Different Null Correlation (with signal) DSC

Last updated: 2020-12-22

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I randomly generate 20 positive definite correlation matrices, V. The sample size is 4000.

\[ \hat{z}_j|z_j \sim N_{5}(z_j, V_j) \] \[ z_j \sim \frac{1}{2}\delta_{0} + \frac{1}{2}N(0, \left(\begin{matrix} 1 & 0_{1\times 4} \\ 0_{4\times 1} & 0_{4\times 4} \end{matrix}\right)) \]

library(ggplot2)
Summary = readRDS('../output/diff_v_signal/summary.rds')

Time

The total running time for each matrix is

Summary$estimate[Summary$estimate == 'current'] = 'mV'
Summary$estimate[Summary$estimate == 'mle'] = 'mVexact'
Summary$DSC = as.factor(Summary$DSC)
Time = Summary[,c('DSC','estimate', 'estimate.DSC_TIME')]
ggplot(Time, aes(x = DSC, y=estimate.DSC_TIME, group = estimate, color = estimate)) + geom_point()

Version	Author	Date
7a0bba6	zouyuxin	2018-12-09

mash log likelihood

loglike = Summary[Summary$summary == 'mashloglik', c('DSC','estimate', 'summary.score', 'summary')]
ggplot(loglike, aes(x = DSC, y=summary.score, group = estimate, color = estimate)) + geom_point() + ylab('mash log likelihood')

Version	Author	Date
7a0bba6	zouyuxin	2018-12-09

loglike_ora = loglike[-which(loglike$estimate == 'oracle'), ]
ggplot(loglike_ora, aes(x = DSC, y=summary.score, group = estimate, color = estimate)) + geom_point() + ylab('mash log likelihood')

Version	Author	Date
f244c97	zouyuxin	2018-12-10

RRMSE

RRMSE = Summary[Summary$summary == 'RRMSE', c('DSC','estimate', 'summary.score', 'summary')]
ggplot(RRMSE, aes(x = DSC, y=summary.score, group = estimate, color = estimate)) + geom_point() + ylab('RRMSE')

Version	Author	Date
7a0bba6	zouyuxin	2018-12-09

RRMSE_ora = RRMSE[-which(RRMSE$estimate == 'oracle'), ]
ggplot(RRMSE_ora, aes(x = DSC, y=summary.score, group = estimate, color = estimate)) + geom_point() + ylab('RRMSE')

Version	Author	Date
f244c97	zouyuxin	2018-12-10

ROC

ROCdir = readRDS('../output/diff_v_signal/ROCdir.rds')
par(mfrow=c(1,2))
for(i in 1:20){
  ind = which(ROCdir$DSC == i)
  ROC.seq = readRDS(paste("../output/diff_v_signal/", ROCdir$ROC.output.file[ind[1]], '.rds', sep=""))
  plot(ROC.seq$data[,'FPR'], ROC.seq$data[,'TPR'], type='l', xlab = 'FPR', ylab='TPR',
       main=paste0('Data ', i, ' True Pos vs False Pos'), cex=1.5, lwd = 1.5, col = 'cyan')
  
  ROC.seq = readRDS(paste("../output/diff_v_signal/", ROCdir$ROC.output.file[ind[2]], '.rds', sep=""))
  lines(ROC.seq$data[,'FPR'], ROC.seq$data[,'TPR'], col='olivedrab', lwd = 1.5)
  
  ROC.seq = readRDS(paste("../output/diff_v_signal/", ROCdir$ROC.output.file[ind[3]], '.rds', sep=""))
  lines(ROC.seq$data[,'FPR'], ROC.seq$data[,'TPR'], col='purple', lwd = 1.5)
  ROC.seq = readRDS(paste("../output/diff_v_signal/", ROCdir$ROC.output.file[ind[4]], '.rds', sep=""))
  lines(ROC.seq$data[,'FPR'], ROC.seq$data[,'TPR'], col='red', lwd = 1.5)
  ROC.seq = readRDS(paste("../output/diff_v_signal/", ROCdir$ROC.output.file[ind[5]], '.rds', sep=""))
  lines(ROC.seq$data[,'FPR'], ROC.seq$data[,'TPR'], col='chartreuse3', lwd = 1.5)
  
  legend('bottomright', c('oracle','identity','simple', 'mV', 'mVexact'),col=c('cyan','olivedrab','purple','red','chartreuse3'),
           lty=c(1,1,1,1,1), lwd=c(1.5,1.5,1.5,1.5,1.5))
}

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7a0bba6	zouyuxin	2018-12-09

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7a0bba6	zouyuxin	2018-12-09

Version	Author	Date
7a0bba6	zouyuxin	2018-12-09

sessionInfo()

R version 4.0.3 (2020-10-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/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] ggplot2_3.3.2   workflowr_1.6.2

loaded via a namespace (and not attached):
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 [9] lifecycle_0.2.0  tibble_3.0.4     gtable_0.3.0     pkgconfig_2.0.3 
[13] rlang_0.4.9      rstudioapi_0.13  yaml_2.2.1       xfun_0.19       
[17] withr_2.3.0      stringr_1.4.0    dplyr_1.0.2      knitr_1.30      
[21] generics_0.1.0   fs_1.5.0         vctrs_0.3.6      rprojroot_2.0.2 
[25] grid_4.0.3       tidyselect_1.1.0 glue_1.4.2       R6_2.5.0        
[29] rmarkdown_2.5    farver_2.0.3     purrr_0.3.4      magrittr_2.0.1  
[33] whisker_0.4      scales_1.1.1     promises_1.1.1   ellipsis_0.3.1  
[37] htmltools_0.5.0  colorspace_2.0-0 httpuv_1.5.4     labeling_0.4.2  
[41] stringi_1.5.3    munsell_0.5.0    crayon_1.3.4

Different Null Correlation (with signal) DSC

Yuxin Zou

2018-12-9

Time

mash log likelihood

RRMSE

ROC