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<h1 class="title toc-ignore">Comparing initialization functions (part II)</h1>
<h4 class="author"><em>Jason Willwerscheid</em></h4>
<h4 class="date"><em>8/28/2018</em></h4>
</div>
<p><strong>Last updated:</strong> 2018-08-29</p>
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<a href="https://github.com/willwerscheid/FLASHvestigations/blob/237072b28f322233c744e4ffc2c4f88b75a33e81/analysis/init_fn3.Rmd" target="_blank">237072b</a>
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<hr />
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>Here I return to the question of which initialization function is best, and in which cases. I run some simple experiments on simulated datasets of various dimensions and with or without missing data.</p>
</div>
<div id="results" class="section level2">
<h2>Results</h2>
<p>I simulate data from both a null model and a rank-one model with <span class="math inline">\(p \in \{1000, 10000\}\)</span> and with <span class="math inline">\(n\)</span> ranging from 10 to 1000. I either retain all of the data or I delete 20% of entries. I initialize using <code>"udv_si"</code>, <code>"udv_si_svd"</code>, and, when there is no missing data, <code>"udv_svd"</code>.</p>
<p>I pre-run the code <a href="#code">below</a> and load the results from file.</p>
<pre class="r"><code>all_res <- readRDS("./data/init_fn3/all_res.rds")
plot_results <- function(res, n, main, colors) {
colors = colors[c("udv_si_svd", "udv_si", "udv_svd")]
plot(log10(n), log10(res[["udv_si_svd"]]), type='l', col=colors[1],
xlab = "log10(n)", ylab = "time elapsed (log10 s)",
ylim = log10(c(min(unlist(res)), max(unlist(res)))),
main = main)
lines(log10(n), log10(res[["udv_si"]]), col=colors[2])
if (length(res) == 3) {
lines(log10(n), log10(res[["udv_svd"]]), col=colors[3])
}
legend.txt <- c("udv_si_svd", "udv_si", "udv_svd")
legend("bottomright", legend.txt[1:length(res)], lty=1,
col=colors[1:length(res)])
}
ns <- c(10, 25, 50, 100, 250, 500, 1000)
colors = RColorBrewer::brewer.pal(3, "Dark2")[1:3]
names(colors) = c("udv_svd", "udv_si", "udv_si_svd")
plot_results(all_res$null_noNA_p1000, ns,
"Null data (no missing), p = 1000", colors)</code></pre>
<p><img src="figure/init_fn3.Rmd/results-1.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>plot_results(all_res$null_noNA_p10000, ns,
"Null data (no missing), p = 10000", colors)</code></pre>
<p><img src="figure/init_fn3.Rmd/results-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>plot_results(all_res$r1_noNA_p1000, ns,
"Rank-one data (no missing), p = 1000", colors)</code></pre>
<p><img src="figure/init_fn3.Rmd/results-3.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>plot_results(all_res$r1_noNA_p10000, ns,
"Rank-one data (no missing), p = 10000", colors)</code></pre>
<p><img src="figure/init_fn3.Rmd/results-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>plot_results(all_res$null_missing_p1000, ns,
"Null data (with missing), p = 1000", colors)</code></pre>
<p><img src="figure/init_fn3.Rmd/results-5.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>plot_results(all_res$null_missing_p10000, ns,
"Null data (with missing), p = 10000", colors)</code></pre>
<p><img src="figure/init_fn3.Rmd/results-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>plot_results(all_res$r1_missing_p1000, ns,
"Rank-one data (with missing), p = 1000", colors)</code></pre>
<p><img src="figure/init_fn3.Rmd/results-7.png" width="672" style="display: block; margin: auto;" /></p>
<pre class="r"><code>plot_results(all_res$r1_missing_p10000, ns,
"Rank-one data (with missing), p = 10000", colors)</code></pre>
<p><img src="figure/init_fn3.Rmd/results-8.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="conclusions" class="section level2">
<h2>Conclusions</h2>
<p>The current default <code>init_fn = "udv_si"</code> is sensible. In cases with missing data, <code>"udv_si"</code> almost always beats <code>"udv_si_svd"</code>; the only exceptions are for small <span class="math inline">\(n\)</span>, but in such cases initialization is very fast anyway.</p>
<p>When there is no missing data, then <code>"udv_svd"</code> is the fastest method for small <span class="math inline">\(n\)</span>, but <code>"udv_si"</code> is again the fastest method when <span class="math inline">\(n\)</span> becomes large. (Interestingly, the relative speeds do not seem to depend on the larger dimension <span class="math inline">\(p\)</span>.)</p>
<p>It would be possible to programmatically set <code>init_fn</code> based on <span class="math inline">\(n\)</span> (or more precisely, based on the smaller of <span class="math inline">\(n\)</span> and <span class="math inline">\(p\)</span>), but I don’t think it’s worth the trouble, since <code>"udv_si_svd"</code> seems to consistently be the fastest (or nearly fastest) method when the speed of initialization actually becomes an issue.</p>
</div>
<div id="code" class="section level2">
<h2>Code</h2>
<pre class="r"><code>devtools::load_all("/Users/willwerscheid/GitHub/flashr")
sim_mat <- function(n, p, type, missing) {
if (type == 1) {
out <- matrix(rnorm(n * p), nrow=n, ncol=p)
} else if (type == 2) {
out <- (outer(rep(1, n), rep(1, p))
+ matrix(rnorm(n * p), nrow=n, ncol=p))
}
if (missing) {
out[rbinom(n * p, 1, 0.2) == 1] <- NA
}
return(out)
}
do_experiment <- function(nreps, ns, p, type, missing, verbose=TRUE) {
res <- list()
if (missing) {
init_fns <- c("udv_si", "udv_si_svd")
} else {
init_fns <- c("udv_svd", "udv_si", "udv_si_svd")
}
for (init_fn in init_fns) {
res[[init_fn]] <- rep(NA, nrow=length(ns))
}
for (i in 1:length(ns)) {
if (verbose) {
message("n = ", ns[i])
}
data <- list()
for (rep in 1:nreps) {
data[[rep]] <- sim_mat(ns[i], p, type, missing)
}
for (init_fn in init_fns) {
t <- system.time({
for (rep in 1:nreps) {
fl <- flash_add_factors_from_data(data[[rep]],
K=5,
init_fn=init_fn,
backfit=FALSE,
verbose=FALSE)
}
})
res[[init_fn]][i] <- t["elapsed"]
}
}
return(res)
}
set.seed(666)
all_res <- list()
nreps <- 5
ns <- c(10, 25, 50, 100, 250, 500, 1000)
p <- 1000
all_res$null_noNA_p1000 <- do_experiment(nreps, ns, p, type=1,
missing=FALSE)
all_res$r1_noNA_p1000 <- do_experiment(nreps, ns, p, type=2,
missing=FALSE)
all_res$null_missing_p1000 <- do_experiment(nreps, ns, p, type=1,
missing=TRUE)
all_res$r1_missing_p1000 <- do_experiment(nreps, ns, p, type=2,
missing=TRUE)
nreps <- 1
ns <- c(10, 25, 50, 100, 250, 500, 1000)
p <- 10000
all_res$null_noNA_p10000 <- do_experiment(nreps, ns, p, type=1,
missing=FALSE)
all_res$r1_noNA_p10000 <- do_experiment(nreps, ns, p, type=2,
missing=FALSE)
all_res$null_missing_p10000 <- do_experiment(nreps, ns, p, type=1,
missing=TRUE)
all_res$r1_missing_p10000 <- do_experiment(nreps, ns, p, type=2,
missing=TRUE)
saveRDS(all_res, "./data/init_fn3/all_res.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 RColorBrewer_1.1-2
[16] tools_3.4.3 stringr_1.3.0 yaml_2.1.17
[19] compiler_3.4.3 htmltools_0.3.6 knitr_1.20 </code></pre>
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