Last updated: 2025-05-02

Checks: 7 0

Knit directory: symmetric_covariance_decomposition/

This reproducible R Markdown analysis was created with workflowr (version 1.7.1). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.

R Markdown file: up-to-date

Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.

Environment: empty

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

Seed: set.seed(20250408)

The command set.seed(20250408) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Session information: recorded

Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

Cache: none

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

File paths: relative

Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.

Repository version: 846345d

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.

The results in this page were generated with repository version 846345d. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.

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 wflow_publish or wflow_git_commit). 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: 


Ignored files:
    Ignored:    .DS_Store
    Ignored:    .Rhistory

Untracked files:
    Untracked:  analysis/symebcovmf_binary_tree_resid_orthog_exploration.Rmd
    Untracked:  analysis/unbal_nonoverlap_exploration.Rmd

Unstaged changes:
    Modified:   analysis/unbal_nonoverlap.Rmd

Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.

These are the previous versions of the repository in which changes were made to the R Markdown (analysis/symebcovmf_binary_tree_resid_exploration.Rmd) and HTML (docs/symebcovmf_binary_tree_resid_exploration.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

File Version Author Date Message
Rmd 846345d Annie Xie 2025-05-02 Add text to residual matrix example
html a1149d8 Annie Xie 2025-05-02 Build site.
Rmd 818d4cf Annie Xie 2025-05-02 Edit text in residual matrix example analysis
html 9ddb9f2 Annie Xie 2025-05-01 Build site.
Rmd 03b6512 Annie Xie 2025-05-01 Edit observations in residual matrix example
html 9a7a4f4 Annie Xie 2025-05-01 Build site.
Rmd f3ba89f Annie Xie 2025-05-01 Add exploration of binary priors in tree residual matrix example

Introduction

In this analysis, I am interested in exploring symEBcovMF with the generalized binary prior in the tree setting. This analysis will focus on the residual matrix example that I investigated in a different analysis.

Motivation

When applying symEBcovMF with generalized binary prior to tree data, I found that instead of population effect factors, the method would group two population effects together. I tried using the point-exponential prior to remedy this, but found that the point-exponential prior also found factors which grouped two population effects. After further exploring this, I found that the method preferred the factor with two population effects – when initialized from the true population effect factor, the method still converged to the factor with two population effects. In this analysis, I am interested in exploring the following question: if the prior is more strictly binary, will the rank-one fit with point-exponential prior find a single population effect factor for the fourth factor?

Packages and Functions

library(ebnm)
library(pheatmap)
library(ggplot2)
source('code/visualization_functions.R')
source('code/symebcovmf_functions.R')

Data Generation

sim_4pops <- function(args) {
  set.seed(args$seed)
  
  n <- sum(args$pop_sizes)
  p <- args$n_genes
  
  FF <- matrix(rnorm(7 * p, sd = rep(args$branch_sds, each = p)), ncol = 7)
  # if (args$constrain_F) {
  #   FF_svd <- svd(FF)
  #   FF <- FF_svd$u
  #   FF <- t(t(FF) * branch_sds * sqrt(p))
  # }
  
  LL <- matrix(0, nrow = n, ncol = 7)
  LL[, 1] <- 1
  LL[, 2] <- rep(c(1, 1, 0, 0), times = args$pop_sizes)
  LL[, 3] <- rep(c(0, 0, 1, 1), times = args$pop_sizes)
  LL[, 4] <- rep(c(1, 0, 0, 0), times = args$pop_sizes)
  LL[, 5] <- rep(c(0, 1, 0, 0), times = args$pop_sizes)
  LL[, 6] <- rep(c(0, 0, 1, 0), times = args$pop_sizes)
  LL[, 7] <- rep(c(0, 0, 0, 1), times = args$pop_sizes)
  
  E <- matrix(rnorm(n * p, sd = args$indiv_sd), nrow = n)
  Y <- LL %*% t(FF) + E
  YYt <- (1/p)*tcrossprod(Y)
  return(list(Y = Y, YYt = YYt, LL = LL, FF = FF, K = ncol(LL)))
}
sim_args = list(pop_sizes = rep(40, 4), n_genes = 1000, branch_sds = rep(2,7), indiv_sd = 1, seed = 1)
sim_data <- sim_4pops(sim_args)

This is a heatmap of the scaled Gram matrix:

plot_heatmap(sim_data$YYt, colors_range = c('blue','gray96','red'), brks = seq(-max(abs(sim_data$YYt)), max(abs(sim_data$YYt)), length.out = 50))

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

This is a scatter plot of the true loadings matrix:

pop_vec <- c(rep('A', 40), rep('B', 40), rep('C', 40), rep('D', 40))
plot_loadings(sim_data$LL, pop_vec)

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

This is a plot of the eigenvalues of the Gram matrix:

S_eigen <- eigen(sim_data$YYt)
plot(S_eigen$values) + abline(a = 0, b = 0, col = 'red')

Version Author Date
9a7a4f4 Annie Xie 2025-05-01 
integer(0)

This is the minimum eigenvalue:

min(S_eigen$values)
[1] 0.3724341

Generalized binary with different scale parameter

First, I will try generalized binary prior with a different scale parameter. The scale parameter refers to the ratio \(\sigma/mu\). If the ratio is small, then the prior will be closer to a strictly binary prior.

ebnm_generalized_binary_fix_scale <- function(x, s, mode = 'estimate', g_init = NULL, fix_g = FALSE, output = ebnm_output_default(), control = NULL){
  ebnm_gb_output <- ebnm::ebnm_generalized_binary(x = x, s = s, mode = mode, 
                                                  scale = 0.01, 
                                                  g_init = g_init, fix_g = fix_g,
                                                  output = output, control = control)
  return(ebnm_gb_output)
}

Residual Matrix

We construct the residual matrix from a fit of three factors.

symebcovmf_gb_fix_scale_rank3_fit <- sym_ebcovmf_fit(S = sim_data$YYt, ebnm_fn = ebnm_generalized_binary_fix_scale, K = 3, maxiter = 500, rank_one_tol = 10^(-8), tol = 10^(-8), refit_lam = TRUE)
rank3_gb_fix_scale_resid_matrix <- sim_data$YYt - tcrossprod(symebcovmf_gb_fix_scale_rank3_fit$L_pm %*% diag(sqrt(symebcovmf_gb_fix_scale_rank3_fit$lambda)))

This is a plot of the loadings estimate.

plot_loadings(symebcovmf_gb_fix_scale_rank3_fit$L_pm %*% diag(sqrt(symebcovmf_gb_fix_scale_rank3_fit$lambda)), pop_vec)

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

This is a heatmap of the residual matrix.

plot_heatmap(rank3_gb_fix_scale_resid_matrix, colors_range = c('blue','gray96','red'), brks = seq(-max(abs(rank3_gb_fix_scale_resid_matrix)), max(abs(rank3_gb_fix_scale_resid_matrix)), length.out = 50))

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

Try fitting fourth factor with point-exponential prior

Now we try fitting a fourth factor using the rank-one fit with point-exponential prior.

symebcovmf_gb_fix_scale_exp_fac4_fit <- sym_ebcovmf_r1_fit(sim_data$YYt, symebcovmf_gb_fix_scale_rank3_fit, ebnm_fn = ebnm_point_exponential, maxiter = 100, tol = 10^(-8))

This is a plot of the fourth factor estimate.

plot(symebcovmf_gb_fix_scale_exp_fac4_fit$L_pm[,4], ylab = 'Fourth Factor')

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

This is a plot of the ELBO when optimizing the fourth factor.

fac4_idx <- which(symebcovmf_gb_fix_scale_exp_fac4_fit$vec_elbo_full == 4)
plot(symebcovmf_gb_fix_scale_exp_fac4_fit$vec_elbo_full[(fac4_idx+1): length(symebcovmf_gb_fix_scale_exp_fac4_fit$vec_elbo_full)], xlab = 'Iter', ylab = 'ELBO')

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

We see that the method still finds a factor with two population effects.

Progression of Estimate

This is the progression of the estimate.

estimates_gb_fix_scale_exp_list <- list(sym_ebcovmf_r1_init(rank3_gb_fix_scale_resid_matrix)$v)
for (i in 1:11){
  estimates_gb_fix_scale_exp_list[[(i+1)]] <- sym_ebcovmf_r1_fit(sim_data$YYt, symebcovmf_gb_fix_scale_rank3_fit, ebnm_fn = ebnm_point_exponential, maxiter = i, tol = 10^(-8))$L_pm[,4]
}
par(mfrow = c(6,2), mar = c(2, 2, 1, 1) + 0.1)
max_y <- max(sapply(estimates_gb_fix_scale_exp_list, max))
min_y <- min(sapply(estimates_gb_fix_scale_exp_list, min))
for (i in 1:12){
  plot(estimates_gb_fix_scale_exp_list[[i]], main = paste('Iter', (i-1)), ylab = 'L', ylim = c(min_y, max_y))
}

Version Author Date
9a7a4f4 Annie Xie 2025-05-01 
par(mfrow = c(1,1))

Try fitting fourth factor initialized at true factor

Now, I will try initializing with the true single population effect factor. This will help us determine if this is a convergence issue.

true_fac4 <- rep(c(1,0), times = c(40, 120))
true_fac4 <- true_fac4/sqrt(sum(true_fac4^2))
symebcovmf_gb_fix_scale_exp_true_init_fac4_fit <- sym_ebcovmf_r1_fit(sim_data$YYt, symebcovmf_gb_fix_scale_rank3_fit, ebnm_fn = ebnm_point_exponential, maxiter = 100, tol = 10^(-8), v_init = true_fac4)

This is a plot of the fourth factor estimate.

plot(symebcovmf_gb_fix_scale_exp_true_init_fac4_fit$L_pm[,4], ylab = 'Fourth Factor')

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

This is a plot of the ELBO when optimizing the fourth factor.

fac4_idx <- which(symebcovmf_gb_fix_scale_exp_true_init_fac4_fit$vec_elbo_full == 4)
plot(symebcovmf_gb_fix_scale_exp_true_init_fac4_fit$vec_elbo_full[(fac4_idx+1): length(symebcovmf_gb_fix_scale_exp_true_init_fac4_fit$vec_elbo_full)], xlab = 'Iter', ylab = 'ELBO')

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

We see that the method still converges to a factor with two population groups. This suggests this method prefers this factor as opposed to the single population effect factor.

Progression of Estimate

This is the progression of the estimate.

estimates_gb_fix_scale_exp_true_init_list <- list(true_fac4)
for (i in 1:11){
  estimates_gb_fix_scale_exp_true_init_list[[(i+1)]] <- sym_ebcovmf_r1_fit(sim_data$YYt, symebcovmf_gb_fix_scale_rank3_fit, ebnm_fn = ebnm_point_exponential, maxiter = i, tol = 10^(-8), v_init = rep(c(1,0), times = c(40, 120)))$L_pm[,4]
}
par(mfrow = c(6,2), mar = c(2, 2, 1, 1) + 0.1)
for (i in 1:12){
  plot(estimates_gb_fix_scale_exp_true_init_list[[i]], main = paste('Iter', (i-1)), ylab = 'L')
}

Version Author Date
9a7a4f4 Annie Xie 2025-05-01 
par(mfrow = c(1,1))

Binormal Prior

Here, I will try the binormal prior. Given that changing the scale of the generalized binary prior didn’t work and it doesn’t appear to be a convergence issue, I don’t really expect this to perform much better. But it’s also possible this prior has better shrinkage or convergence properties, so maybe it will.

dbinormal = function (x,s,s0,lambda,log=TRUE){
  pi0 = 0.5
  pi1 = 0.5
  s2 = s^2
  s02 = s0^2
  l0 = dnorm(x,0,sqrt(lambda^2 * s02 + s2),log=TRUE)
  l1 = dnorm(x,lambda,sqrt(lambda^2 * s02 + s2),log=TRUE)
  logsum = log(pi0*exp(l0) + pi1*exp(l1))
 
  m = pmax(l0,l1)
  logsum = m + log(pi0*exp(l0-m) + pi1*exp(l1-m))
  if (log) return(sum(logsum))
  else return(exp(sum(logsum)))
}
ebnm_binormal = function(x,s, g_init = NULL, fix_g = FALSE, output = ebnm_output_default(), control = NULL){
  # Add g_init to make the method run
  if(is.null(dim(x)) == FALSE){
    x <- c(x)
  }
  s0 = 0.01
  lambda = optimize(function(lambda){-dbinormal(x,s,s0,lambda,log=TRUE)},
              lower = 0, upper = max(x))$minimum
  g = ashr::normalmix(pi=c(0.5,0.5), mean=c(0,lambda), sd=c(lambda * s0,lambda * s0))
  postmean = ashr::postmean(g,ashr::set_data(x,s))
  postsd = ashr::postsd(g,ashr::set_data(x,s))
  log_likelihood <- ashr::calc_loglik(g, ashr::set_data(x,s))
  return(list(fitted_g = g, posterior = data.frame(mean=postmean,sd=postsd), log_likelihood = log_likelihood))
}

Residual Matrix

We construct the residual matrix from a fit of three factors.

symebcovmf_binormal_rank3_fit <- sym_ebcovmf_fit(S = sim_data$YYt, ebnm_fn = ebnm_binormal, K = 3, maxiter = 500, rank_one_tol = 10^(-8), tol = 10^(-8), refit_lam = TRUE)
rank3_binormal_resid_matrix <- sim_data$YYt - tcrossprod(symebcovmf_binormal_rank3_fit$L_pm %*% diag(sqrt(symebcovmf_binormal_rank3_fit$lambda)))

This is a plot of the loadings estimate.

plot_loadings(symebcovmf_binormal_rank3_fit$L_pm %*% diag(sqrt(symebcovmf_binormal_rank3_fit$lambda)), pop_vec)

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

This is a heatmap of the residual matrix.

plot_heatmap(rank3_binormal_resid_matrix, colors_range = c('blue','gray96','red'), brks = seq(-max(abs(rank3_binormal_resid_matrix)), max(abs(rank3_binormal_resid_matrix)), length.out = 50))

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

Try fitting fourth factor with point-exponential prior

Now we try fitting a fourth factor using the rank-one fit with point-exponential prior.

symebcovmf_binormal_exp_fac4_fit <- sym_ebcovmf_r1_fit(sim_data$YYt, symebcovmf_binormal_rank3_fit, ebnm_fn = ebnm_point_exponential, maxiter = 100, tol = 10^(-8))

This is a plot of the fourth factor estimate.

plot(symebcovmf_binormal_exp_fac4_fit$L_pm[,4], ylab = 'Fourth Factor')

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

This is a plot of the ELBO when optimizing the fourth factor.

fac4_idx <- which(symebcovmf_binormal_exp_fac4_fit$vec_elbo_full == 4)
plot(symebcovmf_binormal_exp_fac4_fit$vec_elbo_full[(fac4_idx+1): length(symebcovmf_binormal_exp_fac4_fit$vec_elbo_full)], xlab = 'Iter', ylab = 'ELBO')

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

Again, we see the method fits a factor with two population effects.

Progression of Estimate

This is the progression of the estimate.

estimates_binormal_exp_list <- list(sym_ebcovmf_r1_init(rank3_binormal_resid_matrix)$v)
for (i in 1:11){
  estimates_binormal_exp_list[[(i+1)]] <- sym_ebcovmf_r1_fit(sim_data$YYt, symebcovmf_binormal_rank3_fit, ebnm_fn = ebnm_point_exponential, maxiter = i, tol = 10^(-8))$L_pm[,4]
}
par(mfrow = c(6,2), mar = c(2, 2, 1, 1) + 0.1)
max_y <- max(sapply(estimates_binormal_exp_list, max))
min_y <- min(sapply(estimates_binormal_exp_list, min))
for (i in 1:12){
  plot(estimates_binormal_exp_list[[i]], main = paste('Iter', (i-1)), ylab = 'L', ylim = c(min_y, max_y))
}

Version Author Date
9a7a4f4 Annie Xie 2025-05-01 
par(mfrow = c(1,1))

Try fitting fourth factor initialized at true factor

Now, I will try initializing with the true single population effect factor.

true_fac4 <- rep(c(1,0), times = c(40, 120))
true_fac4 <- true_fac4/sqrt(sum(true_fac4^2))
symebcovmf_binormal_exp_true_init_fac4_fit <- sym_ebcovmf_r1_fit(sim_data$YYt, symebcovmf_binormal_rank3_fit, ebnm_fn = ebnm_point_exponential, maxiter = 100, tol = 10^(-8), v_init = true_fac4)

This is a plot of the fourth factor estimate.

plot(symebcovmf_binormal_exp_true_init_fac4_fit$L_pm[,4], ylab = 'Fourth Factor')

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

This is a plot of the ELBO when optimizing the fourth factor.

fac4_idx <- which(symebcovmf_binormal_exp_true_init_fac4_fit$vec_elbo_full == 4)
plot(symebcovmf_binormal_exp_true_init_fac4_fit$vec_elbo_full[(fac4_idx+1): length(symebcovmf_binormal_exp_true_init_fac4_fit$vec_elbo_full)], xlab = 'Iter', ylab = 'ELBO')

Version Author Date
9a7a4f4 Annie Xie 2025-05-01

Again, the method fits a factor with two population effects, suggesting it prefers this solution.

Progression of Estimate

This is the progression of the estimate.

estimates_binormal_exp_true_init_list <- list(true_fac4)
for (i in 1:11){
  estimates_binormal_exp_true_init_list[[(i+1)]] <- sym_ebcovmf_r1_fit(sim_data$YYt, symebcovmf_binormal_rank3_fit, ebnm_fn = ebnm_point_exponential, maxiter = i, tol = 10^(-8), v_init = rep(c(1,0), times = c(40, 120)))$L_pm[,4]
}
par(mfrow = c(6,2), mar = c(2, 2, 1, 1) + 0.1)
for (i in 1:12){
  plot(estimates_binormal_exp_true_init_list[[i]], main = paste('Iter', (i-1)), ylab = 'L')
}

Version Author Date
9a7a4f4 Annie Xie 2025-05-01 
par(mfrow = c(1,1))

Observations

The results from all the priors are similar, and there is no evidence of convergence issues. This suggests that the strictness of the binary prior does not seem to help find single population effect factors for this dataset. Follow up hypotheses: Is the method picking up structure due to slight correlations in the columns of the \(F\) matrix? Or is the estimation of \(\lambda\) off, leaving behind structural components that should have been taken out?


sessionInfo()
R version 4.3.2 (2023-10-31)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Sonoma 14.4.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/Chicago
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] ggplot2_3.5.1   pheatmap_1.0.12 ebnm_1.1-34     workflowr_1.7.1

loaded via a namespace (and not attached):
 [1] gtable_0.3.5       xfun_0.48          bslib_0.8.0        processx_3.8.4    
 [5] lattice_0.22-6     callr_3.7.6        vctrs_0.6.5        tools_4.3.2       
 [9] ps_1.7.7           generics_0.1.3     tibble_3.2.1       fansi_1.0.6       
[13] highr_0.11         pkgconfig_2.0.3    Matrix_1.6-5       SQUAREM_2021.1    
[17] RColorBrewer_1.1-3 lifecycle_1.0.4    truncnorm_1.0-9    farver_2.1.2      
[21] compiler_4.3.2     stringr_1.5.1      git2r_0.33.0       munsell_0.5.1     
[25] getPass_0.2-4      httpuv_1.6.15      htmltools_0.5.8.1  sass_0.4.9        
[29] yaml_2.3.10        later_1.3.2        pillar_1.9.0       jquerylib_0.1.4   
[33] whisker_0.4.1      cachem_1.1.0       trust_0.1-8        RSpectra_0.16-2   
[37] tidyselect_1.2.1   digest_0.6.37      stringi_1.8.4      dplyr_1.1.4       
[41] ashr_2.2-66        labeling_0.4.3     splines_4.3.2      rprojroot_2.0.4   
[45] fastmap_1.2.0      grid_4.3.2         colorspace_2.1-1   cli_3.6.3         
[49] invgamma_1.1       magrittr_2.0.3     utf8_1.2.4         withr_3.0.1       
[53] scales_1.3.0       promises_1.3.0     horseshoe_0.2.0    rmarkdown_2.28    
[57] httr_1.4.7         deconvolveR_1.2-1  evaluate_1.0.0     knitr_1.48        
[61] irlba_2.3.5.1      rlang_1.1.4        Rcpp_1.0.13        mixsqp_0.3-54     
[65] glue_1.8.0         rstudioapi_0.16.0  jsonlite_1.8.9     R6_2.5.1          
[69] fs_1.6.4