Last updated: 2018-12-13

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rrmse = function(data, model){
  sqrt(mean((data$B - model$result$PosteriorMean)^2)/mean((data$B - data$Bhat)^2))
}

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)

Common noise correlation

We simulate null data which has common noise correlation structure. We fit mash model without and with the estimated correlation structure. There are lots of false positives in the model without the correlation structure. The posterior mean is far from the truth.

library(mvtnorm)
library(mashr)
Loading required package: ashr
set.seed(1)
n = 10000; p = 50
B = matrix(0,n,p)
V = matrix(0.75, p, p); diag(V) = 1
Bhat = rmvnorm(n, sigma = V)
simdata = list(B = B, Bhat = Bhat, Shat = 1)
data = mash_set_data(Bhat, Shat=1)
U.c = cov_canonical(data)
m.ignore = mash(data, U.c, verbose = FALSE)

V.current = estimate_null_correlation(data, U.c)
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.683831515481112,
0.722019936752874, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.366830321465555,
0.431739783022358, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.257653331920547,
0.318902276737782, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.2228623767927,
0.263400313066655, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
m.current = V.current$mash.model

data.true = mash_update_data(data, V = V)
m.true = mash(data.true, U.c, verbose = FALSE)
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.256938810491019,
0.263764043323012, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
ign = c(get_loglik(m.ignore), length(get_significant_results(m.ignore)))

current = c(get_loglik(m.current), length(get_significant_results(m.current)))

true = c(get_loglik(m.true), length(get_significant_results(m.true)))

tmp = rbind(ign, current, true)
row.names(tmp) = c('ignore', 'current', 'true')
colnames(tmp) = c('loglik', '# signif')
tmp %>% kable() %>% kable_styling()
loglik # signif
ignore -543911.7 7712
current -387365.3 0
true -387975.6 0

RRMSE:

tmp = c(rrmse(simdata, m.ignore), rrmse(simdata, m.current), rrmse(simdata, m.true))
barplot(tmp, names.arg = c('ignore', 'current', 'true'))

Two different noise correlations

Now, we simulate data with 2 noise correlation structures. Half of the null data have no noise correlation, the other half have noise correlation.

Bhat1 = rmvnorm(n/2, sigma = diag(p))
Bhat2 = rmvnorm(n/2, sigma = V)
Bhat = rbind(Bhat1, Bhat2)
simdata = list(B = B, Bhat = Bhat, Shat = 1)

data = mash_set_data(Bhat, Shat=1)
U.c = cov_canonical(data)
m.I = mash(data, U.c, verbose = FALSE)
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.0842148939965657,
0.108238075780434, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
data.V = mash_update_data(data, V = V)
m.V = mash(data.V, U.c, verbose = FALSE)
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(8.34122179303798e-19,
4.5044665674793e-18, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
V.current = estimate_null_correlation(data, U.c)
m.current = V.current$mash.model

Vtrue = array(0,dim=c(p,p,n))
Vtrue[,,1:(n/2)] = diag(p)
Vtrue[,,(n/2+1): n] = V
data.true = mash_update_data(data, V = Vtrue)
m.true = mash(data.true, U.c, verbose = FALSE, algorithm.version = 'R')
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.0842148939965657,
0.108238075780432, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
Ionly = c(get_loglik(m.I), length(get_significant_results(m.I)))

Vonly = c(get_loglik(m.V), length(get_significant_results(m.V)))

current = c(get_loglik(m.current), length(get_significant_results(m.current)))

true = c(get_loglik(m.true), length(get_significant_results(m.true)))

tmp = rbind(Ionly, Vonly, current, true)
row.names(tmp) = c('I only', 'V only', 'current', 'true')
colnames(tmp) = c('loglik', '# signif')
tmp %>% kable() %>% kable_styling()
loglik # signif
I only -630201.8 3092
V only -563001.6 4995
current -594555.6 2657
true -548883.6 0

RRMSE:

tmp = c(rrmse(simdata, m.I), rrmse(simdata, m.V), rrmse(simdata, m.current), rrmse(simdata, m.true))
barplot(tmp, names.arg = c('I only', 'V only', 'current', 'true'))

The estimated weights using current method is

barplot(get_estimated_pi(m.current), las=2, cex.names = 0.7)

Data with signals

set.seed(2018)
B1 = matrix(0, n/2, p)
V.1 = matrix(0,p,p); V.1[1,1] = 1
B2 = rmvnorm(n/2, sigma = V.1)
B = rbind(B1, B2)

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
simdata = list(B = B, Bhat=Bhat, Shat = 1)
data = mash_set_data(Bhat, Shat=1)
U.c = cov_canonical(data)
m.I = mash(data, U.c, verbose = FALSE)
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(1.05186092654218e-27,
0.420144751666145, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
data.V = mash_update_data(data, V = V)
m.V = mash(data.V, U.c, verbose = FALSE)
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.436240713095732,
0.000212981465909494, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
V.current = estimate_null_correlation(data, U.c)
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.179187055206072,
0.229340379901397, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.122237754455469,
0.278680409435745, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
m.current = V.current$mash.model

data.true = mash_update_data(data, V = V.random)
m.true = mash(data.true, U.c, verbose = FALSE, algorithm.version = 'R')
Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
               consider reducing rtol
Warning in mixIP(matrix_lik = structure(c(0.436240713095732,
0.420144751666145, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.
Ionly = c(get_loglik(m.I), length(get_significant_results(m.I)), sum(get_significant_results(m.I) <= n/2))

Vonly = c(get_loglik(m.V), length(get_significant_results(m.V)), sum(get_significant_results(m.V) <= n/2))

current = c(get_loglik(m.current), length(get_significant_results(m.current)), sum(get_significant_results(m.current) <= n/2))

true = c(get_loglik(m.true), length(get_significant_results(m.true)), sum(get_significant_results(m.true) <= n/2))

tmp = rbind(Ionly, Vonly, current, true)
row.names(tmp) = c('I only', 'V only', 'current', 'true')
colnames(tmp) = c('loglik', '# signif', 'false positive')
tmp %>% kable() %>% kable_styling()
loglik # signif false positive
I only -633196.5 3137 1570
V only -567485.0 5433 2513
current -599388.7 2776 1341
true -553436.5 457 7

RRMSE:

tmp = c(rrmse(simdata, m.I), rrmse(simdata, m.V), rrmse(simdata, m.current), rrmse(simdata, m.true))
barplot(tmp, names.arg = c('I only', 'V only', 'current', 'true'))

The estimated weights using current method is

barplot(get_estimated_pi(m.current), las=2, cex.names = 0.7)

ROC:

roc.seq = ROC.table(simdata$B, m.true)
plot(roc.seq[,'FPR'], roc.seq[,'TPR'], type='l', xlab = 'FPR', ylab='TPR',
       main=paste0(' True Pos vs False Pos'), cex=1.5, lwd = 1.5, col = 'cyan')
roc.seq = ROC.table(simdata$B, m.current)
lines(roc.seq[,'FPR'], roc.seq[,'TPR'], col='purple', lwd = 1.5)
roc.seq = ROC.table(simdata$B, m.I)
lines(roc.seq[,'FPR'], roc.seq[,'TPR'], col='red', lwd = 1.5)
roc.seq = ROC.table(simdata$B, m.V)
lines(roc.seq[,'FPR'], roc.seq[,'TPR'], col='darkolivegreen4', lwd = 1.5)
legend('bottomright', c('oracle','current', 'I only', 'V only'), col=c('cyan','purple','red','darkolivegreen4'),
           lty=c(1,1,1,1), lwd=c(1.5,1.5,1.5,1.5))

Session information

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14.1

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       

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       pillar_1.3.0     
[10] R.utils_2.7.0     REBayes_1.3       foreach_1.4.4    
[13] plyr_1.8.4        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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