Latent gene list
karltayeb
2022-03-02
Last updated: 2022-04-07
Checks: 7 0
Knit directory: logistic-susie-gsea/
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Introduction
We’ve been thinking about the question “how much information is lost when you discritize?”
Running linear SuSiE on zscores/summary stats isn’t appropriate because you may have genes within an enriched gene set with differing effect sign and magnitude. Additionally, when I raised this at Gilad lab meeting Yoav was very vocal that the threshold free aspect of GSEA was a desirable property.
Borrowing from the work in iDEA, we’re going to treat the interesting/differential expression status of a gene as latent. So z-scores/summary stats are either drawn from a null-component or a non-null/interesting component. Our job is to estimate the probability that each gene is interesting. The prior probability of a gene being interesting will be modeled as a function of genesets/enrichment parameters with a SuSiE prior.
$$ \[\begin{align} \hat z_i \sim \mathcal{N}(z_i, 1) \\ z_i \sim \pi_{0i} f_0 + \pi_{1i} f_1 \end{align}\] $$
\[ \begin{align} \ln \frac{\pi_{1i}}{1 - \pi_{1i}} = \beta^Tx_i \\ \end{align} \]
Where \(x_i\) is a binary vector indicating gene set membership of gene \(i\).
Fortunately, if we look at the ELBO for logistic SuSiE the realized binary indicators \(y_i\) only appear linearly, so we can just pass in \(\mathbb E \gamma_i\) to logistic SuSiE.
All we need to do then is introduce variational approximations for (1) the latent indicators \(\gamma_i\) and (2) the paramters of \(f_0\) and \(f_1\), which for now we’ll leave fixed. We choose \(q(\gamma) = \prod_i q(\gamma_i)\) since we need \(\gamma_i\) to be (conditionally) independent to just pass them to SuSiE.
\[ \begin{align} \ln p(z | X) &= \ln \int p(z |\theta, \gamma) p(\gamma, \beta | X,\beta)p(\theta | X) d\{\beta, \gamma, \theta\} \\ &\geq \mathbb E\left[\ln p(z | \theta, \gamma) + \ln p(\theta | X) +\ln p(\gamma, \beta | X) \right] - \mathbb E_q\left[\ln q\right] \end{align} \\ = \mathbb E_q\left[\ln p(z | \theta, \gamma) + \ln p(\theta | X) \right] - \mathbb E_q\left[\ln q(\gamma, \theta)\right] + \mathbb E_{q(\gamma)} \left[ELBO_{\text{logistic SuSiE}} \right] \]
f <- system.file('data', 'summary_data.RData', package='iDEA'); load(f)
f <- system.file('data', 'annotation_data.RData', package='iDEA'); load(f)
f <- system.file('data', 'humanGeneSets.RData', package='iDEA'); load(f)
f <- system.file('data', 'humanGeneSetsInfo.RData', package='iDEA'); load(f)library(iDEA)
library(tictoc)
data(summary_data)
head(summary_data)
tic('fitting iDEA to example data')
idea <- xfun::cache_rds({
idea <- CreateiDEAObject(summary_data, annotation_data, max_var_beta = 100, min_precent_annot = 0.0025, num_core=8)
idea <- iDEA.fit(
idea, fit_noGS=FALSE, init_beta=NULL, init_tau=c(-2,0.5), min_degene=5,
em_iter=15, mcmc_iter=1000, fit.tol=1e-5, modelVariant = F, verbose=TRUE)
idea <- iDEA.louis(idea)
})
toc()
idea <- iDEA.louis(idea) ##
head(idea@de[["GO_REGULATION_OF_CANONICAL_WNT_SIGNALING_PATHWAY"]]$pip)source('code/logistic_susie_vb.R')
source('code/fit_susie.R')
source('code/fit_baselines.R')Loading required package: MatrixLoaded glmnet 4.1-3source('code/load_gene_sets.R')
library(org.Hs.eg.db)Loading required package: AnnotationDbiLoading required package: stats4Loading required package: BiocGenerics
Attaching package: 'BiocGenerics'The following objects are masked from 'package:stats':
IQR, mad, sd, var, xtabsThe following objects are masked from 'package:base':
anyDuplicated, append, as.data.frame, basename, cbind, colnames,
dirname, do.call, duplicated, eval, evalq, Filter, Find, get, grep,
grepl, intersect, is.unsorted, lapply, Map, mapply, match, mget,
order, paste, pmax, pmax.int, pmin, pmin.int, Position, rank,
rbind, Reduce, rownames, sapply, setdiff, sort, table, tapply,
union, unique, unsplit, which.max, which.minLoading required package: BiobaseWelcome to Bioconductor
Vignettes contain introductory material; view with
'browseVignettes()'. To cite Bioconductor, see
'citation("Biobase")', and for packages 'citation("pkgname")'.Loading required package: IRangesLoading required package: S4Vectors
Attaching package: 'S4Vectors'The following objects are masked from 'package:Matrix':
expand, unnameThe following objects are masked from 'package:base':
expand.grid, I, unnamelibrary(susieR)
library(progress)
library(RColorBrewer)
library(tidyverse)── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──✓ ggplot2 3.3.5 ✓ purrr 0.3.4
✓ tibble 3.1.6 ✓ dplyr 1.0.8
✓ tidyr 1.2.0 ✓ stringr 1.4.0
✓ readr 2.1.2 ✓ forcats 0.5.1── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
x dplyr::collapse() masks IRanges::collapse()
x dplyr::combine() masks Biobase::combine(), BiocGenerics::combine()
x dplyr::desc() masks IRanges::desc()
x tidyr::expand() masks S4Vectors::expand(), Matrix::expand()
x dplyr::filter() masks stats::filter()
x dplyr::first() masks S4Vectors::first()
x dplyr::lag() masks stats::lag()
x tidyr::pack() masks Matrix::pack()
x ggplot2::Position() masks BiocGenerics::Position(), base::Position()
x purrr::reduce() masks IRanges::reduce()
x dplyr::rename() masks S4Vectors::rename()
x dplyr::select() masks AnnotationDbi::select()
x dplyr::slice() masks IRanges::slice()
x tidyr::unpack() masks Matrix::unpack()library(targets)
convert_labels <- function(y){
hs <- org.Hs.eg.db
gene_symbols <- names(y)
symbol2entrez <- AnnotationDbi::select(hs, keys=gene_symbols, columns=c('ENTREZID', 'SYMBOL'), keytype = 'SYMBOL')
symbol2entrez <- symbol2entrez[!duplicated(symbol2entrez$SYMBOL),]
rownames(symbol2entrez) <- symbol2entrez$SYMBOL
ysub <- y[names(y) %in% symbol2entrez$SYMBOL]
names(ysub) <- symbol2entrez[names(ysub),]$ENTREZID
return(ysub)
}
procrustes <- function(X, y){
idx <- intersect(rownames(X), names(y))
return(list(X=X[idx,], y=y[idx]))
}
make_gene_list <- function(z, z_threshold=2){
y <- as.integer(abs(z) > z_threshold)
names(y) <- names(z)
return(y)
}
# emualate susie_plot for wrapped fit functions
susie_plot2 <- function(fit, max_set_size=200, ...){
gs <- colnames(fit$alpha[[1]])
plot(fit$pip[[1]], cex=0.001, ylab='PIP', xlab='Gene Set', ...)
to_plot <- fit$cs[[1]] %>%
mutate(plot = cs_size < 20) %>%
dplyr::select(plot) %>% pluck(1)
n_cs <- sum(to_plot)
cols <- brewer.pal(n_cs,'Set1')
print(n_cs)
color <- 1
for (i in which(to_plot)){
idx = (gs %in% fit$cs[[1]]$cs[[i]])
print(which(idx))
points(x=which(idx), y=fit$pip[[1]][which(idx)], col=cols[color], cex=2, pch=16)
color <- color+1
}
points(fit$pip[[1]], col='black', pch=16, cex=0.5)
}normalize <- function(x){
m <- max(x)
norm <- log(sum(exp(x - m)) +1e-10) + m
return(x - norm)
}
logit <- function(p){
return(log(p) - log(1-p))
}
sigmoid <- function(logit){
1 / (1 + exp(-logit))
}
update_gamma <- function(y, prediction, f0, f1){
u <- bind_cols(f0(y) - prediction, f1(y) + prediction)
u <- cbind(apply(u, 1, normalize))[2,]
names(u) <- names(y)
return(u)
}
compute_ELBO <- function(gamma, y, f0, f1, logistic.susie.fit){
likf0 <-f0(y)
likf1 <- f1(y)
ELBO <- sum(gamma * likf1 + (1-gamma) * likf0)
ELBO <- ELBO - sum((gamma * logit(gamma) + log(1 - gamma + 1e-10)))
ELBO <- ELBO + tail(logistic.susie.fit$elbo, 1)
return(ELBO)
}
predict.logistic.susie <- function(fit, X){
(fit$intercept + X %*% colSums(fit$mu * fit$alpha))[,1]
}
fit.latent.logistic.susie <- function(X, z, f0, f1, outer_maxit=20, ...){
# TODO: check inputs
# Initialization
prediction <- rep(-3, length(z)) # initial prediction, prior log odds DE
gamma <- exp(update_gamma(z, prediction, f0, f1))
res <- logistic.susie(X, gamma)
ELBO <- compute_ELBO(gamma, z, f0, f1, res)
res <- c(res, list(gamma=gamma, prediction=prediction))
# Main loop
for (i in 1:outer_maxit){
prediction <- predict.logistic.susie(res, X)
gamma <- exp(update_gamma(z, prediction, f0, f1))
res$dat$y <- gamma
for (i in 1:10){
res <- logistic.susie.iteration(res)
}
res <- logistic.susie.wrapup(res)
ELBO <- compute_ELBO(gamma, z, f0, f1, res)
res$gamma <- gamma
res$prediction <- prediction
}
return(res)
}# set up
library(targets)
tar_load(X.gonr)
z <- summary_data[,1] / sqrt(summary_data[,2])
names(z) <- rownames(summary_data)
z.entrez <- convert_labels(z)'select()' returned 1:many mapping between keys and columnstmp <- procrustes(X.gonr, z.entrez)
z <- tmp$y
X <- tmp$X# density function
f0 <- function(x){dnorm(x, mean=0, sd=1, log=T)}
f1 <- function(x){dnorm(x, mean=0, sd=100, log=T)}
latent.logistic.susie <- fit.latent.logistic.susie(X, z, f0, f1)New names:
* `` -> ...1
* `` -> ...2Warning in eval(family$initialize): non-integer #successes in a binomial glm!New names:
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* `` -> ...2par(mfrow=c(1, 3))
susie_plot(latent.logistic.susie, 'PIP')
hist(latent.logistic.susie$gamma)
par(mfrow=c(1, 3))
prediction <- latent.logistic.susie$prediction[[10]]
gamma <- latent.logistic.susie$gamma[[10]]
plot(prediction, logit2prob(prediction), main='prior/prediction')
plot(logit(gamma), gamma, main='posterior')
plot(prediction, logit(gamma))
GSEA sensitivity to thresholding in logistic model
logistic.susie.threshold.stability <- purrr::map(
1:10,
~list(fit = logistic.susie(X, (abs(z) > .x), L=10, verbose=T), thresh = .x))
converged
converged
converged
converged
converged
converged
converged
converged
converged
convergedpar(mfrow=c(2, 5))
for (i in 1:10){
susie_plot(logistic.susie.threshold.stability[[i]]$fit, 'PIP', main=paste0('|z|>', i))
}
latent.logistic.susie$sets$cs$L2
[1] 11
$L3
[1] 476
$L1
[1] 582 585logistic.susie.threshold.stability[[2]]$fit$sets$cs$L1
[1] 11
$L2
[1] 585logistic.susie.threshold.stability[[4]]$fit$sets$cs$L1
[1] 11
$L3
[1] 476
$L4
[1] 28
$L5
[1] 582 585logistic.susie.threshold.stability[[6]]$fit$sets$cs$L1
[1] 11
$L3
[1] 600
$L4
[1] 476
$L5
[1] 582
$L6
[1] 552
$L7
[1] 61logistic.susie.threshold.stability[[8]]$fit$sets$cs$L1
[1] 11
$L3
[1] 850The latent model is recovering similar gene set enrichment as the threshold model. They agree most around \(|z| > 4\). What threshold the models tend to agree on should depend a lot on \(f_0\) and \(f_1\) so it would be good to think a bit more closesly what these should look like. Maybe there is an easy way to make this work with ranked lists too.
knitr::knit_exit()