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<h1 class="title toc-ignore">Nonnegative loadings with non-diagonal V</h1>
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<p><strong>Last updated:</strong> 2018-09-05</p>
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<p></details></p>
<hr />
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>Here I again fit nonnegative loadings to the “strong” GTEx dataset, but I now use the trick discussed <a href="https://willwerscheid.github.io/FLASHvestigations/arbitraryV.html">here</a> to fit a non-diagonal error covariance matrix <span class="math inline">\(V\)</span>.</p>
<p>I pre-run the code <a href="#code">below</a> and load the results from file.</p>
</div>
<div id="comparison-with-previous-results" class="section level2">
<h2>Comparison with previous results</h2>
<p>Whereas my <a href="MASHvFLASHnn.html">earlier analysis</a> (which implicitly assumed that <span class="math inline">\(V = I\)</span>) found 39 data-driven loadings, here I was only able to obtain 26.</p>
<div id="similar-loadings" class="section level3">
<h3>Similar loadings</h3>
<p>I first plot the new loadings side by side with the previous loadings to which they most closely correspond. Note that, in general, the previous loadings tend to be sparser than these new loadings. Further, this new approach finds two unique effects (caudate basal ganglia and nucleus accumbens basal ganglia) where the previous approach very plausibly found correlations among three types of basal ganglia (loading 25). However, the adipose tissue effects (loading 11) do not get tangled up with the tibial nerve tissue effect (as they did in the previous approach), and there is a single loading describing correlations among skin tissues (loading 3) rather than two largely overlapping loadings.</p>
<pre class="r"><code>nondiag <- readRDS("./output/MASHvFLASHnondiagonalV/2dRepeat3.rds")
diag <- readRDS("./output/MASHvFLASHnn/fl.rds")
nondiag_order <- c(44:46, 46:54, 54:nondiag$nfactors)
diag_order <- c(1, 3, 6, 31, 10,
4, 9, 7, 15,
5, 13, 8, 23, 20,
21, 12, 14, 16,
17, 18, 19, 2,
24, 25, 34, 32,
25, 28)
diag_not_nondiag <- setdiff(c(1:29, 32:40), diag_order)
tissue_names <- rownames(diag$EL)
missing.tissues <- c(7, 8, 19, 20, 24, 25, 31, 34, 37)
gtex.colors <- read.table("https://github.com/stephenslab/gtexresults/blob/master/data/GTExColors.txt?raw=TRUE", sep = '\t', comment.char = '')[-missing.tissues, 2]
gtex.colors <- as.character(gtex.colors)
par(mfrow=c(2,2))
display_names <- strtrim(tissue_names, 20)
for(i in 1:length(nondiag_order)) {
plot_names <- display_names
next_nondiag <- nondiag$fit$EL[, nondiag_order[i]]
plot_names[next_nondiag < 0.25 * max(next_nondiag)] <- ""
barplot(next_nondiag,
main=paste0('Nondiagonal V, loading ', nondiag_order[i] - 43),
las=2, cex.names=0.4, yaxt='n',
col=gtex.colors, names=plot_names)
barplot(diag$EL[, diag_order[i]],
main=paste0('Diagonal V, loading ', diag_order[i]),
las=2, cex.names=0.4, yaxt='n',
col=gtex.colors, names=plot_names)
}</code></pre>
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</div>
<div id="differences" class="section level3">
<h3>Differences</h3>
<p>Next, I plot previous loadings that do not correspond to any of the new loadings. One of these (loading 11) may indeed be an artefactual loading that corresponds to covariance in errors rather than biological reality. However, one of the others (loading 22) describes a plausible correlation among ovarian, uterine, and vaginal tissues. The remaining are unique effects.</p>
<pre class="r"><code>par(mfrow=c(2,2))
for (i in 1:length(diag_not_nondiag)) {
plot_names <- display_names
next_diag <- diag$EL[, diag_not_nondiag[i]]
plot_names[next_diag < 0.25 * max(next_diag)] <- ""
barplot(next_diag,
main=paste0('Diagonal, loading ', diag_not_nondiag[i]),
las=2, cex.names=0.4, yaxt='n',
col=gtex.colors, names=plot_names)
}</code></pre>
<p><img src="figure/MASHvFLASHnondiagonalV.Rmd/extra-1.png" width="672" style="display: block; margin: auto;" /></p>
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<p></details></p>
</div>
</div>
<div id="code" class="section level2">
<h2>Code</h2>
<p>Click “Code” to view the code used to obtain the above results.</p>
<pre class="r"><code>devtools::load_all("/Users/willwerscheid/GitHub/flashr/")
devtools::load_all("/Users/willwerscheid/GitHub/ebnm/")
library(mashr)
gtex <- readRDS(gzcon(url("https://github.com/stephenslab/gtexresults/blob/master/data/MatrixEQTLSumStats.Portable.Z.rds?raw=TRUE")))
strong <- gtex$strong.z
random <- gtex$random.z
# Step 1. Estimate correlation structure using MASH.
m_random <- mash_set_data(random, Shat = 1)
Vhat <- estimate_null_correlation(m_random)
# Step 2. Estimate data-driven loadings using FLASH.
# Step 2a. Fit Vhat.
n <- nrow(Vhat)
lambda.min <- min(eigen(Vhat, symmetric=TRUE, only.values=TRUE)$values)
data <- flash_set_data(Y, S = sqrt(lambda.min))
W.eigen <- eigen(Vhat - diag(rep(lambda.min, n)), symmetric=TRUE)
# The rank of W is at most n - 1, so we can drop the last eigenval/vec:
W.eigen$values <- W.eigen$values[-n]
W.eigen$vectors <- W.eigen$vectors[, -n, drop=FALSE]
fl <- flash_add_fixed_loadings(data,
LL=W.eigen$vectors,
init_fn="udv_svd",
backfit=FALSE)
ebnm_param_f <- lapply(as.list(W.eigen$values),
function(eigenval) {
list(g = list(a=1/eigenval, pi0=0), fixg = TRUE)
})
ebnm_param_l <- lapply(vector("list", n - 1),
function(k) {list()})
fl <- flash_backfit(data,
fl,
var_type="zero",
ebnm_fn="ebnm_pn",
ebnm_param=(list(f = ebnm_param_f, l = ebnm_param_l)),
nullcheck=FALSE)
# Step 2b. Add nonnegative factors.
ebnm_fn = list(f = "ebnm_pn", l = "ebnm_ash")
ebnm_param = list(f = list(warmstart = TRUE),
l = list(mixcompdist="+uniform"))
fl <- flash_add_greedy(data,
Kmax=50,
f_init=fl,
var_type="zero",
init_fn="udv_svd",
ebnm_fn=ebnm_fn,
ebnm_param=ebnm_param)
saveRDS(fl, "./output/MASHvFLASHVhat/2bGreedy.rds")
# Step 2c (optional). Backfit factors from step 2b.
fl <- flash_backfit(data,
fl,
kset=n:fl$nfactors,
var_type="zero",
ebnm_fn=ebnm_fn,
ebnm_param=ebnm_param,
nullcheck=FALSE)
saveRDS(fl, "./output/MASHvFLASHVhat/2cBackfit.rds")
# Step 2d (optional). Repeat steps 2b and 2c as desired.
fl <- flash_add_greedy(data,
Kmax=50,
f_init=fl,
var_type="zero",
init_fn="udv_svd",
ebnm_fn=ebnm_fn,
ebnm_param=ebnm_param)
fl <- flash_backfit(data,
fl,
kset=n:fl$nfactors,
var_type="zero",
ebnm_fn=ebnm_fn,
ebnm_param=ebnm_param,
nullcheck=FALSE)
saveRDS(fl, "./output/MASHvFLASHVhat/2dRepeat3.rds")</code></pre>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>R version 3.4.3 (2017-11-30)
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/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/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
loaded via a namespace (and not attached):
[1] workflowr_1.0.1 Rcpp_0.12.17 digest_0.6.15
[4] rprojroot_1.3-2 R.methodsS3_1.7.1 backports_1.1.2
[7] git2r_0.21.0 magrittr_1.5 evaluate_0.10.1
[10] stringi_1.1.6 whisker_0.3-2 R.oo_1.21.0
[13] R.utils_2.6.0 rmarkdown_1.8 tools_3.4.3
[16] stringr_1.3.0 yaml_2.1.17 compiler_3.4.3
[19] htmltools_0.3.6 knitr_1.20 </code></pre>
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