Randomizing the order of backfits
Jason Willwerscheid
8/19/2018
Last updated: 2018-08-22
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Introduction
When trying to coax sparse nonnegative factors out of the “strong” GTEx dataset (see here), I noticed that later-added factor/loading pairs are in general much sparser than earlier-added pairs. Here I’d like to determine whether the order of backfitting makes any difference to the factors obtained (and the final objective).
Experiment
I begin with the 34 factor/loading pairs that are added via a single call to flash_add_greedy and backfit using three methods: 1. updating factor/loading pairs sequentially from #1 to #34; 2. updating sequentially in backwards order (from #34 to #1); and 3. updating in a random order.
Results
I pre-run the code below and load the results from file.
devtools::load_all("/Users/willwerscheid/GitHub/flashr/")Loading flashrgtex <- readRDS(gzcon(url("https://github.com/stephenslab/gtexresults/blob/master/data/MatrixEQTLSumStats.Portable.Z.rds?raw=TRUE")))
strong <- t(gtex$strong.z)
strong_data <- flash_set_data(strong, S = 1)
fl_seq <- readRDS("./data/random/fl1.rds")
fl_rev <- readRDS("./data/random/fl2.rds")
fl_rand <- readRDS("./data/random/fl3.rds")The final objective for each method is:
c(sequential = flash_get_objective(strong_data, fl_seq),
reverse = flash_get_objective(strong_data, fl_rev),
random = flash_get_objective(strong_data, fl_rand))sequential reverse random
-1257537 -1257237 -1257406 Most of the factor/loading pairs are nearly indistinguishable to the eye. Below I plot the seven factor/loadings with the largest differences:
normalize_EL <- function(fl) {
norms <- apply(abs(fl$EL), 2, max)
return(sweep(fl$EL, 2, norms, `/`))
}
norm_EL_seq <- normalize_EL(fl_seq)
norm_EL_rev <- normalize_EL(fl_rev)
norm_EL_rand <- normalize_EL(fl_rand)
# Find factor/loading pairs with largest differences
max_diff <- pmax(abs(norm_EL_seq - norm_EL_rev),
abs(norm_EL_seq - norm_EL_rand),
abs(norm_EL_rev - norm_EL_rand))
factors_to_show <- which(apply(max_diff, 2, max) > .05)
missing.tissues <- c(7, 8, 19, 20, 24, 25, 31, 34, 37)
gtex.colors <- read.table("https://github.com/stephenslab/gtexresults/blob/master/data/GTExColors.txt?raw=TRUE", sep = '\t', comment.char = '')[-missing.tissues, 2]
par(mfrow = c(2, 3))
for (i in factors_to_show) {
barplot(fl_seq$EL[, i], main=paste0('Loading ', i, ' (sequential)'),
las=2, cex.names=0.4, yaxt='n', col=as.character(gtex.colors),
names="")
barplot(fl_rev$EL[, i], main=paste0('Loading ', i, ' (reverse)'),
las=2, cex.names=0.4, yaxt='n', col=as.character(gtex.colors),
names="")
barplot(fl_rand$EL[, i], main=paste0('Loading ', i, ' (random)'),
las=2, cex.names=0.4, yaxt='n', col=as.character(gtex.colors),
names="")
}
Conclusions
Results are somewhat inconclusive. There are clearly some differences, but even the largest differences seem to be relatively minor (in a qualitative sense). On the other hand, a difference in objective of 300 is perhaps not to be sneered at.
It might be worthwhile to investigate more systematically with simulated data. Here, the usual sequential method is both slowest and attains the worst final objective. It would be interesting to determine whether this is regularly the case.
Code
Click “Code” to view the code used to obtain the above results.
devtools::load_all("/Users/willwerscheid/GitHub/flashr/") # use "dev" branch
devtools::load_all("/Users/willwerscheid/GitHub/ebnm/")
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)
fl_init <- readRDS("/Users/willwerscheid/GitHub/MASHvFLASH/output/MASHvFLASHnn/fl_g.rds")
# Sequential backfit (from factor/loading 1 to factor/loading 34) -------
#
ebnm_param = list(f = list(), l = list(mixcompdist="+uniform"))
fl1 <- flash_backfit_workhorse(strong_data,
fl_init,
kset = 1:34,
var_type = "zero",
ebnm_fn = "ebnm_ash",
ebnm_param = ebnm_param,
verbose_output = "odLn",
nullcheck = FALSE)
# Use warmstarts to clamp it down:
ebnm_param = list(f = list(warmstart = TRUE),
l = list(mixcompdist = "+uniform", warmstart = TRUE))
fl1 <- flash_backfit_workhorse(strong_data,
fl1,
kset = 1:34,
var_type = "zero",
ebnm_fn = "ebnm_ash",
ebnm_param = ebnm_param,
verbose_output = "odLn",
nullcheck = FALSE)
## 77 + 375 iterations; -1257537
saveRDS(fl1, "./data/random/fl1.rds")
# Sequential backfit in reverse order (from 34 to 1) --------------------
#
ebnm_param = list(f = list(), l = list(mixcompdist="+uniform"))
fl2 <- flash_backfit_workhorse(strong_data,
fl_init,
kset = 34:1,
var_type = "zero",
ebnm_fn = "ebnm_ash",
ebnm_param = ebnm_param,
verbose_output = "odLn",
nullcheck = FALSE)
ebnm_param = list(f = list(warmstart = TRUE),
l = list(mixcompdist = "+uniform", warmstart = TRUE))
fl2 <- flash_backfit_workhorse(strong_data,
fl2,
kset = 34:1,
var_type = "zero",
ebnm_fn = "ebnm_ash",
ebnm_param = ebnm_param,
verbose_output = "odLn",
nullcheck = FALSE)
## 77 + 125 iterations; objective: -1257237
saveRDS(fl2, "./data/random/fl2.rds")
# Backfit the factor/loadings in a random order -------------------------
#
set.seed(666)
ebnm_param = list(f = list(), l = list(mixcompdist="+uniform"))
fl3 <- fl_init
old_obj <- flash_get_objective(strong_data, fl3)
diff <- Inf
iter <- 0
while (diff > .01) {
iter <- iter + 1
fl3 <- flash_backfit_workhorse(strong_data,
fl3,
kset=sample(1:34, 34),
var_type = "zero",
ebnm_fn = "ebnm_ash",
ebnm_param = ebnm_param,
verbose_output = "",
maxiter = 1,
nullcheck = FALSE)
obj <- flash_get_objective(strong_data, fl3)
message("Iteration ", iter, ": ", obj)
diff <- obj - old_obj
old_obj <- obj
}
ebnm_param = list(f = list(warmstart = TRUE),
l = list(mixcompdist = "+uniform", warmstart = TRUE))
old_obj <- flash_get_objective(strong_data, fl3)
diff <- Inf
iter <- 0
while (diff > .01) {
iter <- iter + 1
fl3 <- flash_backfit_workhorse(strong_data,
fl3,
kset=sample(1:34, 34),
var_type = "zero",
ebnm_fn = "ebnm_ash",
ebnm_param = ebnm_param,
verbose_output = "",
maxiter = 1,
nullcheck = FALSE)
obj <- flash_get_objective(strong_data, fl3)
message("Iteration ", iter, ": ", obj)
diff <- obj - old_obj
old_obj <- obj
}
# 52 + 231 iterations; final obj: -1257408
saveRDS(fl3, "./data/random/fl3.rds")Session information
sessionInfo()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 workflowr_1.0.1
[7] R.methodsS3_1.7.1 R.utils_2.6.0 iterators_1.0.9
[10] tools_3.4.3 testthat_2.0.0 digest_0.6.15
[13] tibble_1.4.2 evaluate_0.10.1 memoise_1.1.0
[16] gtable_0.2.0 lattice_0.20-35 rlang_0.2.0
[19] Matrix_1.2-12 foreach_1.4.4 commonmark_1.4
[22] yaml_2.1.17 parallel_3.4.3 ebnm_0.1-12
[25] withr_2.1.1.9000 stringr_1.3.0 roxygen2_6.0.1.9000
[28] xml2_1.2.0 knitr_1.20 devtools_1.13.4
[31] rprojroot_1.3-2 grid_3.4.3 R6_2.2.2
[34] rmarkdown_1.8 ggplot2_2.2.1 ashr_2.2-10
[37] magrittr_1.5 whisker_0.3-2 backports_1.1.2
[40] scales_0.5.0 codetools_0.2-15 htmltools_0.3.6
[43] MASS_7.3-48 assertthat_0.2.0 softImpute_1.4
[46] colorspace_1.3-2 stringi_1.1.6 lazyeval_0.2.1
[49] munsell_0.4.3 doParallel_1.0.11 pscl_1.5.2
[52] truncnorm_1.0-8 SQUAREM_2017.10-1 R.oo_1.21.0 This reproducible R Markdown analysis was created with workflowr 1.0.1