MASH Null

V identity

\[ V = I_{5} \]

set.seed(1)
n = 3000; p = 5
U0 = matrix(0, p,p)
Utrue = list(U0 = U0)
V = diag(p)
data = generate_data(n=n, p=p, V = V, Utrue = Utrue)

mash model

samp = 1:(n/2)
if(is.null(dim(data$Shat))){
  data$Shat = matrix(data$Shat, n, p)
}
data.samp = lapply(data, function(l) l[samp,])

m.data = mash_set_data(Bhat = data.samp$Bhat, Shat = data.samp$Shat)
U.c = cov_canonical(m.data)
# m.1by1 = mash_1by1(m.data)
# strong = get_significant_results(m.1by1)

Vhat = estimate_null_correlation(m.data)
Vhat.em = estimateV(m.data, U.c, init_rho = c(-0.5,0,0.5),tol=1e-4, optmethod='em2')$V
m.data.em = mash_set_data(Bhat=data.samp$Bhat, Shat = data.samp$Shat, V = Vhat.em)
m.model.em = mash(m.data.em, U.c, verbose=FALSE)

res = rbind(c(norm(Vhat.em-diag(5), 'F'), get_loglik(m.model.em), length(get_significant_results(m.model.em))))
colnames(res) = c('F.error', 'loglik', '# significance')
row.names(res) = 'EM'
res %>% kable() %>% kable_styling()

V not idendity

We simulate 20 null data sets with non identity V, and check the mash results.

set.seed(1)
n = 2000; p = 5
U0 = matrix(0, p,p)
Utrue = list(U0 = U0)

for(t in 1:20){
  V = clusterGeneration::rcorrmatrix(p)
  data = generate_data(n=n, p=p, V = V, Utrue = Utrue)
  samp = 1:(n/2)
  if(is.null(dim(data$Shat))){
    data$Shat = matrix(data$Shat, n, p)
  }
  data.samp = lapply(data, function(l) l[samp,])

  m.data = mash_set_data(Bhat = data.samp$Bhat, Shat = data.samp$Shat)
  U.c = cov_canonical(m.data)

  Vhat = estimate_null_correlation(m.data, apply_lower_bound = FALSE)
  Vhat.em = estimateV(m.data, U.c, init_rho = c(-0.5,0,0.5), tol=1e-4, optmethod='em2')

  R <- tryCatch(chol(Vhat.em$V),error = function (e) FALSE)
  if(!is.matrix(R)){
    pd = FALSE
    Vhat.em$V = as.matrix(Matrix::nearPD(Vhat.em$V, conv.norm.type = 'F', keepDiag = TRUE)$mat)
  }else{
    pd = TRUE
  }

  m.data.trunc = mash_set_data(data.samp$Bhat, data.samp$Shat, V = Vhat)
  m.model.trunc = mash(m.data.trunc, U.c)
  m.data.em = mash_set_data(Bhat=data.samp$Bhat, Shat = data.samp$Shat, V = Vhat.em$V)
  m.model.em = mash(m.data.em, U.c)

  saveRDS(list(pd = pd, V.true = V, V.em = Vhat.em, V.trunc = Vhat, data = data, sample = samp, model.trunc = m.model.trunc, model.em = m.model.em),
          paste0('../output/MASHNULL.V.result.',t,'.rds'))
}

files = dir("../output/"); files = files[grep("MASHNULL.V.result",files)]
times = length(files)
result = vector(mode="list",length = times)
for(i in 1:times) {
  result[[i]] = readRDS(paste("../output/", files[[i]], sep=""))
}

par(mfrow=c(1,4))
for(t in 1:20){
  corrplot::corrplot.mixed(result[[t]]$V.true, upper='color',cl.lim=c(-1,1))
  mtext(paste0('Data ', t), at=2.5, line=-5)
}

EM_res = c(); Trunc_res = c()
for(t in 1:20){
  err = norm(result[[t]]$V.em$V - result[[t]]$V.true, type='F')
  loglik = get_loglik(result[[t]]$model.em)
  sig = length(get_significant_results(result[[t]]$model.em))
  EM_res = rbind(EM_res, c(err, loglik, sig))
  
  err = norm(result[[t]]$V.trunc - result[[t]]$V.true, type='F')
  loglik = get_loglik(result[[t]]$model.trunc)
  sig = length(get_significant_results(result[[t]]$model.trunc))
  Trunc_res = rbind(Trunc_res, c(err, loglik, sig))
}

mash results based on EM estimated V

colnames(EM_res) = c('F.error', 'loglik', '# significance')
EM_res %>% kable() %>% kable_styling()

mash results based on original estimated V

colnames(Trunc_res) = c('F.error', 'loglik', '# significance')
Trunc_res %>% kable() %>% kable_styling()

Investigate Data 7

data = result[[7]]$data
V.true = result[[7]]$V.true
V.em = result[[7]]$V.em
model.em = result[[7]]$model.em
barplot(get_estimated_pi(model.em), las=2, cex.names = 0.7)

samp = result[[7]]$sample
D1 = lapply(data, function(m) m[samp,])
D2 = lapply(data, function(m) m[-samp,])

Estimate V on D1

m.data1 = mash_set_data(Bhat = D1$Bhat, Shat = D1$Shat)
U.c = cov_canonical(m.data1)
Vhat.em = estimateV(m.data1, U.c, init_rho = c(-0.5,0,0.5), tol=1e-4, optmethod='em2')

Estimate mixture proportions on D2

m.data2 = mash_set_data(Bhat = D2$Bhat, Shat = D2$Shat, V = Vhat.em$V)
m.model.split = mash(m.data2, U.c, outputlevel = 1)

 - Computing 1000 x 141 likelihood matrix.
 - Likelihood calculations took 0.01 seconds.
 - Fitting model with 141 mixture components.
 - Model fitting took 0.10 seconds.

Estimate posteior on D1

m.data1.em = mash_set_data(Bhat = D1$Bhat, Shat = D1$Shat, V = Vhat.em$V)
m.model.split$result = mash_compute_posterior_matrices(m.model.split, m.data1.em)

length(get_significant_results(m.model.split))

[1] 2

Session information

sessionInfo()

R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.6

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] kableExtra_0.9.0 knitr_1.20       mashr_0.2-11     ashr_2.2-10     

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.18      highr_0.7         pillar_1.3.0     
 [4] compiler_3.5.1    git2r_0.23.0      plyr_1.8.4       
 [7] workflowr_1.1.1   R.methodsS3_1.7.1 R.utils_2.6.0    
[10] iterators_1.0.10  tools_3.5.1       corrplot_0.84    
[13] digest_0.6.15     viridisLite_0.3.0 tibble_1.4.2     
[16] evaluate_0.11     lattice_0.20-35   pkgconfig_2.0.2  
[19] rlang_0.2.2       Matrix_1.2-14     foreach_1.4.4    
[22] rstudioapi_0.7    yaml_2.2.0        parallel_3.5.1   
[25] mvtnorm_1.0-8     xml2_1.2.0        httr_1.3.1       
[28] stringr_1.3.1     REBayes_1.3       hms_0.4.2        
[31] rprojroot_1.3-2   grid_3.5.1        R6_2.2.2         
[34] rmarkdown_1.10    rmeta_3.0         readr_1.1.1      
[37] magrittr_1.5      whisker_0.3-2     scales_1.0.0     
[40] backports_1.1.2   codetools_0.2-15  htmltools_0.3.6  
[43] MASS_7.3-50       rvest_0.3.2       assertthat_0.2.0 
[46] colorspace_1.3-2  stringi_1.2.4     Rmosek_8.0.69    
[49] munsell_0.5.0     doParallel_1.0.11 pscl_1.5.2       
[52] truncnorm_1.0-8   SQUAREM_2017.10-1 crayon_1.3.4     
[55] R.oo_1.22.0