Estimate Cor heter R = 50

Last updated: 2018-12-13

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File	Version	Author	Date	Message
Rmd	2c0de61	zouyuxin	2018-12-13	wflow_publish(“analysis/EstimateCorHeterR50.Rmd”)
html	6b96908	zouyuxin	2018-12-13	Build site.
Rmd	77b8312	zouyuxin	2018-12-13	wflow_publish(“analysis/EstimateCorHeterR50.Rmd”)

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, optmethod = 'mixSQP')

V.current = estimate_null_correlation(data, U.c, optmethod = 'mixSQP')
m.current = V.current$mash.model

data.true = mash_update_data(data, V = V)
m.true = mash(data.true, U.c, verbose = FALSE, optmethod = 'mixSQP')

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	-388072.0	4
true	-388713.9	4

RRMSE:

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

Expand here to see past versions of unnamed-chunk-5-1.png:

Version	Author	Date
6b96908	zouyuxin	2018-12-13

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, optmethod = 'mixSQP')

data.V = mash_update_data(data, V = V)
m.V = mash(data.V, U.c, verbose = FALSE, optmethod = 'mixSQP')

V.current = estimate_null_correlation(data, U.c, optmethod = 'mixSQP')
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', optmethod = 'mixSQP')

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	-549877.5	5

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'))

Expand here to see past versions of unnamed-chunk-8-1.png:

Version	Author	Date
6b96908	zouyuxin	2018-12-13

The estimated weights using current method is

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

Expand here to see past versions of unnamed-chunk-9-1.png:

Version	Author	Date
6b96908	zouyuxin	2018-12-13

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, optmethod = 'mixSQP')

data.V = mash_update_data(data, V = V)
m.V = mash(data.V, U.c, verbose = FALSE, optmethod = 'mixSQP')

V.current = estimate_null_correlation(data, U.c, optmethod = 'mixSQP')
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', optmethod = 'mixSQP')

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	-555850.9	144	1

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'))

Expand here to see past versions of unnamed-chunk-13-1.png:

Version	Author	Date
6b96908	zouyuxin	2018-12-13

The estimated weights using current method is

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

Expand here to see past versions of unnamed-chunk-14-1.png:

Version	Author	Date
6b96908	zouyuxin	2018-12-13

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))

Expand here to see past versions of unnamed-chunk-15-1.png:

Version	Author	Date
6b96908	zouyuxin	2018-12-13

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   colorspace_1.3-2  htmltools_0.3.6  
 [4] viridisLite_0.3.0 yaml_2.2.0        rlang_0.3.0.1    
 [7] R.oo_1.22.0       mixsqp_0.1-92     pillar_1.3.0     
[10] R.utils_2.7.0     foreach_1.4.4     plyr_1.8.4       
[13] stringr_1.3.1     munsell_0.5.0     workflowr_1.1.1  
[16] rvest_0.3.2       R.methodsS3_1.7.1 codetools_0.2-15 
[19] evaluate_0.12     doParallel_1.0.14 pscl_1.5.2       
[22] parallel_3.5.1    highr_0.7         Rcpp_1.0.0       
[25] readr_1.1.1       scales_1.0.0      backports_1.1.2  
[28] rmeta_3.0         truncnorm_1.0-8   abind_1.4-5      
[31] hms_0.4.2         digest_0.6.18     stringi_1.2.4    
[34] grid_3.5.1        rprojroot_1.3-2   tools_3.5.1      
[37] magrittr_1.5      tibble_1.4.2      crayon_1.3.4     
[40] whisker_0.3-2     pkgconfig_2.0.2   MASS_7.3-50      
[43] Matrix_1.2-14     SQUAREM_2017.10-1 xml2_1.2.0       
[46] assertthat_0.2.0  rmarkdown_1.10    httr_1.3.1       
[49] rstudioapi_0.8    iterators_1.0.10  R6_2.3.0         
[52] git2r_0.23.0      compiler_3.5.1

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Estimate Cor heter R = 50

Yuxin Zou

2018-12-13

Common noise correlation

Two different noise correlations

Data with signals

Session information