Last updated: 2019-09-30

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Rmd 255ebde zihao12 2019-09-28 Compare ebpm vs ash_pois

Compare ebpm_exponential_mixture vs ash_pois

I use ebpm from https://github.com/stephenslab/ebpm, (branch “zihao”)  and ash_pois from https://github.com/stephens999/ashr/blob/master/R/ash_pois.R

Experiment setup

I simulate \(x_i \sim pois(s_i \lambda_i), \lambda_i \sim \sum_k^{K} \pi_k exp(b_k), \forall i = 1 ,..., 4000\) with \(K = 50\). I use \(s_i = 1\).
Then I fit ash_pois and ebpm_exponential_mixture on given \(x, s\)s

library(gtools)
library(ebpm)
library(ashr)
library(ggplot2)
Warning: package 'ggplot2' was built under R version 3.5.2
library(mixsqp)

n = 4000
d = 50
sim_mgamma <- function(a,b,pi){
  idx = which(rmultinom(1,1,pi) == 1)
  return(rgamma(1, shape = a[idx], rate =  b[idx]))
}

## simulate a poisson mean problem
simulate_pm  <-  function(n, d, seed = 123){
  set.seed(seed)
  ## simulate grid
  a = replicate(d,1)
  b = 10*runif(d)
  grid  = list(a = a, b = b)
  pi <- rdirichlet(1,rep(1/d, d))
  lam_true = replicate(n, sim_mgamma(a,b,pi))
  s = replicate(length(lam_true), 1)
  #s = 2*runif(length(lam_true))
  x  = rpois(length(lam_true),s*lam_true)
  ll_lam = sum(dpois(x, s*lam_true, log = T))
  return(list(x =  x, s = s, lam_true = lam_true, pi = pi, grid = grid))
}

rmse <- function(x,y){
  return(sqrt(mean((x-y)^2)))
}
sim = simulate_pm(n = n, d = d)

start = proc.time()
out_ebpm_exponential_mixture = ebpm::ebpm_exponential_mixture(sim$x, s = sim$s, m = 1.1)
out_ebpm_exponential_mixture[["runtime"]] = (proc.time() - start)[[3]]

start = proc.time()
out_ash = ash_pois(sim$x, scale = sim$s, link = "identity")
out_ash[["runtime"]] = (proc.time() - start)[[3]]

print(sprintf("runtime for ebpm_exponential_mixture: %f", out_ebpm_exponential_mixture$runtime))
[1] "runtime for ebpm_exponential_mixture: 0.195000"
print(sprintf("runtime for ash_pois                : %f", out_ash$runtime))
[1] "runtime for ash_pois                : 3.184000"

compare RMSE against \(\lambda_{true}\)

df = data.frame(n = 1:length(sim$x), x = sim$x, s =  sim$s, lam_true = sim$lam_true, 
                lam_hat_ebpm_exponential_mixture = out_ebpm_exponential_mixture$posterior$mean,
                lam_hat_ash_pois = out_ash$result[["PosteriorMean"]])

print(sprintf("rmse(lam_ash_pois, lam_true)                     = %f", rmse(df$lam_true, df$lam_hat_ash_pois)))
[1] "rmse(lam_ash_pois, lam_true)                     = 0.122928"
print(sprintf("rmse(lam_hat_ebpm_exponential_mixture, lam_true) = %f", rmse(df$lam_true, df$lam_hat_ebpm_exponential_mixture)))
[1] "rmse(lam_hat_ebpm_exponential_mixture, lam_true) = 0.122431"

visualize poasterior means

ggplot(df) +
  geom_point(aes(x = lam_hat_ash_pois, y = lam_hat_ebpm_exponential_mixture), color = "blue") +
  labs(x = "lam_hat_ash_pois", y = "lam_hat_ebpm_exponential_mixture")+
  geom_abline(slope = 1, intercept = 0)

Version Author Date
5cec335 zihao12 2019-09-28
c966a85 zihao12 2019-09-28

Below I sort \(x\) and plot \(\lambda\)s against the sorting index. Expecting to see horizontal lines (\(x\) takes value in integers,and for fixed \(x\), the posterior mean is fixed).

df_sort = df[order(df$x),]
df_sort$n = 1:length(sim$x)

ggplot(df_sort) +
  geom_point(aes(x = n, y = lam_true, color = "true"), cex = 0.5) +
    labs(x = "index", y = "lam", title = "ash_pois vs ebpm_exponential_mixture") +
  geom_point(aes(x = n, y = lam_hat_ebpm_exponential_mixture, color = "ebpm_exponential_mixture"), cex = 0.5) +
  geom_point(aes(x = n, y = lam_hat_ash_pois, color = "ash"), cex = 0.5) +
  guides(fill = "color")

Version Author Date
5cec335 zihao12 2019-09-28
c966a85 zihao12 2019-09-28 

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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] mixsqp_0.1-120  ggplot2_3.2.1   ashr_2.2-38     ebpm_0.0.0.9000
[5] gtools_3.8.1   

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.2        pillar_1.4.2      compiler_3.5.1   
 [4] git2r_0.25.2      workflowr_1.4.0   iterators_1.0.12 
 [7] tools_3.5.1       digest_0.6.21     evaluate_0.14    
[10] tibble_2.1.3      gtable_0.3.0      lattice_0.20-38  
[13] pkgconfig_2.0.3   rlang_0.4.0       Matrix_1.2-17    
[16] foreach_1.4.7     yaml_2.2.0        parallel_3.5.1   
[19] xfun_0.8          withr_2.1.2       dplyr_0.8.1      
[22] stringr_1.4.0     knitr_1.25        fs_1.3.1         
[25] tidyselect_0.2.5  rprojroot_1.3-2   grid_3.5.1       
[28] glue_1.3.1        R6_2.4.0          rmarkdown_1.13   
[31] purrr_0.3.2       magrittr_1.5      whisker_0.3-2    
[34] backports_1.1.4   scales_1.0.0      codetools_0.2-16 
[37] htmltools_0.3.6   MASS_7.3-51.4     assertthat_0.2.1 
[40] colorspace_1.4-1  labeling_0.3      stringi_1.4.3    
[43] lazyeval_0.2.2    doParallel_1.0.15 pscl_1.5.2       
[46] munsell_0.5.0     truncnorm_1.0-8   SQUAREM_2017.10-1
[49] crayon_1.3.4