Last updated: 2022-11-28

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Rmd 4a6005a DongyueXie 2022-11-28 wflow_publish("analysis/smooth_angles_benchmark_new.Rmd")

Introduction

In this analysis we look at the results from generating data as

\[y_i\sim Poisson(\exp(b_i+\epsilon_i)),\epsilon_i\sim N(0,\sigma^2).\] The \(\exp(b)\) is smooth and has block structures as follows:

library(tidyverse)
── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.3.6      ✔ purrr   0.3.5 
✔ tibble  3.1.8      ✔ dplyr   1.0.10
✔ tidyr   1.2.1      ✔ stringr 1.4.1 
✔ readr   2.1.3      ✔ forcats 0.5.2 
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
out = readRDS('output/poisson_smooth_simulation/new_simu/angles30_n_1024_snr_1_count_size_3.rds')
plot(exp(out$sim_data$b),type='l',ylab='')

We set \(n=1024\), repeat 30 times, and count size \(=max(\exp(b))\in \{3,10,100\}\), and \(snr = var(b)/\sigma^2\in \{1,3\}\).

source('code/poisson_smooth/simulation_summary_smooth.R')
all_methods = names(out$output[[1]]$mse_smooth)
include_methods = c('vst_smooth','lik_exp_logx_nug_top','lik_exp_logx_smooth','split_smashpoi_ndwt','split_smashpoi_dwt','smash_two_step_hetero','smash')
rm_methods = all_methods[!(all_methods%in%include_methods)]

count size = 3

snr = 1

out = readRDS('output/poisson_smooth_simulation/new_simu/angles30_n_1024_snr_1_count_size_3.rds')
get_mse_mean(out,rm_method = rm_methods)


|                      |      mean|        sd|
|:---------------------|---------:|---------:|
|smash_two_step_hetero | 0.0309531| 0.0095811|
|smash                 | 0.0396589| 0.0165088|
|vst_smooth            | 0.0414001| 0.0128203|
|split_smashpoi_ndwt   | 0.0494287| 0.0141389|
|split_smashpoi_dwt    | 0.0608428| 0.0159582|
|lik_exp_logx_smooth   | 0.2069340| 0.0390366|
|lik_exp_logx_nug_top  | 0.2553825| 0.0444868|

get_runtime(out,rm_method = rm_methods)

for(method in include_methods){
  plot_all_curves(out,method=method)
}

snr = 3

out = readRDS('output/poisson_smooth_simulation/new_simu/angles30_n_1024_snr_3_count_size_3.rds')
get_mse_mean(out,rm_method = rm_methods)


|                      |      mean|        sd|
|:---------------------|---------:|---------:|
|smash_two_step_hetero | 0.0254256| 0.0087872|
|smash                 | 0.0256060| 0.0097329|
|vst_smooth            | 0.0470157| 0.0137242|
|split_smashpoi_ndwt   | 0.0539747| 0.0150439|
|split_smashpoi_dwt    | 0.0578065| 0.0151372|
|lik_exp_logx_smooth   | 0.2060669| 0.0410352|
|lik_exp_logx_nug_top  | 0.2531711| 0.0462308|

get_runtime(out,rm_method = rm_methods)

for(method in include_methods){
  plot_all_curves(out,method=method)
}

count size = 10

snr = 1

out = readRDS('output/poisson_smooth_simulation/new_simu/angles30_n_1024_snr_1_count_size_10.rds')
get_mse_mean(out,rm_method = rm_methods)


|                      |       mean|        sd|
|:---------------------|----------:|---------:|
|split_smashpoi_ndwt   |  0.3447979| 0.1170142|
|vst_smooth            |  0.4731400| 0.2440202|
|split_smashpoi_dwt    |  0.6606017| 0.1772298|
|smash_two_step_hetero |  0.6646382| 0.2186747|
|lik_exp_logx_smooth   |  0.8251299| 0.2811992|
|lik_exp_logx_nug_top  |  0.9321922| 0.3104204|
|smash                 | 15.7252226| 3.9634624|

get_runtime(out,rm_method = rm_methods)

for(method in include_methods){
  plot_all_curves(out,method=method)
}

snr = 3

out = readRDS('output/poisson_smooth_simulation/new_simu/angles30_n_1024_snr_3_count_size_10.rds')
get_mse_mean(out,rm_method = rm_methods)


|                      |      mean|        sd|
|:---------------------|---------:|---------:|
|vst_smooth            | 0.1870640| 0.0619821|
|split_smashpoi_ndwt   | 0.2055731| 0.0781469|
|smash_two_step_hetero | 0.3795118| 0.1209138|
|split_smashpoi_dwt    | 0.4265718| 0.1059923|
|lik_exp_logx_smooth   | 0.5542755| 0.1571507|
|lik_exp_logx_nug_top  | 0.6127307| 0.1584986|
|smash                 | 2.0894546| 0.6156045|

get_runtime(out,rm_method = rm_methods)

for(method in include_methods){
  plot_all_curves(out,method=method)
}

count size = 100

snr = 1

out = readRDS('output/poisson_smooth_simulation/new_simu/angles30_n_1024_snr_1_count_size_100.rds')
get_mse_mean(out,rm_method = rm_methods)


|                      |        mean|         sd|
|:---------------------|-----------:|----------:|
|lik_exp_logx_nug_top  |    54.57807|   24.18572|
|split_smashpoi_ndwt   |    55.23756|   28.48649|
|lik_exp_logx_smooth   |    64.49398|   29.74338|
|split_smashpoi_dwt    |    90.23235|   28.25920|
|smash_two_step_hetero |    91.35546|   44.90445|
|vst_smooth            |  1282.34929| 2202.58693|
|smash                 | 15333.36040| 6729.09957|

get_runtime(out,rm_method = rm_methods)

for(method in include_methods){
  plot_all_curves(out,method=method)
}

snr = 3

out = readRDS('output/poisson_smooth_simulation/new_simu/angles30_n_1024_snr_3_count_size_100.rds')
get_mse_mean(out,rm_method = rm_methods)


|                      |       mean|         sd|
|:---------------------|----------:|----------:|
|split_smashpoi_ndwt   |   26.24050|   8.890036|
|lik_exp_logx_nug_top  |   31.07092|   9.718367|
|lik_exp_logx_smooth   |   31.58060|  12.005586|
|smash_two_step_hetero |   43.13123|  10.179750|
|vst_smooth            |   45.85319|  30.004548|
|split_smashpoi_dwt    |   46.73828|  11.896783|
|smash                 | 1410.74067| 361.377803|

get_runtime(out,rm_method = rm_methods)

for(method in include_methods){
  plot_all_curves(out,method=method)
}


sessionInfo()
R version 4.2.1 (2022-06-23)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.5 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0

locale:
 [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
 [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
 [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
[10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   

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

other attached packages:
 [1] forcats_0.5.2   stringr_1.4.1   dplyr_1.0.10    purrr_0.3.5    
 [5] readr_2.1.3     tidyr_1.2.1     tibble_3.1.8    ggplot2_3.3.6  
 [9] tidyverse_1.3.2 workflowr_1.7.0

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.9          lubridate_1.9.0     getPass_0.2-2      
 [4] ps_1.7.1            assertthat_0.2.1    rprojroot_2.0.3    
 [7] digest_0.6.29       utf8_1.2.2          plyr_1.8.7         
[10] R6_2.5.1            cellranger_1.1.0    backports_1.4.1    
[13] reprex_2.0.2        evaluate_0.17       highr_0.9          
[16] httr_1.4.4          pillar_1.8.1        rlang_1.0.6        
[19] readxl_1.4.1        googlesheets4_1.0.1 rstudioapi_0.14    
[22] whisker_0.4         callr_3.7.2         jquerylib_0.1.4    
[25] rmarkdown_2.17      labeling_0.4.2      googledrive_2.0.0  
[28] munsell_0.5.0       broom_1.0.1         compiler_4.2.1     
[31] httpuv_1.6.6        modelr_0.1.9        xfun_0.33          
[34] pkgconfig_2.0.3     htmltools_0.5.3     tidyselect_1.2.0   
[37] fansi_1.0.3         crayon_1.5.2        withr_2.5.0        
[40] tzdb_0.3.0          dbplyr_2.2.1        later_1.3.0        
[43] grid_4.2.1          jsonlite_1.8.2      gtable_0.3.1       
[46] lifecycle_1.0.3     DBI_1.1.3           git2r_0.30.1       
[49] magrittr_2.0.3      scales_1.2.1        cli_3.4.1          
[52] stringi_1.7.8       cachem_1.0.6        farver_2.1.1       
[55] reshape2_1.4.4      fs_1.5.2            promises_1.2.0.1   
[58] xml2_1.3.3          bslib_0.4.0         ellipsis_0.3.2     
[61] generics_0.1.3      vctrs_0.4.2         tools_4.2.1        
[64] glue_1.6.2          hms_1.1.2           processx_3.7.0     
[67] fastmap_1.1.0       yaml_2.3.5          timechange_0.1.1   
[70] colorspace_2.0-3    gargle_1.2.1        rvest_1.0.3        
[73] knitr_1.40          haven_2.5.1         sass_0.4.2