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<h1 class="title toc-ignore">Nonnegative FLASH loadings</h1>
</div>
<p><strong>Last updated:</strong> 2018-08-13</p>
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<p><details> <summary> <strong style="color:blue;">✔</strong> <strong>Repository version:</strong> <a href="https://github.com/willwerscheid/MASHvFLASH/tree/07c51b75fd5abff0c3556bd09feceb3b9ce7c643" target="_blank">07c51b7</a> </summary></p>
Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility. The version displayed above was the version of the Git repository at the time these results were generated. <br><br> Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use <code>wflow_publish</code> or <code>wflow_git_commit</code>). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:
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<a href="https://github.com/willwerscheid/MASHvFLASH/blob/07c51b75fd5abff0c3556bd09feceb3b9ce7c643/analysis/MASHvFLASHnn.Rmd" target="_blank">07c51b7</a>
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<p></details></p>
<hr />
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>I argued in the <a href="conclusions.html">previous analysis</a> that better loadings might be obtained if nonnegative priors were used. Here I fit a flash object to the “strong” GTEx dataset using “+uniform” ash priors on the loadings.</p>
</div>
<div id="fitting-procedure" class="section level2">
<h2>Fitting procedure</h2>
<p>I alternate between greedily adding factor/loading pairs (with “+uniform” ash priors on the loadings and normal-mixture ash priors on the factors) and backfitting the entire flash object. For the backfits, I set <code>tol = 1</code> because convergence can be very slow. I repeat these two steps until <code>flash_add_greedy</code> no longer adds any additional factor/loadings.</p>
<pre class="r"><code>iteration <- 1:7
factors_added <- c(34, 1, 1, 1, 2, 1, 0)
factors_zeroed_out <- c(0, 0, 1, 0, 0, 0, 0)
objective <- -1250000 - c(7689, 7595, 7140, 6685, 6362, 6098, 6098)
minutes_taken <- c(61, 3, 13, 26, 8, 16, 0)
data <- data.frame("Iteration" = iteration,
"Factors added" = factors_added,
"Factors deleted" = factors_zeroed_out,
"Final objective" = objective,
"Minutes" = minutes_taken)
knitr::kable(data)</code></pre>
<table>
<thead>
<tr class="header">
<th align="right">Iteration</th>
<th align="right">Factors.added</th>
<th align="right">Factors.deleted</th>
<th align="right">Final.objective</th>
<th align="right">Minutes</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">1</td>
<td align="right">34</td>
<td align="right">0</td>
<td align="right">-1257689</td>
<td align="right">61</td>
</tr>
<tr class="even">
<td align="right">2</td>
<td align="right">1</td>
<td align="right">0</td>
<td align="right">-1257595</td>
<td align="right">3</td>
</tr>
<tr class="odd">
<td align="right">3</td>
<td align="right">1</td>
<td align="right">1</td>
<td align="right">-1257140</td>
<td align="right">13</td>
</tr>
<tr class="even">
<td align="right">4</td>
<td align="right">1</td>
<td align="right">0</td>
<td align="right">-1256685</td>
<td align="right">26</td>
</tr>
<tr class="odd">
<td align="right">5</td>
<td align="right">2</td>
<td align="right">0</td>
<td align="right">-1256362</td>
<td align="right">8</td>
</tr>
<tr class="even">
<td align="right">6</td>
<td align="right">1</td>
<td align="right">0</td>
<td align="right">-1256098</td>
<td align="right">16</td>
</tr>
<tr class="odd">
<td align="right">7</td>
<td align="right">0</td>
<td align="right">0</td>
<td align="right">-1256098</td>
<td align="right">0</td>
</tr>
</tbody>
</table>
<p>Finally, I tighten the tolerance to 0.1 and run a final backfit, which increases the objective to -1256080 (this takes 25 minutes).</p>
</div>
<div id="loadings" class="section level2">
<h2>Loadings</h2>
<p>I load the results from file.</p>
<pre class="r"><code>devtools::load_all("/Users/willwerscheid/GitHub/flashr/")</code></pre>
<pre><code>Loading flashr</code></pre>
<pre class="r"><code>fl <- readRDS("./output/MASHvFLASHnn/fl.rds")
fl_g <- readRDS("./output/MASHvFLASHnn/fl_g.rds")</code></pre>
<div id="equal-effects" class="section level3">
<h3>Equal effects</h3>
<p>The first loading is well represented by the canonical “equal effects” loading.</p>
<pre class="r"><code>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]
pve <- flash_get_pve(fl, drop_zero_factors = FALSE)
par(mar=c(1,1,1,1))
barplot(fl$EL[, 1],
main=paste0('Loading 1: PVE = ', signif(pve[1], digits=3)),
las=2, cex.names=0.4, yaxt='n',
col=as.character(gtex.colors), names="")</code></pre>
<p><img src="figure/MASHvFLASHnn.Rmd/mean_effect-1.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="unique-effects" class="section level3">
<h3>Unique effects</h3>
<p>Many loadings are well approximated by canonical “unique effects.” Loadings 3, 4, 7, 9-10, 14-16, 18-21, 26-29, and 32-40 place nearly all of their weight on a single tissue.</p>
<pre class="r"><code>uniq <- c(3, 4, 7, 9, 10, 14:16, 18:21, 26:29, 32:40)
uniq_order <- order(pve[uniq], decreasing = TRUE)
tissue_names <- rownames(fl$EL)
par(mar=c(1,1,1,1))
par(mfrow=c(3,2))
for(i in uniq[uniq_order]){
barplot(fl$EL[, i],
main=paste0(tissue_names[which.max(fl$EL[, i])],
': PVE = ', signif(pve[i], digits=3)),
las=2, cex.names=0.4, yaxt='n',
col=as.character(gtex.colors), names="")
}</code></pre>
<p><img src="figure/MASHvFLASHnn.Rmd/uniq-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/uniq-2.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/uniq-3.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/uniq-4.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/uniq-5.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="multi-tissue-effects" class="section level3">
<h3>Multi-tissue effects</h3>
<p>The remaining loadings pick up on effects that are strongly correlated across several tissues. These are the loadings I’m especially interested in, since they correspond to correlation structures that are not covered by canonical loadings.</p>
<pre class="r"><code>multi <- c(2, 5, 6, 8, 11:13, 17, 22:25, 31)
multi_order <- order(pve[multi], decreasing = TRUE)
display_names <- strtrim(tissue_names, 10)
for(i in multi[multi_order]){
plot_names <- display_names
plot_names[fl$EL[, i] < 0.25 * max(fl$EL[, i])] <- ""
barplot(fl$EL[, i],
main=paste0('Loading ', i,
': PVE = ', signif(pve[i], digits=3)),
las=2, cex.names=0.8, yaxt='n',
col=as.character(gtex.colors), names=plot_names)
}</code></pre>
<p><img src="figure/MASHvFLASHnn.Rmd/multi-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-2.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-3.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-4.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-5.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-6.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-7.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-8.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-9.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-10.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-11.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-12.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/multi-13.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="greedy-multi-tissue-effects" class="section level3">
<h3>Greedy multi-tissue effects</h3>
<p>As indicated <a href="#fitting_procedure">above</a>, these loadings take about two and a half hours to obtain. However, loadings that are qualitatively very similar can be obtained via a single call to <code>flash_add_greedy</code> (with no backfitting), which takes less than 15 minutes. A comparison between these easily obtained loadings and the loadings yielded by the more laborious procedure detailed above follows:</p>
<pre class="r"><code>par(mfrow=c(2,2))
display_names <- strtrim(tissue_names, 20)
for(i in multi[multi_order]){
plot_names <- display_names
plot_names[fl_g$EL[, i] < 0.25 * max(fl_g$EL[, i])] <- ""
barplot(fl_g$EL[, i],
main=paste0('Greedy loading ', i),
las=2, cex.names=0.4, yaxt='n',
col=as.character(gtex.colors), names=plot_names)
barplot(fl$EL[, i],
main=paste0('Backfitted loading ', i),
las=2, cex.names=0.4, yaxt='n',
col=as.character(gtex.colors), names=plot_names)
}</code></pre>
<p><img src="figure/MASHvFLASHnn.Rmd/greedy_multi-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/greedy_multi-2.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/greedy_multi-3.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/greedy_multi-4.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/greedy_multi-5.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/greedy_multi-6.png" width="672" style="display: block; margin: auto;" /><img src="figure/MASHvFLASHnn.Rmd/greedy_multi-7.png" width="672" style="display: block; margin: auto;" /></p>
</div>
</div>
<div id="code" class="section level2">
<h2>Code</h2>
<p>Click “Code” to view the code used to obtain the above results.</p>
<pre class="r"><code>devtools::load_all("/Users/willwerscheid/GitHub/flashr/")
gtex <- readRDS(gzcon(url("https://github.com/stephenslab/gtexresults/blob/master/data/MatrixEQTLSumStats.Portable.Z.rds?raw=TRUE")))
strong <- t(gtex$strong.z)
strong_data <- flash_set_data(strong, S = 1)
ebnm_param = list(f = list(), l = list(mixcompdist="+uniform"))
system.time(
fl <- flash_add_greedy(strong_data,
100,
var_type="zero",
ebnm_fn="ebnm_ash",
ebnm_param=ebnm_param)
)
saveRDS(fl, "/Users/willwerscheid/GitHub/MASHvFLASH/output/MASHvFLASHnn/fl_g.rds")
system.time(
fl <- flash_backfit(strong_data,
f_init=fl,
var_type="zero",
ebnm_fn="ebnm_ash",
ebnm_param=ebnm_param,
tol=1)
)
# Repeat the following two steps until flash_add_greedy no longer adds
# any factors:
system.time(
fl <- flash_add_greedy(strong_data,
100,
f_init=fl,
var_type="zero",
ebnm_fn="ebnm_ash",
ebnm_param=ebnm_param)
)
system.time(
fl <- flash_backfit(strong_data,
f_init=fl,
var_type="zero",
ebnm_fn="ebnm_ash",
ebnm_param=ebnm_param,
tol=1)
)
saveRDS(fl, "/Users/willwerscheid/GitHub/MASHvFLASH/output/MASHvFLASHnn/fl.rds")
# Tighten the tolerance and run a final backfit:
system.time(
fl <- flash_backfit(strong_data,
f_init=fl,
var_type="zero",
ebnm_fn="ebnm_ash",
ebnm_param=ebnm_param,
tol=0.1)
)
saveRDS(fl, "/Users/willwerscheid/GitHub/MASHvFLASH/output/MASHvFLASHnn/fl.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
other attached packages:
[1] flashr_0.5-14
loaded via a namespace (and not attached):
[1] Rcpp_0.12.17 pillar_1.2.1 plyr_1.8.4
[4] compiler_3.4.3 git2r_0.21.0 highr_0.6
[7] workflowr_1.0.1 R.methodsS3_1.7.1 R.utils_2.6.0
[10] iterators_1.0.9 tools_3.4.3 testthat_2.0.0
[13] digest_0.6.15 tibble_1.4.2 evaluate_0.10.1
[16] memoise_1.1.0 gtable_0.2.0 lattice_0.20-35
[19] rlang_0.2.0 Matrix_1.2-12 foreach_1.4.4
[22] commonmark_1.4 yaml_2.1.17 parallel_3.4.3
[25] ebnm_0.1-12 withr_2.1.1.9000 stringr_1.3.0
[28] roxygen2_6.0.1.9000 xml2_1.2.0 knitr_1.20
[31] devtools_1.13.4 rprojroot_1.3-2 grid_3.4.3
[34] R6_2.2.2 rmarkdown_1.8 ggplot2_2.2.1
[37] ashr_2.2-10 magrittr_1.5 whisker_0.3-2
[40] scales_0.5.0 backports_1.1.2 codetools_0.2-15
[43] htmltools_0.3.6 MASS_7.3-48 assertthat_0.2.0
[46] softImpute_1.4 colorspace_1.3-2 stringi_1.1.6
[49] lazyeval_0.2.1 munsell_0.4.3 doParallel_1.0.11
[52] pscl_1.5.2 truncnorm_1.0-8 SQUAREM_2017.10-1
[55] R.oo_1.21.0 </code></pre>
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