Different Cov

Last updated: 2018-12-19

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knitr::read_chunk("code/DifferentCov.R")

library(plyr)

DifferentCov = function(data, Ulist,
                        gridmult= sqrt(2),
                        control = list(),
                        pi_thresh = 1e-10,
                        outputlevel = 2){

  grid = mashr:::autoselect_grid(data, gridmult)
  Ulist = mashr:::normalize_Ulist(Ulist)
  prior = "uniform"
  L = length(Ulist)

  grid.full = c(0, grid)
  xUlist.null = rep(Ulist, length(grid.full))
  xUlist = mashr:::expand_cov(Ulist,grid.full,FALSE)

  xUlist.full = Map("+", xUlist.null, xUlist)

  lm = calc_relative_lik_matrix(data,xUlist.full)

  prior = mashr:::set_prior(ncol(lm$loglik_matrix),prior)

  pi_s = mashr:::optimize_pi(exp(lm$loglik_matrix),prior=prior,optmethod='mixSQP', control=control)

  which.comp = (pi_s > pi_thresh)
  posterior_weights = mashr:::compute_posterior_weights(pi_s,exp(lm$loglik_matrix))
  if (outputlevel > 1) {
    xUlistinv = rep(lapply(xUlist.null[1:L], function(U) solve(U)), length(grid.full))
    posterior_cov = mashr:::expand_cov(Ulist,sqrt((grid.full^2)/(1+grid.full^2)),FALSE)
    posterior_matrices = compute_posterior_matrices(data,xUlistinv, posterior_cov, posterior_weights)
  } else {
    posterior_matrices = NULL
  }

  vloglik = mashr:::compute_vloglik_from_matrix_and_pi(pi_s,lm, data$Shat_alpha)
  loglik = sum(vloglik)
  null_loglik = compute_null_loglik_from_matrix(pi_s, lm, data$Shat_alpha, L)
  alt_loglik = compute_alt_loglik_from_matrix_and_pi(pi_s, lm, data$Shat_alpha, L)

  # results
  fitted_g = list(pi=pi_s, Ulist=Ulist, grid=grid.full, usepointmass=FALSE)
  m=list(result = posterior_matrices,
         loglik = loglik, vloglik = vloglik,
         null_loglik = null_loglik,
         alt_loglik = alt_loglik,
         fitted_g = fitted_g,
         posterior_weights = posterior_weights,
         alpha=data$alpha)
  #for debugging
  if(outputlevel==4){m = c(m,list(lm=lm))}
  return(m)
}

#' Compute vector of null loglikelihoods from a matrix of log-likelihoods
#' @param lm the results of a likelihood matrix calculation from \code{calc_relative_lik_matrix}
#' whose first column corresponds to null
#' @param Shat_alpha matrix of Shat^alpha
compute_null_loglik_from_matrix = function(pi_s, lm,Shat_alpha, L){
  return(log(exp(lm$loglik_matrix[,1:L,drop=FALSE]) %*% (pi_s[1:L]/(1-sum(pi_s[-c(1:L)])))) +lm$lfactors-rowSums(log(Shat_alpha)))
}

#' Compute vector of alternative loglikelihoods from a matrix of log-likelihoods and fitted pi
#' @param pi_s the vector of mixture proportions, with first element corresponding to null
#' @param lm the results of a likelihood matrix calculation from \code{calc_relative_lik_matrix}
#' whose first column corresponds to null
#' @param Shat_alpha matrix of Shat^alpha
compute_alt_loglik_from_matrix_and_pi = function(pi_s,lm,Shat_alpha,L){
  return(log(exp(lm$loglik_matrix[,-c(1:L),drop=FALSE]) %*% (pi_s[-c(1:L)]/(1-sum(pi_s[1:L]))))+lm$lfactors-rowSums(log(Shat_alpha)))
}

calc_lik_matrix_common_cov = function(data, Ulist, log = FALSE){
  res <- laply(Ulist,function(U)
      dmvnorm(x = data$Bhat,sigma = U,log = log))
  dimnames(res) = NULL # just to make result identical to the non-common-cov version
  return(t(res))
}


calc_lik_matrix <- function (data, Ulist, log = FALSE) {

  res <- calc_lik_matrix_common_cov(data,Ulist,log)
  if (nrow(res) == 1)
    res <- matrix(res)
  if (ncol(res) > 1)
    colnames(res) <- names(Ulist)

  # Give a warning if any columns have -Inf likelihoods.
  rows <- which(apply(res,2,function (x) any(is.infinite(x))))
  if (length(rows) > 0)
    warning(paste("Some mixture components result in non-finite likelihoods,",
                  "either\n","due to numerical underflow/overflow,",
                  "or due to invalid covariance matrices",
                  paste(rows,collapse=", "),
                  "\n"))
  return(res)

}

calc_relative_lik_matrix <-
  function (data, Ulist) {

    # Compute the J x P matrix of conditional log-likelihoods.
    matrix_llik <- calc_lik_matrix(data,Ulist,log = TRUE)

    # Avoid numerical issues (overflow or underflow) by subtracting the
    # largest entry in each row.
    lfactors    <- apply(matrix_llik,1,max)
    matrix_llik <- matrix_llik - lfactors
    return(list(loglik_matrix = matrix_llik,
                lfactors   = lfactors))
  }

posterior_mean <- function(bhat, Vinv, U1){
  return(U1 %*% (Vinv %*% bhat))
}

#' @title posterior_mean_matrix
#' @param Bhat J by R matrix of observations
#' @param Vinv R x R inverse covariance matrix for the likelihood
#' @param U1 R x R posterior covariance matrix, computed using posterior_cov
#' @return R vector of posterior mean
#' @description Computes posterior mean under multivariate normal model for each row of matrix Bhat.
#' Note that if bhat is N_R(b,V) and b is N_R(0,U) then b|bhat N_R(mu1,U1).
#' This function returns a matrix with jth row equal to mu1(bhat) for bhat= Bhat[j,].
posterior_mean_matrix <- function(Bhat, Vinv, U1){
  return(Bhat %*% (Vinv %*% U1))
}

compute_posterior_matrices <-
  function (data, Ulistinv, posterior_cov, posterior_weights) {

    R = mashr:::n_conditions(data)
    # keep data dimension names
    effect_names = rownames(data$Bhat)
    condition_names = colnames(data$Bhat)
    posterior_matrices = compute_posterior_matrices_general_R(data, Ulistinv, posterior_cov, posterior_weights)
    # Set dimension names
    for (i in names(posterior_matrices)) {
      if (length(dim(posterior_matrices[[i]])) == 2) {
        colnames(posterior_matrices[[i]]) <- condition_names
        rownames(posterior_matrices[[i]]) <- effect_names
      }
    }
    if (length(dim(posterior_matrices$PosteriorCov)) == 3)
      dimnames(posterior_matrices$PosteriorCov) <- list(condition_names, condition_names, effect_names)
    return(posterior_matrices)
}

compute_posterior_matrices_general_R=function(data,Ulistinv, posterior_cov,posterior_weights){
  R=mashr:::n_conditions(data)
  J=mashr:::n_effects(data)
  P=length(posterior_cov)

  # allocate arrays for returned results
  res_post_mean=array(NA,dim=c(J,R))
  res_post_mean2 = array(NA,dim=c(J,R)) #mean squared value
  res_post_zero=array(NA,dim=c(J,R))
  res_post_neg=array(NA,dim=c(J,R))

  # allocate arrays for temporary calculations
  post_mean=array(NA,dim=c(P,R))
  post_mean2 = array(NA,dim=c(P,R)) #mean squared value
  post_zero=array(NA,dim=c(P,R))
  post_neg=array(NA,dim=c(P,R))

  U1 = posterior_cov

  for(j in 1:J){
    bhat=as.vector(t(data$Bhat[j,]))##turn j into a R x 1 vector

    for(p in 1:P){
      mu1 <- as.array(posterior_mean(bhat, Ulistinv[[p]], U1[[p]]))
      # Transformation for mu
      muA <- (mu1 * data$Shat_alpha[j,])

      # Transformation for Cov
      covU = data$Shat_alpha[j,] * t(data$Shat_alpha[j,] * U1[[p]])
      pvar = covU

      post_var = pmax(0,diag(pvar)) # Q vector posterior variance
      post_mean[p,]= muA
      post_mean2[p,] = muA^2 + post_var #post_var is the posterior variance

      post_neg[p,] = ifelse(post_var==0,0,pnorm(0,mean=muA,sqrt(post_var),lower.tail=T))
      post_zero[p,] = ifelse(post_var==0,1,0)

    }
    res_post_mean[j,] = posterior_weights[j,] %*% post_mean
    res_post_mean2[j,] = posterior_weights[j,] %*% post_mean2
    res_post_zero[j,] = posterior_weights[j,] %*% post_zero
    res_post_neg[j,] = posterior_weights[j,] %*% post_neg
  }
  res_post_sd = sqrt(res_post_mean2 - res_post_mean^2)
  res_lfsr = compute_lfsr(res_post_neg,res_post_zero)

  posterior_matrices = list(PosteriorMean = res_post_mean,
                            PosteriorSD   = res_post_sd,
                            lfdr          = res_post_zero,
                            NegativeProb  = res_post_neg,
                            lfsr          = res_lfsr)
  return(posterior_matrices)
}

ROC.table = function(data, model){
  sign.test = data*model$result$PosteriorMean
  thresh.seq = seq(0, 1, by=0.005)[-1]
  m.seq = matrix(0,length(thresh.seq), 2)
  colnames(m.seq) = c('TPR', 'FPR')
  for(t in 1:length(thresh.seq)){
    m.seq[t,] = c(sum(sign.test>0 & model$result$lfsr <= thresh.seq[t])/sum(data!=0),
                  sum(data==0 & model$result$lfsr <=thresh.seq[t])/sum(data==0))
  }
  return(m.seq)
}

library(knitr)
library(kableExtra)
library(mvtnorm)
library(mashr)

Loading required package: ashr

Attaching package: 'mashr'

The following object is masked _by_ '.GlobalEnv':

    compute_posterior_matrices

The model is on z scores \[ \hat{\mathbf{z}}_j \sim \sum_{k=1}^{K} \sum_{l=1}^{L} \pi_{kl} N(0, (1+\omega_{l})U_{k}) \] We can also write the model as \[ \hat{\mathbf{z}}_j | \mathbf{z}_j, \gamma_{j}=(k, l) \sim N(\mathbf{z}_j, U_{k}) \\ \mathbf{z}_j|\gamma_{j}=(k, l) \sim N(0, \omega_{l}U_{k}) \\ P(\gamma_{j}=(l,k)) = \pi_{kl} \] We assume \(U_k\) are all invertible. Under the null, \(\omega_l = 0\).

set.seed(1)
n = 10000; p = 2
B = matrix(0,n,p)
Bhat = rmvnorm(n, sigma = diag(p))
data = mash_set_data(Bhat=Bhat, Shat=1)

Ulist = cov_canonical(data, cov_methods = c('identity', 'simple_het'))

model = DifferentCov(data, Ulist)
m.model = mash(data, Ulist, verbose = FALSE)

loglike = c(get_loglik(model), get_loglik(m.model))
sig = c(length(get_significant_results(model)), length(get_significant_results(m.model)))
rrmse = c(sqrt(mean((B - model$result$PosteriorMean)^2)/mean((B - Bhat)^2)), sqrt(mean((B - m.model$result$PosteriorMean)^2)/mean((B - Bhat)^2)))
tmp = cbind(loglike, sig, rrmse)
colnames(tmp) = c('logliklihood', '#sig', 'RRMSE')
rownames(tmp) = c('new', 'mash')
tmp %>% kable() %>% kable_styling()

par(mfrow=c(1,2))
barplot(get_estimated_pi(model, dimension = 'grid'), las=2, names.arg = round(model$fitted_g$grid, 2), main='new')
barplot(get_estimated_pi(model), las=2, main='new')

barplot(get_estimated_pi(m.model), las=2, main='mash')

set.seed(1)
B = matrix(0,n,p)
Bhat1 = rmvnorm(n/2, sigma = diag(p))
V = matrix(0.75, p,p); diag(V) = 1
Bhat2 = rmvnorm(n/2, sigma = V)
Bhat = rbind(Bhat1, Bhat2)
V.true = array(0,dim=c(p,p,n))
V.true[,,1:(n/2)] = diag(p)
V.true[,,(n/2 + 1):n] = V
data = mash_set_data(Bhat=Bhat, Shat=1)

Ulist = cov_canonical(data, cov_methods = c('identity', 'simple_het'))

model = DifferentCov(data, Ulist)

Vhat = estimate_null_correlation(data, Ulist)
m.model.current = Vhat$mash.model

data.true = mash_update_data(data, V = V.true)
m.model.true = mash(data.true, Ulist, algorithm.version = 'R', verbose=FALSE)

loglike = c(get_loglik(model), get_loglik(m.model.current), get_loglik(m.model.true))
sig = c(length(get_significant_results(model)), length(get_significant_results(m.model.current)), length(get_significant_results(m.model.true)))
rrmse = c(sqrt(mean((B - model$result$PosteriorMean)^2)/mean((B - Bhat)^2)), sqrt(mean((B - m.model.current$result$PosteriorMean)^2)/mean((B - Bhat)^2)), sqrt(mean((B - m.model.true$result$PosteriorMean)^2)/mean((B - Bhat)^2)))
tmp = cbind(loglike, sig, rrmse)
colnames(tmp) = c('logliklihood', '#sig', 'RRMSE')
rownames(tmp) = c('new', 'mash current', 'mash true')
tmp %>% kable() %>% kable_styling()

par(mfrow=c(1,2))
barplot(get_estimated_pi(model, dimension = 'grid'), las=2, names.arg = round(model$fitted_g$grid, 2), main='new')
barplot(get_estimated_pi(model), las=2, main='new')

barplot(get_estimated_pi(m.model.current), las=2, main='mash current')

barplot(get_estimated_pi(m.model.true), las=2, main='mash true')

set.seed(1)
B1 = matrix(0,n/2,p)
B2 = matrix(rnorm((n/2)*p),n/2,p)
B = rbind(B1, B2)
Ehat = rmvnorm(n, sigma = diag(p))
Bhat = B + Ehat

data = mash_set_data(Bhat=Bhat, Shat=1)

Ulist = cov_canonical(data, cov_methods = c('identity', 'simple_het'))

model = DifferentCov(data, Ulist)
m.model = mash(data, Ulist, verbose = FALSE)

loglike = c(get_loglik(model), get_loglik(m.model))
sig = c(length(get_significant_results(model)), length(get_significant_results(m.model)))
fd = c(sum(get_significant_results(model)<=5000), sum(get_significant_results(m.model)<=5000))
rrmse = c(sqrt(mean((B - model$result$PosteriorMean)^2)/mean((B - Bhat)^2)), sqrt(mean((B - m.model$result$PosteriorMean)^2)/mean((B - Bhat)^2)))
tmp = cbind(loglike, sig, fd, rrmse)
colnames(tmp) = c('logliklihood', '#sig', 'false pos','RRMSE')
rownames(tmp) = c('new', 'mash')
tmp %>% kable() %>% kable_styling()

roc.seq = ROC.table(B, model)
plot(roc.seq[,'FPR'], roc.seq[,'TPR'], type='l', xlab = 'FPR', ylab='TPR',
       main=paste0(' True Pos vs False Pos'), cex=1.5, lwd = 1.5, col = 'cyan')
roc.seq = ROC.table(B, m.model)
lines(roc.seq[,'FPR'], roc.seq[,'TPR'], col='purple', lwd = 1.5)
legend('bottomright', c('new','mash'), col=c('cyan','purple'),
           lty=c(1,1), lwd=c(1.5,1.5))

par(mfrow=c(1,2))
barplot(get_estimated_pi(model, dimension = 'grid'), las=2, names.arg = round(model$fitted_g$grid, 2), main='new')
barplot(get_estimated_pi(model), las=2, main='new')

barplot(get_estimated_pi(m.model), las=2, main='mash')

set.seed(1)
B1 = matrix(0,n/2,p)
B2 = rmvnorm(n/2, sigma = V)
B = rbind(B1, B2)

Ehat1 = rmvnorm(n/2, sigma = diag(p))
Ehat2 = rmvnorm(n/2, sigma = V)
Ehat = rbind(Ehat1, Ehat2)

V.true = array(0,dim=c(p,p,n))
V.true[,,1:(n/2)] = diag(p)
V.true[,,(n/2 + 1):n] = V

# V.random = array(0, dim=c(p,p,n))
# ind = sample(1:n, n/2)
# V.random[,,ind] = V
# V.random[,,-ind] = diag(p)

# Ehat = matrix(0, n, p)
# Ehat[ind,] = rmvnorm(n/2, sigma = V)
# Ehat[-ind,] = rmvnorm(n/2, sigma = diag(p))

Bhat = B + Ehat

data = mash_set_data(Bhat=Bhat, Shat=1)

Ulist = cov_canonical(data, cov_methods = c('identity', 'simple_het'))

model = DifferentCov(data, Ulist)

Vhat = estimate_null_correlation(data, Ulist)
m.model.current = Vhat$mash.model

data.true = mash_update_data(data, V = V.true)
m.model.true = mash(data.true, Ulist, algorithm.version = 'R', verbose = FALSE)

loglike = c(get_loglik(model), get_loglik(m.model.current), get_loglik(m.model.true))
sig = c(length(get_significant_results(model)), length(get_significant_results(m.model.current)), length(get_significant_results(m.model.true)))
fd = c(sum(get_significant_results(model)<=5000), sum(get_significant_results(m.model.current)<=5000), sum(get_significant_results(m.model.true)<=5000))
rrmse = c(sqrt(mean((B - model$result$PosteriorMean)^2)/mean((B - Bhat)^2)), sqrt(mean((B - m.model.current$result$PosteriorMean)^2)/mean((B - Bhat)^2)), sqrt(mean((B - m.model.true$result$PosteriorMean)^2)/mean((B - Bhat)^2)))
tmp = cbind(loglike, sig, fd, rrmse)
colnames(tmp) = c('logliklihood', '#sig', 'false pos','RRMSE')
rownames(tmp) = c('new', 'mash current', 'mash true')
tmp %>% kable() %>% kable_styling()

roc.seq = ROC.table(B, model)
plot(roc.seq[,'FPR'], roc.seq[,'TPR'], type='l', xlab = 'FPR', ylab='TPR',
       main=paste0(' True Pos vs False Pos'), cex=1.5, lwd = 1.5, col = 'cyan')
roc.seq = ROC.table(B, m.model.current)
lines(roc.seq[,'FPR'], roc.seq[,'TPR'], col='purple', lwd = 1.5)
roc.seq = ROC.table(B, m.model.true)
lines(roc.seq[,'FPR'], roc.seq[,'TPR'], col='red', lwd = 1.5)
legend('bottomright', c('new','mash current', 'mash true'), col=c('cyan','purple', 'red'),
           lty=c(1,1,1), lwd=c(1.5,1.5, 1.5))

par(mfrow=c(1,2))
barplot(get_estimated_pi(model, dimension = 'grid'), las=2, names.arg = round(model$fitted_g$grid, 2), main='new')
barplot(get_estimated_pi(model), las=2, main='new')

barplot(get_estimated_pi(m.model.current), las=2, main='mash current')

barplot(get_estimated_pi(m.model.true), las=2, main='mash true')

sessionInfo()

R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14.2

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] mashr_0.2.19.0555 ashr_2.2-23       mvtnorm_1.0-8     kableExtra_0.9.0 
[5] knitr_1.20        plyr_1.8.4       

loaded via a namespace (and not attached):
 [1] lattice_0.20-35   Rmosek_8.0.69     colorspace_1.3-2 
 [4] htmltools_0.3.6   viridisLite_0.3.0 yaml_2.2.0       
 [7] rlang_0.3.0.1     R.oo_1.22.0       mixsqp_0.1-92    
[10] pillar_1.3.0      R.utils_2.7.0     REBayes_1.3      
[13] foreach_1.4.4     stringr_1.3.1     munsell_0.5.0    
[16] workflowr_1.1.1   rvest_0.3.2       R.methodsS3_1.7.1
[19] codetools_0.2-15  evaluate_0.12     doParallel_1.0.14
[22] pscl_1.5.2        parallel_3.5.1    highr_0.7        
[25] Rcpp_1.0.0        readr_1.1.1       scales_1.0.0     
[28] backports_1.1.2   rmeta_3.0         truncnorm_1.0-8  
[31] abind_1.4-5       hms_0.4.2         digest_0.6.18    
[34] stringi_1.2.4     grid_3.5.1        rprojroot_1.3-2  
[37] tools_3.5.1       magrittr_1.5      tibble_1.4.2     
[40] crayon_1.3.4      whisker_0.3-2     pkgconfig_2.0.2  
[43] MASS_7.3-50       Matrix_1.2-14     SQUAREM_2017.10-1
[46] xml2_1.2.0        assertthat_0.2.0  rmarkdown_1.10   
[49] httr_1.3.1        rstudioapi_0.8    iterators_1.0.10 
[52] R6_2.3.0          git2r_0.23.0      compiler_3.5.1   

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