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<h1 class="title toc-ignore">Estimate Cor heter</h1>
<h4 class="author"><em>Yuxin Zou</em></h4>
<h4 class="date"><em>2018-12-3</em></h4>
</div>
<p><strong>Last updated:</strong> 2018-12-13</p>
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<p></details></p>
<hr />
<pre class="r"><code>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$lfsr <=thresh.seq[t])/sum(data==0))
}
return(m.seq)
}
library(knitr)
library(kableExtra)</code></pre>
<div id="common-noise-correlation" class="section level2">
<h2>Common noise correlation</h2>
<p>We simulate null data which has common noise correlation structure. We fit mash model without and with the estimated correlation structure. There are lots of false positives in the model without the correlation structure. The posterior mean is far from the truth.</p>
<pre class="r"><code>library(mvtnorm)
library(mashr)</code></pre>
<pre><code>Loading required package: ashr</code></pre>
<pre class="r"><code>set.seed(1)
n = 10000; p = 5
B = matrix(0,n,p)
V = matrix(0.75, p, p); diag(V) = 1
Bhat = rmvnorm(n, sigma = V)
simdata = list(B = B, Bhat = Bhat, Shat = 1)</code></pre>
<pre class="r"><code>data = mash_set_data(Bhat, Shat=1)
U.c = cov_canonical(data)
m.ignore = mash(data, U.c, verbose = FALSE)
V.current = estimate_null_correlation(data, U.c)
m.current = V.current$mash.model
data.true = mash_update_data(data, V = V)
m.true = mash(data.true, U.c, verbose = FALSE)</code></pre>
<pre class="r"><code>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()</code></pre>
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<p>RRMSE:</p>
<pre class="r"><code>tmp = c(rrmse(simdata, m.ignore), rrmse(simdata, m.current), rrmse(simdata, m.true))
barplot(tmp, names.arg = c('ignore', 'current', 'true'))</code></pre>
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</div>
<div id="two-different-noise-correlations" class="section level2">
<h2>Two different noise correlations</h2>
<p>Now, we simulate data with 2 noise correlation structures. Half of the null data have no noise correlation, the other half have noise correlation.</p>
<pre class="r"><code>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)
data.V = mash_update_data(data, V = V)
m.V = mash(data.V, U.c, verbose = FALSE)
V.current = estimate_null_correlation(data, U.c)
m.current = V.current$mash.model
Vtrue = array(0,dim=c(p,p,n))
Vtrue[,,1:(n/2)] = diag(p)
Vtrue[,,(n/2+1): n] = V
data.true = mash_update_data(data, V = Vtrue)
m.true = mash(data.true, U.c, verbose = FALSE, algorithm.version = 'R')</code></pre>
<p>The estimated V is</p>
<pre class="r"><code>V.current$V</code></pre>
<pre><code> [,1] [,2] [,3] [,4] [,5]
[1,] 1.0000000 0.3866502 0.4018458 0.3783971 0.3990991
[2,] 0.3866502 1.0000000 0.3913344 0.3688566 0.3936946
[3,] 0.4018458 0.3913344 1.0000000 0.4172119 0.3878397
[4,] 0.3783971 0.3688566 0.4172119 1.0000000 0.3830625
[5,] 0.3990991 0.3936946 0.3878397 0.3830625 1.0000000</code></pre>
<pre class="r"><code>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()</code></pre>
<table class="table" style="margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align:left;">
</th>
<th style="text-align:right;">
loglik
</th>
<th style="text-align:right;">
# signif
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
I only
</td>
<td style="text-align:right;">
-67844.31
</td>
<td style="text-align:right;">
597
</td>
</tr>
<tr>
<td style="text-align:left;">
V only
</td>
<td style="text-align:right;">
-65457.36
</td>
<td style="text-align:right;">
1904
</td>
</tr>
<tr>
<td style="text-align:left;">
current
</td>
<td style="text-align:right;">
-65793.59
</td>
<td style="text-align:right;">
28
</td>
</tr>
<tr>
<td style="text-align:left;">
true
</td>
<td style="text-align:right;">
-60618.07
</td>
<td style="text-align:right;">
0
</td>
</tr>
</tbody>
</table>
<p>RRMSE:</p>
<pre class="r"><code>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'))</code></pre>
<p><img src="figure/EstimateCorHeter.Rmd/unnamed-chunk-9-1.png" width="672" style="display: block; margin: auto;" /></p>
<details> <summary><em>Expand here to see past versions of unnamed-chunk-9-1.png:</em></summary>
<table style="border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/zouyuxin/mash_application/blob/66be60b49313136a48972c8de6e5fa3030060bf3/docs/figure/EstimateCorHeter.Rmd/unnamed-chunk-9-1.png" target="_blank">66be60b</a>
</td>
<td style="text-align:left;">
zouyuxin
</td>
<td style="text-align:left;">
2018-12-07
</td>
</tr>
</tbody>
</table>
<p></details></p>
</div>
<div id="data-with-signals" class="section level2">
<h2>Data with signals</h2>
<pre class="r"><code>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)</code></pre>
<pre class="r"><code>data = mash_set_data(Bhat, Shat=1)
U.c = cov_canonical(data)
m.I = mash(data, U.c, verbose = FALSE)
data.V = mash_update_data(data, V = V)
m.V = mash(data.V, U.c, verbose = FALSE)</code></pre>
<pre><code>Warning in REBayes::KWDual(A, rep(1, k), normalize(w), control = control): estimated mixing distribution has some negative values:
consider reducing rtol</code></pre>
<pre><code>Warning in mixIP(matrix_lik = structure(c(0.110553314193142,
0.153957533037059, : Optimization step yields mixture weights that are
either too small, or negative; weights have been corrected and renormalized
after the optimization.</code></pre>
<pre class="r"><code>V.current = estimate_null_correlation(data, U.c)
m.current = V.current$mash.model
data.true = mash_update_data(data, V = V.random)
m.true = mash(data.true, U.c, verbose = FALSE, algorithm.version = 'R')</code></pre>
<p>The estimated V is</p>
<pre class="r"><code>V.current$V</code></pre>
<pre><code> [,1] [,2] [,3] [,4] [,5]
[1,] 1.0000000 0.3546903 0.3429767 0.3490963 0.3441630
[2,] 0.3546903 1.0000000 0.3990047 0.3829697 0.3814803
[3,] 0.3429767 0.3990047 1.0000000 0.3706125 0.3784724
[4,] 0.3490963 0.3829697 0.3706125 1.0000000 0.3832408
[5,] 0.3441630 0.3814803 0.3784724 0.3832408 1.0000000</code></pre>
<pre class="r"><code>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()</code></pre>
<table class="table" style="margin-left: auto; margin-right: auto;">
<thead>
<tr>
<th style="text-align:left;">
</th>
<th style="text-align:right;">
loglik
</th>
<th style="text-align:right;">
# signif
</th>
<th style="text-align:right;">
false positive
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
I only
</td>
<td style="text-align:right;">
-70068.62
</td>
<td style="text-align:right;">
741
</td>
<td style="text-align:right;">
344
</td>
</tr>
<tr>
<td style="text-align:left;">
V only
</td>
<td style="text-align:right;">
-68333.69
</td>
<td style="text-align:right;">
2588
</td>
<td style="text-align:right;">
999
</td>
</tr>
<tr>
<td style="text-align:left;">
current
</td>
<td style="text-align:right;">
-68468.46
</td>
<td style="text-align:right;">
114
</td>
<td style="text-align:right;">
16
</td>
</tr>
<tr>
<td style="text-align:left;">
true
</td>
<td style="text-align:right;">
-63908.31
</td>
<td style="text-align:right;">
340
</td>
<td style="text-align:right;">
5
</td>
</tr>
</tbody>
</table>
<p>RRMSE:</p>
<pre class="r"><code>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'))</code></pre>
<p><img src="figure/EstimateCorHeter.Rmd/unnamed-chunk-14-1.png" width="672" style="display: block; margin: auto;" /></p>
<details> <summary><em>Expand here to see past versions of unnamed-chunk-14-1.png:</em></summary>
<table style="border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/zouyuxin/mash_application/blob/66be60b49313136a48972c8de6e5fa3030060bf3/docs/figure/EstimateCorHeter.Rmd/unnamed-chunk-14-1.png" target="_blank">66be60b</a>
</td>
<td style="text-align:left;">
zouyuxin
</td>
<td style="text-align:left;">
2018-12-07
</td>
</tr>
</tbody>
</table>
<p></details></p>
<p>ROC:</p>
<pre class="r"><code>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))</code></pre>
<p><img src="figure/EstimateCorHeter.Rmd/unnamed-chunk-15-1.png" width="672" style="display: block; margin: auto;" /></p>
<details> <summary><em>Expand here to see past versions of unnamed-chunk-15-1.png:</em></summary>
<table style="border-collapse:separate; border-spacing:5px;">
<thead>
<tr>
<th style="text-align:left;">
Version
</th>
<th style="text-align:left;">
Author
</th>
<th style="text-align:left;">
Date
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;">
<a href="https://github.com/zouyuxin/mash_application/blob/66be60b49313136a48972c8de6e5fa3030060bf3/docs/figure/EstimateCorHeter.Rmd/unnamed-chunk-15-1.png" target="_blank">66be60b</a>
</td>
<td style="text-align:left;">
zouyuxin
</td>
<td style="text-align:left;">
2018-12-07
</td>
</tr>
</tbody>
</table>
<p></details></p>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>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 </code></pre>
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