tmpname]
tmp1 <- tmpMean*tmpQ/(1-tmpQ)
NAOnes <- which(is.na(tmp1)|tmp1<0)
#print(length(NAOnes))
PNotIn <- 1-10^-6
R.NotIn <- tmpMean[NAOnes]*PNotIn/(1-PNotIn)
R.out <- tmp1
R.out[NAOnes] <- R.NotIn
R.out
R.norm <- rep(100, nrow(DataList[[i]]))
names(R.norm) <- rownames(DataList[[i]])
R.norm[names(R.out)] <- R.out
R.norm
})
}
}
RPairsListIn.unlist.raw <- sapply(1:(NumCond-1),function(lv)unlist(RPairsListIn[[lv]]))
rownames(RPairsListIn.unlist.raw) <- rownames(DataListIn.unlist)
# Penalty on R
if(PenalizeLowMed==FALSE)RPairsListIn.unlist <- RPairsListIn.unlist.raw
if(PenalizeLowMed==TRUE){
RPairsListIn.unlist <- RPairsListIn.unlist.raw
MedQt <- apply(MedList.In,2,function(jj)quantile(jj,PenalizeLowMedQt))
for(kk in 1:(NumCond-1)){
WhichLowMed <- which(MedList.In[,kk]<=MedQt[kk])
RPairsListIn.unlist[WhichLowMed,kk] <- RPairsListIn.unlist.raw[WhichLowMed,kk]* PenalizeLowMedVal
}
}
NumOfEachGroupIn <- sapply(1:NoneZeroLength, function(i)max(0,dim(DataList.In[[i]])[1]))
NumOfEachGroupNotIn <- sapply(1:NoneZeroLength, function(i)max(0,dim(DataList.NotIn[[i]])[1]))
# Remove any transcripts with Input NA
NumPPDim <- NumTranStage
#NumGene <- nrow(DataList.In[[1]])
NumGene <- nrow(DataListIn.unlist)
NumPoints <- NumCond-1
NamesGene <- rownames(DataListIn.unlist)
NamesTranStage <- paste("St",1:NumTranStage,sep="")
NamesPoints <- paste("Pt",1:NumPoints,sep="")
#GeneNameMap <- NamesGene
#names(GeneNameMap) <- IsoNamesIn
GeneNameMap <- IsoNamesIn
if(is.null(Pi0)){Pi0 <- rep(1/NumTranStage, NumTranStage)}
# transition matrix.. homo
# define as from rowname to colname
if(is.null(Tran)&&homo==TRUE){
if(NumTranStage==2){
if(NoTrend==FALSE)Tran <- matrix(c(.7,.3,.3,.7), ncol=NumTranStage,nrow=NumTranStage)
if(NoTrend==TRUE)Tran <- matrix(c(.5,.5,.5,.5), ncol=NumTranStage,nrow=NumTranStage)
}
if(NumTranStage==3){
if(NoTrend==FALSE)Tran <- matrix(c(.6,.2,.2,.2,.6,.2,.2,.2,.6),
ncol=NumTranStage,nrow=NumTranStage)
if(NoTrend==TRUE)Tran <- matrix(c(.5,.5,.5,.5,.5,.5,.5,.5,.5),
ncol=NumTranStage,nrow=NumTranStage)
}
}
# non-homo, 3d matrix, third dim is T-1 transitions
if(is.null(Tran)&&homo==FALSE){
if(NumTranStage==2){
Tran <- array(1/NumTranStage, dim=c(NumTranStage,NumTranStage,NumPoints-1))
if(NoTrend==FALSE) for(i in 1:(NumPoints-1))Tran[,,i] <- c(.7,.3,.3,.7)
if(NoTrend==TRUE) for(i in 1:(NumPoints-1))Tran[,,i] <- c(.5,.5,.5,.5)
}
if(NumTranStage==3){
Tran <- array(1/NumTranStage, dim=c(NumTranStage,NumTranStage,NumPoints-1))
if(NoTrend==FALSE)for(i in 1:(NumPoints-1))Tran[,,i] <- c(.6,.2,.2,.2,.6,.2,.2,.2,.6)
if(NoTrend==FALSE)for(i in 1:(NumPoints-1))Tran[,,i] <- c(.5,.5,.5,.5,.5,.5,.5,.5,.5)
}
}
# Beta parameter
# Time points x Dim
if(is.null(FCParam)){
if(NumTranStage==2)FCParam <- cbind(c(1/sqrt(PriorFC), sqrt(PriorFC)),
c(sqrt(PriorFC), 1/sqrt(PriorFC)))
if(NumTranStage==3)FCParam <- cbind(c(1/sqrt(PriorFC),1, sqrt(PriorFC)),
c(sqrt(PriorFC),1, 1/sqrt(PriorFC)))
if(WithinCondR==TRUE){
# If within condition R based on t-1
if(NumTranStage==2)FCParam <- cbind(c(1, 1),
c(PriorFC, 1/PriorFC))
if(NumTranStage==3)FCParam <- cbind(c(1,1, 1),
c(PriorFC,1, 1/PriorFC))
}
}
AlphaIn <- 1
BetaIn <- rep(1,NoneZeroLength)
# Name them
rownames(FCParam) <- NamesTranStage
if(homo==TRUE)rownames(Tran)=colnames(Tran)=NamesTranStage
if(homo==FALSE){
dimnames(Tran)[[1]]=dimnames(Tran)[[2]]=NamesTranStage
dimnames(Tran)[[3]] <- paste("Cp",1:(NumPoints-1),sep="")
}
TranTrack <- list(Tran)
FCParamTrack <- list(FCParam)
Pi0Track <- Pi0
AlphaTrack <- AlphaIn
BetaTrack <- BetaIn
################################
# Iter
################################
for (iter in 1:maxround){
Time.start <- proc.time()[3]
# Forward
# rows are States; cols are genes
B <- sapply(1:NumPoints,function(pp)
sapply(1:NumTranStage,function(ss){
idx1 <- which(Conditions==levels(Conditions)[pp])
idx2 <- which(Conditions==levels(Conditions)[pp+1])
#
t1 <- matrix(DataListIn.unlist[,idx1],nrow=dim(DataListIn.unlist)[1])
t2 <- matrix(DataListIn.unlist[,idx2],nrow=dim(DataListIn.unlist)[1])
tmpdata <- cbind(t1,t2)
rownames(tmpdata) <- rownames(DataListIn.unlist)
Rtmp1 <- outer(RPairsListIn.unlist[,pp],sizeFactors[idx1])
Rtmp2 <- outer(RPairsListIn.unlist[,pp],sizeFactors[idx2])
Log <- f0(tmpdata,
AlphaIn=AlphaIn, BetaIn=BetaIn,
cbind(Rtmp1*FCParam[ss,1],
Rtmp2*FCParam[ss,2]), NumOfGroups=NumOfEachGroupIn, log=FALSE)
}),simplify=FALSE)
for(i in 1:NumPoints){
B[[i]] <- t(B[[i]])
rownames(B[[i]]) <- NamesTranStage
colnames(B[[i]]) <- NamesGene
}
# alpha_g,0 = pi_i * b_i (O_g)
# row gene column stages
Alpha0 <- B[[1]]*Pi0
Alpha.tmp <- Alpha0
AlphaMat <- NULL
AlphaMat <- list(Alpha0)
# step
for (ctr in 2:(NumPoints)){
if(homo==TRUE)
Sumpart <- t(Tran)%*%Alpha.tmp
if(homo==FALSE)
Sumpart <- t(Tran[,,ctr-1])%*%Alpha.tmp
Alpha.upd <- Sumpart*B[[ctr]]
Alpha.tmp <- Alpha.upd
AlphaMat <- c(AlphaMat,list(Alpha.upd))
}
# P (O| lambda)= sum_i alpha_T-1 (i)
#P_O_lmbda=colSums(Alpha.upd)
#Back
Beta_T1 <- matrix(1,ncol=NumGene,nrow=NumTranStage)
Beta.tmp <- Beta_T1
BetaMat <- vector("list",NumPoints)
BetaMat[[NumPoints]] <- Beta_T1
if(is.null(Tran)&&homo==TRUE){Tran <- matrix(1/NumTranStage, ncol=NumTranStage,nrow=NumTranStage)}
# non-homo, 3d matrix, third dim is T-1 transitions
for(ctr in (NumPoints-1):1){
if(homo==TRUE)tranuse <- Tran
if(homo==FALSE)tranuse <- Tran[,,ctr]
tmpupd <- B[[ctr+1]]*Beta.tmp
Beta.upd <- tranuse%*%tmpupd
Beta.tmp <- Beta.upd
BetaMat[[ctr]] <- Beta.tmp
}
# T-1 elements
# col genes row states
Gamma_i_num <- sapply(1:(NumPoints-1),function(i)AlphaMat[[i]]*BetaMat[[i]],simplify=FALSE)
Gamma_i_denom <- sapply(1:(NumPoints-1),function(i)colSums(Gamma_i_num[[i]]))
Gamma_i <- sapply(1:(NumPoints-1),function(i)t(t(Gamma_i_num[[i]])/Gamma_i_denom[,i]),simplify=FALSE)
# Update Pi and Tran
Pi.Up.allgene <- Gamma_i[[1]]
Pi.Up <- rowMeans(Pi.Up.allgene,na.rm=TRUE)
# Sum g first
#Gamma_i_sumg <- sapply(1:(NumPoints),function(i)rowSums(Gamma_i_num[[i]],na.rm=TRUE))
#Pi.Up <- Gamma_i_sumg[,1]/sum(Gamma_i_sumg[,1],na.rm=TRUE)
# dims: i, j, T-1, g
Gamma_ij_array_raw = Eta_ij_array_raw=
array(data=NA,dim=c(NumTranStage, NumTranStage, NumPoints-1, NumGene))
for(i in 1:NumTranStage){
for(j in 1:NumTranStage){
for(k in 1:(NumPoints-1)){
for(l in 1:NumGene){
if(homo==TRUE)tranuse <- Tran
if(homo==FALSE)tranuse <- Tran[,,k]
Gamma_ij_array_raw[i,j,k,l] <- tranuse[i,j]*AlphaMat[[k]][i,l]*BetaMat[[k+1]][j,l]*B[[k+1]][j,l]
}}
}
}
# eta first... then Sum g first!
for(i in 1:NumTranStage){
for(j in 1:NumTranStage){
for(k in 1:(NumPoints-1)){
for(l in 1:NumGene){
Eta_ij_array_raw[i,j,k,l] <- Gamma_ij_array_raw[i,j,k,l]/sum(Gamma_ij_array_raw[,,k,l],na.rm=TRUE)
}}
}
}
Eta_ij_array_raw_sumg <- apply(Eta_ij_array_raw,c(1,2,3),function(oo)sum(oo,na.rm=TRUE))
Eta_ij_array_raw_sumgj <- sapply(1:(NumPoints-1),function(i)rowSums(Eta_ij_array_raw_sumg[,,i],
na.rm=TRUE),simplify=FALSE)
if(homo==FALSE){
Tran.Up.raw <- sapply(1:(NumPoints-1),function(i)
Eta_ij_array_raw_sumg[,,i]/Eta_ij_array_raw_sumgj[[i]],
simplify=FALSE)
Tran.Up <- array(data=NA,dim=c(NumTranStage, NumTranStage, NumPoints-1))
for(i in 1:(NumPoints-1))Tran.Up[,,i] <- Tran.Up.raw[[i]]
}
if(homo==TRUE){
Eta_ij_array_raw_sumgt <- apply(Eta_ij_array_raw_sumg,c(1,2),function(oo)sum(oo,na.rm=TRUE))
Eta_ij_array_raw_sumgjt_raw <- do.call(cbind,Eta_ij_array_raw_sumgj)
Eta_ij_array_raw_sumgjt <- rowSums(Eta_ij_array_raw_sumgjt_raw, na.rm=TRUE)
Tran.Up <- Eta_ij_array_raw_sumgt/Eta_ij_array_raw_sumgjt
}
##############################
#Optim
if (EM==TRUE){
StartValue <- c(AlphaIn, BetaIn)
AlphaToEMraw <- do.call(cbind, AlphaMat)* do.call(cbind, BetaMat)
AlphaToEM <- as.vector(t(AlphaToEMraw))
#print(summary(AlphaToEM))
AlphaToEM[which(is.na(AlphaToEM))] <- 10^-6
AlphaToEM[which(AlphaToEM==Inf)] <- 10^6
InputPool <- list(DataListIn.unlist, AlphaToEM, NumPoints,
NumGene, NumTranStage, RPairsListIn.unlist, sizeFactors,
Conditions, NumOfEachGroupIn, FCParam)
###################
Result<-optim(par=StartValue,fn=LikefunNBHMM,InputPool=InputPool)
out1 <- Result[[1]]
AlphaIn <- out1[1]
BetaIn <- out1[2:(1+length(NumOfEachGroupIn))]
AlphaTrack <- c(AlphaTrack,AlphaIn)
BetaTrack <- rbind(BetaTrack,BetaIn)
}
if(UpdateParam==TRUE){
Pi0Track <- rbind(Pi0Track,Pi.Up)
TranTrack <- c(TranTrack,list(Tran.Up))
Pi0 <- Pi.Up
Tran <- Tran.Up
}
Time.end <- proc.time()[3]
Time.use <- Time.end-Time.start
cat(paste("\n iteration","time",round(Time.use,1), "\n"))
}
#############
# R for all
# NA take mean of others
#############
RPairsListAll <- matrix(NA,ncol=(NumCond-1),nrow=nrow(DataList.unlist))
rownames(RPairsListAll) <- rownames(DataList.unlist)
for(lv in 1:(NumCond-1)){
tmpName <- names(unlist(PairRList[[lv]][[1]]))
tmp1 <- unlist(PairRList[[lv]][[1]])
tmpMean <- unlist(PairRList[[lv]][[2]])
NAOnes <- which(is.na(tmp1)|tmp1<0)
PNotIn <- 1-10^-6
R.NotIn <- tmpMean[NAOnes]*PNotIn/(1-PNotIn)
R.out <- tmp1
R.out[NAOnes] <- R.NotIn
RPairsListAll[tmpName,lv] <- R.out
}
RMean <- rowMeans(RPairsListAll,na.rm=TRUE)
WhichNA <- which(is.na(RPairsListAll),arr.ind=TRUE)
if(nrow(WhichNA)>0)for(i in 1:nrow(WhichNA))RPairsListAll[WhichNA[i]] <- RMean[WhichNA[i,1]]
# Penalty on R
if(PenalizeLowMed==FALSE)RPairsListAllPen <- RPairsListAll
if(PenalizeLowMed==TRUE){
RPairsListAllPen <- RPairsListAll
MedQt <- apply(MedList,2,function(jj)quantile(jj,PenalizeLowMedQt))
for(kk in 1:(NumCond-1)){
WhichLowMed <- which(MedList[,kk]<=MedQt[kk])
RPairsListAllPen[WhichLowMed,kk] <- RPairsListAll[WhichLowMed,kk]* PenalizeLowMedVal
}
}
AllStList <- vector("list",NumPoints-1)
for(i in 1: (NumPoints))AllStList[[i]] <- StateNames
AllPosi <- expand.grid(AllStList)
LogB <- sapply(1:NumPoints,function(pp)
sapply(1:NumTranStage,function(ss){
idx1 <- which(Conditions==levels(Conditions)[pp])
idx2 <- which(Conditions==levels(Conditions)[pp+1])
t1 <- matrix(DataList.unlist[,idx1],nrow=dim(DataList.unlist)[1])
t2 <- matrix(DataList.unlist[,idx2],nrow=dim(DataList.unlist)[1])
tmpdata <- cbind(t1,t2)
rownames(tmpdata) <- rownames(DataList.unlist)
Rtmp1 <- outer(RPairsListAllPen[,pp],sizeFactors[idx1])
Rtmp2 <- outer(RPairsListAllPen[,pp],sizeFactors[idx2])
Log <- f0(tmpdata,
AlphaIn=AlphaIn, BetaIn=BetaIn,
cbind(Rtmp1*FCParam[ss,1],
Rtmp2*FCParam[ss,2]), NumOfGroups=NumOfEachGroupIn+NumOfEachGroupNotIn, log=TRUE)
}),simplify=FALSE)
for(i in 1:NumPoints){
LogB[[i]] <- t(LogB[[i]])
rownames(LogB[[i]]) <- NamesTranStage
colnames(LogB[[i]]) <- rownames(DataList.unlist)
}
AlllogPost <- sapply(1:nrow(AllPosi),function(i){
logPi0.use <- log(Pi0[AllPosi[i,1]])
logB.use <- sapply(1:NumPoints,function(j)LogB[[j]][AllPosi[i,j],])
# gene by time
logB.sumtime <- rowSums(logB.use)
if(homo==TRUE)tran.use <- sapply(1:(NumPoints-1),function(j)Tran[as.numeric(AllPosi[i,j]),as.numeric(AllPosi[i,j+1])])
if(homo==FALSE)tran.use <- sapply(1:(NumPoints-1),function(j)Tran[as.numeric(AllPosi[i,j]),as.numeric(AllPosi[i,j+1]),j])
logtran.sum=sum(log(tran.use))
logPi0.use+logB.sumtime+logtran.sum
})
AlllogPost.Max <- apply(AlllogPost,1,max)
PostSum <- apply(exp(AlllogPost),1,sum)
Which0 <- which(PostSum==0)
AlllogPost.Adj0 <- AlllogPost
if(length(Which0)>0)AlllogPost.Adj0[Which0,] <- AlllogPost[Which0,]-AlllogPost.Max[Which0]
PostSum.Adj0 <- rowSums(exp(AlllogPost.Adj0))
PPraw <- exp(AlllogPost.Adj0)/PostSum.Adj0
PP <- PPraw
LogPostSum.Adj0 <- log(PostSum.Adj0)
LogPostSum <- LogPostSum.Adj0
if(length(Which0)>0)LogPostSum[Which0] <- LogPostSum.Adj0[Which0]+AlllogPost.Max[Which0]
#PP[which(is.na(PP),arr.ind=TRUE)]=-Inf
WhichMax <- apply(PP,1,function(oo){
tt <- which.max(oo)
if(length(tt)>0)out <- tt
if(length(tt)==0)out <- NA
out})
WhichMax.NonNA.ind <- which(!is.na(WhichMax))
WhichMax.NonNA <- WhichMax[WhichMax.NonNA.ind]
MatTerm <- AllPosi[WhichMax.NonNA,]
rownames(MatTerm) <- rownames(Data)[WhichMax.NonNA.ind]
AllStListNum <- vector("list",NumPoints-1)
for(i in 1: (NumPoints))AllStListNum[[i]] <- 1:2
AllPosiNum <- expand.grid(AllStListNum)
MatTermNum <- AllPosiNum[WhichMax.NonNA,]
rownames(MatTermNum) <- rownames(Data)[WhichMax.NonNA.ind]
PostSumForLL <- log(PostSum)
ISNA <- which(PostSumForLL==-Inf | is.na(PostSumForLL))
#print(ISNA)
if(length(ISNA)>0)ISNOTNA <- c(1:length(PostSumForLL))[-ISNA]
if(length(ISNA)==0)ISNOTNA <- c(1:length(PostSumForLL))
Min.ISNOT <- min(PostSumForLL[ISNOTNA])
PostSumForLL[ISNA] <- Min.ISNOT
PostSumForLL.Sum <- sum(PostSumForLL)
NameOut <- as.character(IsoNamesIn[rownames(PP)])
#message(str(NameOut))
rownames(MatTerm) = rownames(MatTermNum)=
NameOut[WhichMax.NonNA.ind]
rownames(PP)=
names(WhichMax)=names(LogPostSum)=
names(PostSum)=rownames(AlllogPost)=
NameOut
tmp <- AllPosi
tmpL <- levels(tmp[[1]])
qq <- sapply(1:nrow(tmp),function(i)paste0(tmpL[as.numeric(tmp[i,])],collapse="-"))
colnames(PP) <- qq
out <- list(MAPTerm=MatTerm, MAPTermNum=MatTermNum,
AllTerm=AllPosi, PP=PP, WhichMax=WhichMax, Allf=AlllogPost,
Pi0Track=Pi0Track,
TranTrack=TranTrack,
AlphaTrack=AlphaTrack,
BetaTrack=BetaTrack,
GeneNameMap=GeneNameMap,
LogLike=LogPostSum,
LL=PostSum, LLAll=PostSumForLL.Sum
)
}
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Defines functions EBHMMNBfun
Documented in EBHMMNBfun
#' @title Baum-Welch algorithm for a single hidden markov chain
#' @usage EBHMMNBfun(Data,NgVector=NULL,Conditions, sizeFactors,
#' PriorFC=1.5,homo=TRUE, maxround=5,
#' Pi0=NULL, Tran=NULL,NoTrend=FALSE, NumTranStage=3,
#' FCParam=NULL, AlphaIn=NULL,BetaIn=NULL,
#' StateNames=c("Up","NC","Down"),
#' EM=TRUE, UpdateParam=TRUE, Print=TRUE,
#' OnlyQ=FALSE,WithinCondR=TRUE,
#' PenalizeLowMed=TRUE, PenalizeLowMedQt=.2,PenalizeLowMedVal=10)
#' @param Data input data, rows are genes/isoforms and columns are samples
#' @param NgVector Ng vector; NULL for gene level data
#' @param Conditions A factor indicates the condition (time/spatial point) which each sample belongs to.
#' @param sizeFactors a vector indicates library size factors
#' @param Tran initial values for transition matrices
#' @param Pi0 initial values for starting probabilities
#' @param NumTranStage number of states
#' @param PriorFC target FC for gridient change
#' @param StateNames name of the hidden states
#' @param homo whether the chain is assumed to be homogenious
#' @param maxround max number of iteration
#' @param AlphaIn,BetaIn If the parameters are known and the user
#' doesn't want to estimate them from the data, user may
#' specify them here.
#' @param NoTrend if NoTrend=TRUE, initial transition probabilities will be set to be equal
#' @param FCParam not in use
#' @param EM Whether estimate the prior parameters of the beta distribution by EM
#' @param UpdateParam Whether update starting probabilities and transition probabilities
#' @param OnlyQ If OnlyQ=TRUE, the function will only return estimated q's.
#' @param WithinCondR By defining WithinCondR=TRUE, estimation of r's are obtained within each condition. (WithinCondR=FALSE is not suggested here)
#' @param Print Whether print the elapsed-time while running the test.
#' @param PenalizeLowMed,PenalizeLowMedQt,PenalizeLowMedVal
#' Transcripts with median quantile < = PenalizeLowMedQt will be penalized
#' @author Ning Leng
#' @examples
#' data(GeneExampleData)
#' CondVector <- rep(paste("t",1:5,sep=""),each=3)
#' Conditions <- factor(CondVector, levels=c("t1","t2","t3","t4","t5"))
#' Sizes <- MedianNorm(GeneExampleData)
#' tmp <- EBHMMNBfun(Data=GeneExampleData, sizeFactors=Sizes, Conditions=Conditions,
#' maxround=2, OnlyQ=TRUE)
#' @details EBHMMNBfun() function implements the Balm-Welch algorithm that estimates the starting probabilities and transition probabilities
#' of a single hidden Markov model. Here the emission distribution of each gene is assumed to be a
#' Beta-Negative Binomial distribution with parameters (r_g, alpha, beta)
#' , in which alpha and beta are shared by all the genes and r_g is gene specific.
#' If not specified, r_g, alpha and beta will be estimated using method of moments.
#' For isoform data, we assume isoforms from the same Ig group share the same beta^Ig. alpha is shared by all the isoforms and r_gi is isoform specific.
#' The user also needs to specify an expected FC.
#' @return MAPTerm: the most likely path of each gene/isoform. MAPTermNum: numeric version of MAPTerm.
#'
#' AllTerm: all possible expression paths considered in the model. PP: posterior probability of being each expression path.
#'
#' WhichMax: index of the most likely path. Allf: prior probability of being each path.
#'
#' Pi0Track: estimated starting probabilities of each iteration.
#'
#' TranTrack: estimated transition probabilities of each iteration.
#'
#' AlphaTrack, BetaTrack: estimated alpha and beta(s).
#'
#' LLAll=PostSumForLL.Sum: log likelihood of the model.
EBHMMNBfun <- function(
Data,NgVector=NULL,Conditions, sizeFactors,
PriorFC=1.5,homo=TRUE, maxround=5,
Pi0=NULL, Tran=NULL,NoTrend=FALSE, NumTranStage=3,
FCParam=NULL, AlphaIn=NULL,BetaIn=NULL,
StateNames=c("Up","NC","Down"),
EM=TRUE, UpdateParam=TRUE, Print=TRUE, OnlyQ=FALSE,WithinCondR=TRUE,
PenalizeLowMed=TRUE, PenalizeLowMedQt=.2,PenalizeLowMedVal=10
){
Dataraw <- Data
AllZeroNames <- which(rowMeans(Data)==0)
NotAllZeroNames <- which(rowMeans(Data)>0)
if(length(AllZeroNames)>0 & Print==TRUE) cat("Remove transcripts with all zero \n")
Data <- Data[NotAllZeroNames,]
if(!is.null(NgVector))NgVector <- NgVector[NotAllZeroNames]
if(is.null(NgVector))NgVector <- rep(1,nrow(Data))
if(!is.factor(Conditions))Conditions <- as.factor(Conditions)
#Rename Them
IsoNamesIn <- rownames(Data)
Names <- paste("I",c(1:dim(Data)[1]),sep="")
names(IsoNamesIn) <- Names
rownames(Data) <- paste("I",c(1:dim(Data)[1]),sep="")
names(NgVector) <- paste("I",c(1:dim(Data)[1]),sep="")
if(!length(sizeFactors)==ncol(Data)){
rownames(sizeFactors) <- rownames(Data)
colnames(sizeFactors) <- Conditions
}
NumOfNg <- nlevels(as.factor(NgVector))
NameList <- sapply(1:NumOfNg,function(i)Names[NgVector==i],simplify=FALSE)
names(NameList) <- paste("Ng",c(1:NumOfNg),sep="")
NotNone <- NULL
for (i in 1:NumOfNg) {
if (length(NameList[[i]])!=0)
NotNone <- c(NotNone,names(NameList)[i])
}
NameList <- NameList[NotNone]
NumCond <- nlevels(Conditions)
CondLevels <- levels(Conditions)
NoneZeroLength <- nlevels(as.factor(NgVector))
NameList <- sapply(1:NoneZeroLength,function(i)names(NgVector)[NgVector==i],simplify=FALSE)
DataList <- sapply(1:NoneZeroLength , function(i) Data[NameList[[i]],],simplify=FALSE)
names(DataList) <- names(NameList)
NumEachGroup <- sapply(1:NoneZeroLength , function(i)dim(DataList)[i])
# Unlist
DataList.unlist <- do.call(rbind, DataList)
# Divide by SampleSize factor
if(length(sizeFactors)==ncol(Data))
DataList.unlist.dvd <- t(t( DataList.unlist)/sizeFactors)
if(length(sizeFactors)!=ncol(Data))
DataList.unlist.dvd <- DataList.unlist/sizeFactors
# Calculate R for all conditions
# median for conditions
PairRList <- vector("list",NumCond-1)
MedList <- matrix(0,ncol=NumCond,nrow=nrow(DataList.unlist))
rownames(MedList) <- rownames(DataList.unlist)
for (lv in 1:(NumCond-1)){
idx1 <- which(Conditions==levels(Conditions)[lv])
idx2 <- which(Conditions==levels(Conditions)[lv+1])
t1 <- matrix(DataList.unlist[,idx1],nrow=dim(DataList.unlist)[1])
t2 <- matrix(DataList.unlist[,idx2],nrow=dim(DataList.unlist)[1])
tmpdata <- cbind(t1,t2)
rownames(tmpdata) <- rownames(DataList.unlist)
Cond.use <- as.factor(as.vector(Conditions)[c(idx1,idx2)])
PairRList[[lv]] <- EBTest_ext(Data=tmpdata,NgVector=NgVector,
Conditions=Cond.use,sizeFactors=sizeFactors[c(idx1,idx2)],
maxround=5, OnlyCalcR=TRUE,Print=FALSE)
tt1 <- matrix(DataList.unlist.dvd[,idx1],nrow=dim(DataList.unlist)[1])
tt2 <- matrix(DataList.unlist.dvd[,idx2],nrow=dim(DataList.unlist)[1])
MedList[,i] <- apply(tt1,1,median)
MedList[,i+1] <- apply(tt2,1,median)
}
# if only need Q
if(OnlyQ==TRUE)return(PairRList)
# Only use genes with R in all conditions
NamesInR <- sapply(PairRList,function(i)names(unlist(i[[1]])),simplify=FALSE)
GoodData0 <- Reduce(intersect, NamesInR)
GoodData <- rownames(DataList.unlist)# consider all
NotIn <- setdiff(rownames(DataList.unlist), GoodData)
# Only Use Data has Good q's
DataList.In <- sapply(1:NoneZeroLength, function(i)DataList[[i]][GoodData[GoodData%in%rownames(DataList[[i]])],],simplify=FALSE)
DataList.NotIn <- sapply(1:NoneZeroLength, function(i)DataList[[i]][NotIn[NotIn%in%rownames(DataList[[i]])],],simplify=FALSE)
DataListIn.unlist <- do.call(rbind, DataList.In)
DataListNotIn.unlist <- do.call(rbind, DataList.NotIn)
MedList.In <- MedList[GoodData,]
# R for good ones
# pairwise R
RPairsListIn <- vector("list",NumCond-1)
for(lv in 1:(NumCond-1)){
RPairsListIn[[lv]] <- sapply(1:NoneZeroLength,
function(i){
tmpname <- GoodData0[GoodData0%in%rownames(DataList[[i]])]
tmp1 <- PairRList[[lv]][[1]][[i]][tmpname]
tmpMean <- PairRList[[lv]][[2]][[i]][tmpname]
tmpVar <- PairRList[[lv]][[3]][[i]][tmpname]
NAOnes <- which(is.na(tmp1)|tmp1<0)
#print(length(NAOnes))
PNotIn <- 1-10^-6
R.NotIn <- tmpMean[NAOnes]*PNotIn/(1-PNotIn)
R.out <- tmp1
R.out[NAOnes] <- R.NotIn
R.out
R.norm <- rep(100, nrow(DataList[[i]]))
names(R.norm) <- rownames(DataList[[i]])
R.norm[names(R.out)] <- R.out
R.norm
})
# not pairwise
if(WithinCondR==TRUE){
# If calculate R from t-1 but not jointly
RPairsListIn[[lv]] <- sapply(1:NoneZeroLength,
function(i){
tmpname <- GoodData0[GoodData0%in%rownames(DataList[[i]])]
tmpMean <- PairRList[[lv]]$C1Mean[[i]][tmpname]
tmpVar <- PairRList[[lv]]$C1EstVar[[i]][tmpname]
tmpQ <- PairRList[[lv]]$QList1[[i]][tmpname]
tmp1 <- tmpMean*tmpQ/(1-tmpQ)
NAOnes <- which(is.na(tmp1)|tmp1<0)
#print(length(NAOnes))
PNotIn <- 1-10^-6
R.NotIn <- tmpMean[NAOnes]*PNotIn/(1-PNotIn)
R.out <- tmp1
R.out[NAOnes] <- R.NotIn
R.out
R.norm <- rep(100, nrow(DataList[[i]]))
names(R.norm) <- rownames(DataList[[i]])
R.norm[names(R.out)] <- R.out
R.norm
})
}
}
RPairsListIn.unlist.raw <- sapply(1:(NumCond-1),function(lv)unlist(RPairsListIn[[lv]]))
rownames(RPairsListIn.unlist.raw) <- rownames(DataListIn.unlist)
# Penalty on R
if(PenalizeLowMed==FALSE)RPairsListIn.unlist <- RPairsListIn.unlist.raw
if(PenalizeLowMed==TRUE){
RPairsListIn.unlist <- RPairsListIn.unlist.raw
MedQt <- apply(MedList.In,2,function(jj)quantile(jj,PenalizeLowMedQt))
for(kk in 1:(NumCond-1)){
WhichLowMed <- which(MedList.In[,kk]<=MedQt[kk])
RPairsListIn.unlist[WhichLowMed,kk] <- RPairsListIn.unlist.raw[WhichLowMed,kk]* PenalizeLowMedVal
}
}
NumOfEachGroupIn <- sapply(1:NoneZeroLength, function(i)max(0,dim(DataList.In[[i]])[1]))
NumOfEachGroupNotIn <- sapply(1:NoneZeroLength, function(i)max(0,dim(DataList.NotIn[[i]])[1]))
# Remove any transcripts with Input NA
NumPPDim <- NumTranStage
#NumGene <- nrow(DataList.In[[1]])
NumGene <- nrow(DataListIn.unlist)
NumPoints <- NumCond-1
NamesGene <- rownames(DataListIn.unlist)
NamesTranStage <- paste("St",1:NumTranStage,sep="")
NamesPoints <- paste("Pt",1:NumPoints,sep="")
#GeneNameMap <- NamesGene
#names(GeneNameMap) <- IsoNamesIn
GeneNameMap <- IsoNamesIn
if(is.null(Pi0)){Pi0 <- rep(1/NumTranStage, NumTranStage)}
# transition matrix.. homo
# define as from rowname to colname
if(is.null(Tran)&&homo==TRUE){
if(NumTranStage==2){
if(NoTrend==FALSE)Tran <- matrix(c(.7,.3,.3,.7), ncol=NumTranStage,nrow=NumTranStage)
if(NoTrend==TRUE)Tran <- matrix(c(.5,.5,.5,.5), ncol=NumTranStage,nrow=NumTranStage)
}
if(NumTranStage==3){
if(NoTrend==FALSE)Tran <- matrix(c(.6,.2,.2,.2,.6,.2,.2,.2,.6),
ncol=NumTranStage,nrow=NumTranStage)
if(NoTrend==TRUE)Tran <- matrix(c(.5,.5,.5,.5,.5,.5,.5,.5,.5),
ncol=NumTranStage,nrow=NumTranStage)
}
}
# non-homo, 3d matrix, third dim is T-1 transitions
if(is.null(Tran)&&homo==FALSE){
if(NumTranStage==2){
Tran <- array(1/NumTranStage, dim=c(NumTranStage,NumTranStage,NumPoints-1))
if(NoTrend==FALSE) for(i in 1:(NumPoints-1))Tran[,,i] <- c(.7,.3,.3,.7)
if(NoTrend==TRUE) for(i in 1:(NumPoints-1))Tran[,,i] <- c(.5,.5,.5,.5)
}
if(NumTranStage==3){
Tran <- array(1/NumTranStage, dim=c(NumTranStage,NumTranStage,NumPoints-1))
if(NoTrend==FALSE)for(i in 1:(NumPoints-1))Tran[,,i] <- c(.6,.2,.2,.2,.6,.2,.2,.2,.6)
if(NoTrend==FALSE)for(i in 1:(NumPoints-1))Tran[,,i] <- c(.5,.5,.5,.5,.5,.5,.5,.5,.5)
}
}
# Beta parameter
# Time points x Dim
if(is.null(FCParam)){
if(NumTranStage==2)FCParam <- cbind(c(1/sqrt(PriorFC), sqrt(PriorFC)),
c(sqrt(PriorFC), 1/sqrt(PriorFC)))
if(NumTranStage==3)FCParam <- cbind(c(1/sqrt(PriorFC),1, sqrt(PriorFC)),
c(sqrt(PriorFC),1, 1/sqrt(PriorFC)))
if(WithinCondR==TRUE){
# If within condition R based on t-1
if(NumTranStage==2)FCParam <- cbind(c(1, 1),
c(PriorFC, 1/PriorFC))
if(NumTranStage==3)FCParam <- cbind(c(1,1, 1),
c(PriorFC,1, 1/PriorFC))
}
}
AlphaIn <- 1
BetaIn <- rep(1,NoneZeroLength)
# Name them
rownames(FCParam) <- NamesTranStage
if(homo==TRUE)rownames(Tran)=colnames(Tran)=NamesTranStage
if(homo==FALSE){
dimnames(Tran)[[1]]=dimnames(Tran)[[2]]=NamesTranStage
dimnames(Tran)[[3]] <- paste("Cp",1:(NumPoints-1),sep="")
}
TranTrack <- list(Tran)
FCParamTrack <- list(FCParam)
Pi0Track <- Pi0
AlphaTrack <- AlphaIn
BetaTrack <- BetaIn
################################
# Iter
################################
for (iter in 1:maxround){
Time.start <- proc.time()[3]
# Forward
# rows are States; cols are genes
B <- sapply(1:NumPoints,function(pp)
sapply(1:NumTranStage,function(ss){
idx1 <- which(Conditions==levels(Conditions)[pp])
idx2 <- which(Conditions==levels(Conditions)[pp+1])
#
t1 <- matrix(DataListIn.unlist[,idx1],nrow=dim(DataListIn.unlist)[1])
t2 <- matrix(DataListIn.unlist[,idx2],nrow=dim(DataListIn.unlist)[1])
tmpdata <- cbind(t1,t2)
rownames(tmpdata) <- rownames(DataListIn.unlist)
Rtmp1 <- outer(RPairsListIn.unlist[,pp],sizeFactors[idx1])
Rtmp2 <- outer(RPairsListIn.unlist[,pp],sizeFactors[idx2])
Log <- f0(tmpdata,
AlphaIn=AlphaIn, BetaIn=BetaIn,
cbind(Rtmp1*FCParam[ss,1],
Rtmp2*FCParam[ss,2]), NumOfGroups=NumOfEachGroupIn, log=FALSE)
}),simplify=FALSE)
for(i in 1:NumPoints){
B[[i]] <- t(B[[i]])
rownames(B[[i]]) <- NamesTranStage
colnames(B[[i]]) <- NamesGene
}
# alpha_g,0 = pi_i * b_i (O_g)
# row gene column stages
Alpha0 <- B[[1]]*Pi0
Alpha.tmp <- Alpha0
AlphaMat <- NULL
AlphaMat <- list(Alpha0)
# step
for (ctr in 2:(NumPoints)){
if(homo==TRUE)
Sumpart <- t(Tran)%*%Alpha.tmp
if(homo==FALSE)
Sumpart <- t(Tran[,,ctr-1])%*%Alpha.tmp
Alpha.upd <- Sumpart*B[[ctr]]
Alpha.tmp <- Alpha.upd
AlphaMat <- c(AlphaMat,list(Alpha.upd))
}
# P (O| lambda)= sum_i alpha_T-1 (i)
#P_O_lmbda=colSums(Alpha.upd)
#Back
Beta_T1 <- matrix(1,ncol=NumGene,nrow=NumTranStage)
Beta.tmp <- Beta_T1
BetaMat <- vector("list",NumPoints)
BetaMat[[NumPoints]] <- Beta_T1
if(is.null(Tran)&&homo==TRUE){Tran <- matrix(1/NumTranStage, ncol=NumTranStage,nrow=NumTranStage)}
# non-homo, 3d matrix, third dim is T-1 transitions
for(ctr in (NumPoints-1):1){
if(homo==TRUE)tranuse <- Tran
if(homo==FALSE)tranuse <- Tran[,,ctr]
tmpupd <- B[[ctr+1]]*Beta.tmp
Beta.upd <- tranuse%*%tmpupd
Beta.tmp <- Beta.upd
BetaMat[[ctr]] <- Beta.tmp
}
# T-1 elements
# col genes row states
Gamma_i_num <- sapply(1:(NumPoints-1),function(i)AlphaMat[[i]]*BetaMat[[i]],simplify=FALSE)
Gamma_i_denom <- sapply(1:(NumPoints-1),function(i)colSums(Gamma_i_num[[i]]))
Gamma_i <- sapply(1:(NumPoints-1),function(i)t(t(Gamma_i_num[[i]])/Gamma_i_denom[,i]),simplify=FALSE)
# Update Pi and Tran
Pi.Up.allgene <- Gamma_i[[1]]
Pi.Up <- rowMeans(Pi.Up.allgene,na.rm=TRUE)
# Sum g first
#Gamma_i_sumg <- sapply(1:(NumPoints),function(i)rowSums(Gamma_i_num[[i]],na.rm=TRUE))
#Pi.Up <- Gamma_i_sumg[,1]/sum(Gamma_i_sumg[,1],na.rm=TRUE)
# dims: i, j, T-1, g
Gamma_ij_array_raw = Eta_ij_array_raw=
array(data=NA,dim=c(NumTranStage, NumTranStage, NumPoints-1, NumGene))
for(i in 1:NumTranStage){
for(j in 1:NumTranStage){
for(k in 1:(NumPoints-1)){
for(l in 1:NumGene){
if(homo==TRUE)tranuse <- Tran
if(homo==FALSE)tranuse <- Tran[,,k]
Gamma_ij_array_raw[i,j,k,l] <- tranuse[i,j]*AlphaMat[[k]][i,l]*BetaMat[[k+1]][j,l]*B[[k+1]][j,l]
}}
}
}
# eta first... then Sum g first!
for(i in 1:NumTranStage){
for(j in 1:NumTranStage){
for(k in 1:(NumPoints-1)){
for(l in 1:NumGene){
Eta_ij_array_raw[i,j,k,l] <- Gamma_ij_array_raw[i,j,k,l]/sum(Gamma_ij_array_raw[,,k,l],na.rm=TRUE)
}}
}
}
Eta_ij_array_raw_sumg <- apply(Eta_ij_array_raw,c(1,2,3),function(oo)sum(oo,na.rm=TRUE))
Eta_ij_array_raw_sumgj <- sapply(1:(NumPoints-1),function(i)rowSums(Eta_ij_array_raw_sumg[,,i],
na.rm=TRUE),simplify=FALSE)
if(homo==FALSE){
Tran.Up.raw <- sapply(1:(NumPoints-1),function(i)
Eta_ij_array_raw_sumg[,,i]/Eta_ij_array_raw_sumgj[[i]],
simplify=FALSE)
Tran.Up <- array(data=NA,dim=c(NumTranStage, NumTranStage, NumPoints-1))
for(i in 1:(NumPoints-1))Tran.Up[,,i] <- Tran.Up.raw[[i]]
}
if(homo==TRUE){
Eta_ij_array_raw_sumgt <- apply(Eta_ij_array_raw_sumg,c(1,2),function(oo)sum(oo,na.rm=TRUE))
Eta_ij_array_raw_sumgjt_raw <- do.call(cbind,Eta_ij_array_raw_sumgj)
Eta_ij_array_raw_sumgjt <- rowSums(Eta_ij_array_raw_sumgjt_raw, na.rm=TRUE)
Tran.Up <- Eta_ij_array_raw_sumgt/Eta_ij_array_raw_sumgjt
}
##############################
#Optim
if (EM==TRUE){
StartValue <- c(AlphaIn, BetaIn)
AlphaToEMraw <- do.call(cbind, AlphaMat)* do.call(cbind, BetaMat)
AlphaToEM <- as.vector(t(AlphaToEMraw))
#print(summary(AlphaToEM))
AlphaToEM[which(is.na(AlphaToEM))] <- 10^-6
AlphaToEM[which(AlphaToEM==Inf)] <- 10^6
InputPool <- list(DataListIn.unlist, AlphaToEM, NumPoints,
NumGene, NumTranStage, RPairsListIn.unlist, sizeFactors,
Conditions, NumOfEachGroupIn, FCParam)
###################
Result<-optim(par=StartValue,fn=LikefunNBHMM,InputPool=InputPool)
out1 <- Result[[1]]
AlphaIn <- out1[1]
BetaIn <- out1[2:(1+length(NumOfEachGroupIn))]
AlphaTrack <- c(AlphaTrack,AlphaIn)
BetaTrack <- rbind(BetaTrack,BetaIn)
}
if(UpdateParam==TRUE){
Pi0Track <- rbind(Pi0Track,Pi.Up)
TranTrack <- c(TranTrack,list(Tran.Up))
Pi0 <- Pi.Up
Tran <- Tran.Up
}
Time.end <- proc.time()[3]
Time.use <- Time.end-Time.start
cat(paste("\n iteration","time",round(Time.use,1), "\n"))
}
#############
# R for all
# NA take mean of others
#############
RPairsListAll <- matrix(NA,ncol=(NumCond-1),nrow=nrow(DataList.unlist))
rownames(RPairsListAll) <- rownames(DataList.unlist)
for(lv in 1:(NumCond-1)){
tmpName <- names(unlist(PairRList[[lv]][[1]]))
tmp1 <- unlist(PairRList[[lv]][[1]])
tmpMean <- unlist(PairRList[[lv]][[2]])
NAOnes <- which(is.na(tmp1)|tmp1<0)
PNotIn <- 1-10^-6
R.NotIn <- tmpMean[NAOnes]*PNotIn/(1-PNotIn)
R.out <- tmp1
R.out[NAOnes] <- R.NotIn
RPairsListAll[tmpName,lv] <- R.out
}
RMean <- rowMeans(RPairsListAll,na.rm=TRUE)
WhichNA <- which(is.na(RPairsListAll),arr.ind=TRUE)
if(nrow(WhichNA)>0)for(i in 1:nrow(WhichNA))RPairsListAll[WhichNA[i]] <- RMean[WhichNA[i,1]]
# Penalty on R
if(PenalizeLowMed==FALSE)RPairsListAllPen <- RPairsListAll
if(PenalizeLowMed==TRUE){
RPairsListAllPen <- RPairsListAll
MedQt <- apply(MedList,2,function(jj)quantile(jj,PenalizeLowMedQt))
for(kk in 1:(NumCond-1)){
WhichLowMed <- which(MedList[,kk]<=MedQt[kk])
RPairsListAllPen[WhichLowMed,kk] <- RPairsListAll[WhichLowMed,kk]* PenalizeLowMedVal
}
}
AllStList <- vector("list",NumPoints-1)
for(i in 1: (NumPoints))AllStList[[i]] <- StateNames
AllPosi <- expand.grid(AllStList)
LogB <- sapply(1:NumPoints,function(pp)
sapply(1:NumTranStage,function(ss){
idx1 <- which(Conditions==levels(Conditions)[pp])
idx2 <- which(Conditions==levels(Conditions)[pp+1])
t1 <- matrix(DataList.unlist[,idx1],nrow=dim(DataList.unlist)[1])
t2 <- matrix(DataList.unlist[,idx2],nrow=dim(DataList.unlist)[1])
tmpdata <- cbind(t1,t2)
rownames(tmpdata) <- rownames(DataList.unlist)
Rtmp1 <- outer(RPairsListAllPen[,pp],sizeFactors[idx1])
Rtmp2 <- outer(RPairsListAllPen[,pp],sizeFactors[idx2])
Log <- f0(tmpdata,
AlphaIn=AlphaIn, BetaIn=BetaIn,
cbind(Rtmp1*FCParam[ss,1],
Rtmp2*FCParam[ss,2]), NumOfGroups=NumOfEachGroupIn+NumOfEachGroupNotIn, log=TRUE)
}),simplify=FALSE)
for(i in 1:NumPoints){
LogB[[i]] <- t(LogB[[i]])
rownames(LogB[[i]]) <- NamesTranStage
colnames(LogB[[i]]) <- rownames(DataList.unlist)
}
AlllogPost <- sapply(1:nrow(AllPosi),function(i){
logPi0.use <- log(Pi0[AllPosi[i,1]])
logB.use <- sapply(1:NumPoints,function(j)LogB[[j]][AllPosi[i,j],])
# gene by time
logB.sumtime <- rowSums(logB.use)
if(homo==TRUE)tran.use <- sapply(1:(NumPoints-1),function(j)Tran[as.numeric(AllPosi[i,j]),as.numeric(AllPosi[i,j+1])])
if(homo==FALSE)tran.use <- sapply(1:(NumPoints-1),function(j)Tran[as.numeric(AllPosi[i,j]),as.numeric(AllPosi[i,j+1]),j])
logtran.sum=sum(log(tran.use))
logPi0.use+logB.sumtime+logtran.sum
})
AlllogPost.Max <- apply(AlllogPost,1,max)
PostSum <- apply(exp(AlllogPost),1,sum)
Which0 <- which(PostSum==0)
AlllogPost.Adj0 <- AlllogPost
if(length(Which0)>0)AlllogPost.Adj0[Which0,] <- AlllogPost[Which0,]-AlllogPost.Max[Which0]
PostSum.Adj0 <- rowSums(exp(AlllogPost.Adj0))
PPraw <- exp(AlllogPost.Adj0)/PostSum.Adj0
PP <- PPraw
LogPostSum.Adj0 <- log(PostSum.Adj0)
LogPostSum <- LogPostSum.Adj0
if(length(Which0)>0)LogPostSum[Which0] <- LogPostSum.Adj0[Which0]+AlllogPost.Max[Which0]
#PP[which(is.na(PP),arr.ind=TRUE)]=-Inf
WhichMax <- apply(PP,1,function(oo){
tt <- which.max(oo)
if(length(tt)>0)out <- tt
if(length(tt)==0)out <- NA
out})
WhichMax.NonNA.ind <- which(!is.na(WhichMax))
WhichMax.NonNA <- WhichMax[WhichMax.NonNA.ind]
MatTerm <- AllPosi[WhichMax.NonNA,]
rownames(MatTerm) <- rownames(Data)[WhichMax.NonNA.ind]
AllStListNum <- vector("list",NumPoints-1)
for(i in 1: (NumPoints))AllStListNum[[i]] <- 1:2
AllPosiNum <- expand.grid(AllStListNum)
MatTermNum <- AllPosiNum[WhichMax.NonNA,]
rownames(MatTermNum) <- rownames(Data)[WhichMax.NonNA.ind]
PostSumForLL <- log(PostSum)
ISNA <- which(PostSumForLL==-Inf | is.na(PostSumForLL))
#print(ISNA)
if(length(ISNA)>0)ISNOTNA <- c(1:length(PostSumForLL))[-ISNA]
if(length(ISNA)==0)ISNOTNA <- c(1:length(PostSumForLL))
Min.ISNOT <- min(PostSumForLL[ISNOTNA])
PostSumForLL[ISNA] <- Min.ISNOT
PostSumForLL.Sum <- sum(PostSumForLL)
NameOut <- as.character(IsoNamesIn[rownames(PP)])
#message(str(NameOut))
rownames(MatTerm) = rownames(MatTermNum)=
NameOut[WhichMax.NonNA.ind]
rownames(PP)=
names(WhichMax)=names(LogPostSum)=
names(PostSum)=rownames(AlllogPost)=
NameOut
tmp <- AllPosi
tmpL <- levels(tmp[[1]])
qq <- sapply(1:nrow(tmp),function(i)paste0(tmpL[as.numeric(tmp[i,])],collapse="-"))
colnames(PP) <- qq
out <- list(MAPTerm=MatTerm, MAPTermNum=MatTermNum,
AllTerm=AllPosi, PP=PP, WhichMax=WhichMax, Allf=AlllogPost,
Pi0Track=Pi0Track,
TranTrack=TranTrack,
AlphaTrack=AlphaTrack,
BetaTrack=BetaTrack,
GeneNameMap=GeneNameMap,
LogLike=LogPostSum,
LL=PostSum, LLAll=PostSumForLL.Sum
)
}
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