---
title: "Regression Based Approach for Motif Selection"
author: "Dania Machlab, Lukas Burger, Charlotte Soneson, Michael Stadler"
date: "`r Sys.Date()`"
bibliography: monaLisa-refs.bib
output: 
  BiocStyle::html_document:
    toc_float: true
vignette: >
  %\VignetteIndexEntry{selecting_motifs_with_randLassoStabSel}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
    collapse = TRUE,
    comment = "#>",
    fig.width = 7,
    fig.height = 5,
    out.width = "80%",
    fig.align = "center",
    crop = NULL # suppress "The magick package is required to crop" issue
)
library(BiocStyle)
```

<img src="monaLisa_logo_v1.png" style="display: block; margin-left: auto;
margin-right: auto; width: 50%; border: 0" />

# Introduction

Identifying important transcription factor (TF) motifs, as shown in 
`r Biocpkg("monaLisa", vignette="monaLisa.html", label="the main vignette")`, 
could also be done using a regression-based approach, where motifs have to
compete against each other for selection. In this framework, the response vector
can be the observed experimental measure of interest, e.g. log-fold changes of
accessibility for a set of regions, and the predictors consist of the TF motif
hits across those regions. In `r Biocpkg("monaLisa")`, we implement the
randomized lasso stability selection proposed by @StabSel with the improved
error bounds introduced by @compStabs. We have modified the
`stabs::glmnet.lasso` function used by `stabs::stabsel` from the 
`r CRANpkg("stabs")` package to implement the randomized lasso.

Lasso stability selection performs the lasso regression multiple times on
subsamples of the data, and returns a selection probability for each predictor
(number of times selected divided by number of regressions done). With the
randomized lasso, a weakness parameter is additionally used  to vary the lasso
penalty term $\lambda$ to a randomly chosen value between [$\lambda$,
$\lambda$/weakness] for each predictor. This type of regularization has
advantages in cases where the number of predictors exceeds the number of
observations, in selecting variables consistently, demonstrating better error
control and not depending strongly on the penalization parameter [@StabSel].

With this approach, TF motifs compete against each other to explain the 
response vector, and we can also include additional predictors like GC content 
to compete against the TF motifs for selection. This is especially useful if 
the response is biased by sequence composition, for example if regions with 
higher GC content tend to have higher response values.

It is worth noting that, as with any regression analysis, the interpretability 
of the results depends strongly on the quality of the predictors. Hence, 
increasing the size of the motif database is not, in itself, a guarantee for 
more interpretable results, since the added motifs may be unrelated to the 
signal of interest. In addition, as discussed in section \@ref(collinearity), a 
high level of redundancy, resulting in strong correlations among the motifs, 
may result in more ambiguous selection probabilities in the regression 
approach. In fact, also for the binned approach, although the motifs are 
evaluated independently for association with the outcome, a high degree of 
redundancy can lead to large collections of very similar motifs showing
significant enrichments, complicating interpretability of the results. 


# Motif selection with Randomized Lasso Stability Selection{#stabsel}

In the example below, we select for TF motifs explaining log-fold changes in 
chromatin accessibility (ATAC-seq) across the enhancers between mouse liver and 
lung tissue at P0, but this can be applied to other data types as well 
(ChIP-seq, RNA-seq, methylation etc.). Positive log2-fold changes indicate 
more accessibility in the liver tissue, whereas negative values indicate 
more accessibility in the lung tissue.

## Load packages

We start by loading the needed packages: 

```{r libs, message=FALSE}
library(monaLisa)
library(JASPAR2020)
library(TFBSTools)
library(BSgenome.Mmusculus.UCSC.mm10)
library(Biostrings)
library(SummarizedExperiment)
library(ComplexHeatmap)
library(circlize)
```

## Load dataset

In this example dataset from ENCODE [@encode2012], and available in 
`r Biocpkg("monaLisa")`, we have quantified ATAC-seq reads on enhancers in mouse P0
lung and liver tissues. The log2-fold change (our response vector in this
example) is for liver vs lung chromatin accessibility. We are using a set of
10,000 randomly sampled enhancers to illustrate how randomized lasso stability
selection can be used to select TF motifs.

```{r loadData}
# load GRanges object with logFC and peaks
gr_path <- system.file("extdata", "atac_liver_vs_lung.rds", 
                       package = "monaLisa")
gr <- readRDS(gr_path)
```


## Get TFBS per motif and peak

We will now construct the transcription factor binding site (TFBS) matrix for
known motifs (from a database like `r Biocpkg("JASPAR2020")`) in the given peak
regions. We use the `findMotifHits` function to scan for TF motif hits. This
matrix will be the predictor matrix in our regression. This step may take a
while, and it may be useful to parallelize it using the `BPPARAM` argument (e.g.
to run on `n` parallel threads using the multi-core backend, you can use:
`findMotifHits(..., BPPARAM = BiocParallel::MulticoreParam(n))`).

As mentioned, this framework offers the flexibility to add additional 
predictors to compete against the TF motifs for selection. Here, we add the 
fraction of G+C and CpG observed/expected ratio as predictors, to ensure that 
selected TF motifs are not just detecting a simple trend in GC or CpG 
composition.

```{r predictorMatrix, warning=FALSE}
# get PFMs (vertebrate TFs from Jaspar)
pfms <- getMatrixSet(JASPAR2020, list(matrixtype = "PFM", 
                                      tax_group = "vertebrates"))

# randomly sample 300 PFMs for illustration purposes (for quick runtime)
set.seed(4563)
pfms <- pfms[sample(length(pfms), size = 300)]

# convert PFMs to PWMs
pwms <- toPWM(pfms)

# get TFBS on given GRanges (peaks)
# suppress warnings generated by matchPWM due to the presence of Ns 
# in the sequences
peakSeq <- getSeq(BSgenome.Mmusculus.UCSC.mm10, gr)
suppressWarnings({
  hits <- findMotifHits(query = pwms, subject = peakSeq, min.score = 10.0,
                        BPPARAM = BiocParallel::SerialParam())
})

# get TFBS matrix
TFBSmatrix <- unclass(table(factor(seqnames(hits), levels = seqlevels(hits)),
                            factor(hits$pwmname, levels = name(pwms))))
TFBSmatrix[1:6, 1:6]

# remove TF motifs with 0 binding sites in all regions
zero_TF <- colSums(TFBSmatrix) == 0
sum(zero_TF)
TFBSmatrix <- TFBSmatrix[, !zero_TF]

# calculate G+C and CpG obs/expected
fMono <- oligonucleotideFrequency(peakSeq, width = 1L, as.prob = TRUE)
fDi <- oligonucleotideFrequency(peakSeq, width = 2L, as.prob = TRUE)
fracGC <- fMono[, "G"] + fMono[, "C"]
oeCpG <- (fDi[, "CG"] + 0.01) / (fMono[, "G"] * fMono[, "C"] + 0.01)

# add GC and oeCpG to predictor matrix
TFBSmatrix <- cbind(fracGC, oeCpG, TFBSmatrix)
TFBSmatrix[1:6, 1:6]
```

### A note on collinearity{#collinearity}
At this point it is useful for the user to get an overall feeling of the
collinearity structure in the TFBS matrix. Motifs that share a lot of similar
binding sites across the peaks will be highly correlated. High collinearity
between predictors is a well known problem in linear regression. It particularly
manifests itself in the lasso regression for example, where if variables are
equally highly correlated with the response, not all are co-selected as
predictors (if they are signal variables). Instead, one is arbitrarily chosen
while the others’ coefficients are set to zero. The rationale is that the
non-selected correlated predictors do not provide much additional information to
explain the response. It is good to be aware of these properties of regression,
and to place more weight on the meaning of the selected motif itself, rather
than the specific TF name when interpreting the results.

If many cases of high correlations exist and this is a concern, one may consider
selecting a representative set of predictors to use. This may for example be
achieved by clustering the weight matrices beforehand and using only one
representative motif per cluster for running the regression, using tools such as
for example RSAT [@RSAT]. RSAT-derived clusters of Jaspar weight matrices can be
found at https://jaspar.genereg.net/matrix-clusters/vertebrates/.

If the user is interested in working with all correlated motifs, the binned
approach is preferable as the motifs are independently tested for significance
(see the `r Biocpkg("monaLisa", vignette="monaLisa.html", label="binned
enrichment vignette")`). In the regression-based approach on the other hand, we
can more clearly understand the relative contributions of TF motifs to the
response in the context of each other.


## Identify important TFs

We can now run randomized lasso stability selection to identify TFs that are
likely to explain the log-fold changes in accessibility. The exact choice of
parameter values for this approach will depend largely on how stringent the user
wishes to be and how much signal there is in the data. For example, for more
stringent selections, one may decrease the value of the `weakness` parameter
which will make it harder for a variable to get selected. The user is in control
of false discoveries with the `PFER` parameter, which indicates the number of
falsely selected variables. As for the selection probability cutoff, @StabSel argue that
values in the range of [0.6, 0.9] should give similar results. See the
`randLassoStabSel` function for more details and default parameter values as
well as the `stabs::stabsel` function for the default assumptions on the
stability selection implementation by @compStabs.

```{r stabSelTFs}
## randLassoStabSel() is stochastic, so if we run with parallelization
##   (`mc.cores` argument), we must select a random number generator that can
##   provide multiple streams of random numbers used in the `parallel` package
##   and set its seed for reproducible results
# RNGkind("L'Ecuyer-CMRG")
# set.seed(123)
# se <- randLassoStabSel(x = TFBSmatrix, y = gr$logFC_liver_vs_lung, 
#                        cutoff = 0.8, mc.preschedule = TRUE, 
#                        mc.set.seed = TRUE, mc.cores = 2L)

# if not running in parallel mode, it is enough to use set.seed() before 
#   the call to ensure reproducibility (`mc.sores = 1`)
set.seed(123)
se <- randLassoStabSel(x = TFBSmatrix, y = gr$logFC_liver_vs_lung, 
                       cutoff = 0.8)
se

# selected TFs
colnames(se)[se$selected]
```


The stability paths visualize how predictors get selected over decreasing 
regularization stringency (from left to right): 

```{r plotStabilityPaths}
plotStabilityPaths(se)
```

Each line corresponds to a predictor, and we can see the selection 
probabilities as a function of the regularization steps, corresponding to 
decreasing values for the lambda regularization parameter in lasso. The 
predictor (TF motif) selection happens at the last step, given the specified 
minimum probability.

We can also visualize the selection probabilities of the selected TF motifs,
optionally multiplied by the sign of the correlation to the response vector, to
know how the TF relates to the change of accessibility (`directional`
parameter). In our example, positive correlations to the response vector
indicate a correlation with enhancers more accessible in the liver, whereas
negative ones indicate a correlation with enhancers more accessible in the lung.
Note that although one can vary the `selProbMinPlot` argument which sets the
selection probability cutoff, it is best to re-run randomized lasso stability
selection with the new cutoff, as this influences other parameter choices the
model uses internally. See @StabSel for more details.

```{r plotSelProbs, fig.width=8, fig.height=5}
plotSelectionProb(se, directional = TRUE)
```

Next, we visualize the correlation structure of the selected TF motifs within
the TFBS matrix. While the collinearity of predictors is a general issue in
regression-based approaches, randomized lasso stability selection normally does
better at co-selecting intermediately correlated predictors. In practice, we see
it select predictors with correlations as high as 0.9. However, it is good to
keep in mind that this can be an issue, and that predictors that are highly
correlated with each other might not end up being co-selected (see section
\@ref(collinearity)).

```{r TFBScor_selected, fig.width=10, fig.height=7}
# subset the selected TFs
sel <- colnames(se)[se$selected]
se_sub <- se[, sel]

# exclude oeCpG and fracGC
excl <- colnames(se_sub) %in% c("oeCpG", "fracGC")
se_sub <- se_sub[, !excl]

# correlation matrix 
TFBSmatrixCorSel <- cor(TFBSmatrix[, colnames(se_sub)], method = "pearson")

# heatmap
pfmsSel <- pfms[match(colnames(TFBSmatrixCorSel), name(pfms))]
maxwidth <- max(sapply(TFBSTools::Matrix(pfmsSel), ncol))
seqlogoGrobs <- lapply(pfmsSel, seqLogoGrob, xmax = maxwidth)

hmSeqlogo <- rowAnnotation(logo = annoSeqlogo(seqlogoGrobs, which = "row"),
                           annotation_width = unit(2, "inch"), 
                           show_annotation_name = FALSE
)

colAnn <- HeatmapAnnotation(AUC = se_sub$selAUC, selProb = se_sub$selProb,
                            show_legend = TRUE, 
                            show_annotation_name = TRUE,
                            col = list(
                              AUC = colorRamp2(c(0, 1), 
                                               c("white", "brown")),
                              selProb = colorRamp2(c(0, 1), 
                                                   c("white", "steelblue")))
)

Heatmap(TFBSmatrixCorSel, 
        show_row_names = TRUE, 
        show_column_names = TRUE, 
        name = "Pear. Cor.", column_title = "Selected TFs",
        col = colorRamp2(c(-1, 0, 1), c("blue", "white", "red")), 
        right_annotation = hmSeqlogo,
        top_annotation = colAnn)
```

\  

We can examine the peaks that have hits for a selected TF motif of interest, 
ordered by absolute accessibility changes.

```{r topPeaks}
TF <- sel[2]
TF

i <- which(assay(se, "x")[, TF] > 0) # peaks that contain TF hits...
nm <- names(sort(abs(gr$logFC_liver_vs_lung[i]), 
                 decreasing = TRUE)) # ... order by |logFC|

gr[nm]
```


# Session info and logo
The monaLisa logo uses a drawing that was obtained from 
http://vectorish.com/lisa-simpson.html
under the Creative Commons attribution - non-commercial 3.0 license: 
https://creativecommons.org/licenses/by-nc/3.0/.

This vignette was built using:  
```{r, session}
sessionInfo()
```

# References