Plots and tables summarizing results of Poisson simulations

Last updated: 2018-12-20

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File	Version	Author	Date	Message
Rmd	b3f5b57	Peter Carbonetto	2018-12-20	wflow_publish(“poisson.Rmd”)
Rmd	d36bfca	Peter Carbonetto	2018-12-20	Misc. revisions to READMEs and documentation.
Rmd	7aa0b11	Peter Carbonetto	2018-12-20	Working on poisson analysis.
Rmd	3c562ea	Peter Carbonetto	2018-12-19	Moved poisson_tables.Rmd to poisson.Rmd.
Rmd	25ff9c3	Peter Carbonetto	2018-12-19	Re-organized some of the files used in the Poisson numerical comparisons.

This script produces supplementary tables for Poisson simulations.

Explain which set of results correspond to the plots given in the main text.

Analysis settings

We will extract the results from these methods:

methods <- c("ash","BMSM","haarfisz_R")

Specify the row and column names for the tables:

table.row.names <- c("SMASH","BMSM","Haar-Fisz")
table.col.names <- c("intensity (0.01,3)","intensity (1/8,8)",
                     "intensity (1/128,128)")

These are settings used in plotting the test functions:

n <- 1024
t <- 1:n/n

Set up environment

Add text here.

library(ggplot2)
library(cowplot)
library(xtable)

Some of the test functions are defined in signals.R:

source("../code/signals.R")

Load results

Load the results of the simulation experiments.

load("../output/pois.RData")

Spikes data

This is the function used to simulate the “Spikes” data sets:

mu.s <- spike.f(t)
plot(t,mu.s,xlab = "",ylab = "",type = "l",
     main = "Spikes intensity function")

Summarize the results from the Spikes simulations in a table.

Comparison of methods for denoising Poisson data for the “Spikes” test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.

mise.s.table   <- cbind(mise.s.1[methods],
                        mise.s.8[methods],
                        mise.s.128[methods])
rownames(mise.s.table) <- table.row.names
colnames(mise.s.table) <- table.col.names
print(xtable(mise.s.table),type = "html")

	intensity (0.01,3)	intensity (1/8,8)	intensity (1/128,128)
SMASH	690.01	329.26	48.87
BMSM	1007.34	397.79	41.88
Haar-Fisz	722.19	287.44	18.06

Summarize the results from the Spikes simulations in combined violin and boxplots.

mise.hf.ti.r.s.1   <- colMeans(rbind(mise.hf.ti.r.4.s.1,
                                     mise.hf.ti.r.5.s.1,
                                     mise.hf.ti.r.6.s.1,
                                     mise.hf.ti.r.7.s.1))
mise.hf.ti.r.s.8   <- colMeans(rbind(mise.hf.ti.r.4.s.8,
                                     mise.hf.ti.r.5.s.8,
                                     mise.hf.ti.r.6.s.8,
                                     mise.hf.ti.r.7.s.8))
mise.hf.ti.r.s.128 <- colMeans(rbind(mise.hf.ti.r.4.s.128,
                                     mise.hf.ti.r.5.s.128,
                                     mise.hf.ti.r.6.s.128,
                                     mise.hf.ti.r.7.s.128))
n     <- length(mise.ash.s.1)
pdat1 <- data.frame(method = rep(c("SMASH","BMSM","HF"),each = n),
                    mise   = c(mise.ash.s.1,mise.BMSM.s.1,mise.hf.ti.r.s.1))
p1 <- ggplot(pdat1,aes(x = method,y = mise)) +
      geom_violin(fill = "skyblue",color = "skyblue") +
      geom_boxplot(width = 0.15,outlier.shape = NA) +
      coord_flip()
      labs(x = "",y = "MISE") +
     theme(axis.line = element_blank(),
           axis.ticks.y = element_blank())
# NULL

Combine the results of the simulation experiments into several larger tables.

mise.ang.table <- cbind(mise.ang.1[methods],
                        mise.ang.8[methods],
                        mise.ang.128[methods])
mise.bur.table <- cbind(mise.bur.1[methods],
                        mise.bur.8[methods],
                        mise.bur.128[methods])
mise.cb.table  <- cbind(mise.cb.1[methods],
                        mise.cb.8[methods],
                        mise.cb.128[methods])
mise.b.table   <- cbind(mise.b.1[methods],
                        mise.b.8[methods],
                        mise.b.128[methods])
mise.hs.table  <- cbind(mise.hs.1[methods],
                        mise.hs.8[methods],
                        mise.hs.128[methods])
rownames(mise.ang.table) <- table.row.names
rownames(mise.b.table)   <- table.row.names
rownames(mise.cb.table)  <- table.row.names
rownames(mise.hs.table)  <- table.row.names
rownames(mise.bur.table) <- table.row.names
colnames(mise.ang.table) <- table.col.names
colnames(mise.b.table)   <- table.col.names
colnames(mise.cb.table)  <- table.col.names
colnames(mise.hs.table)  <- table.col.names
colnames(mise.bur.table) <- table.col.names

Angles data

print(xtable(mise.ang.table,caption="Comparison of methods for denoising Poisson data for the ``Angles'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_ang",digits=2),type = "html")

Comparison of methods for denoising Poisson data for the ``Angles’’ test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.
	intensity (0.01,3)	intensity (1/8,8)	intensity (1/128,128)
SMASH	145.26	68.47	10.25
BMSM	147.40	73.87	10.49
Haar-Fisz	314.41	122.79	9.08

Heavisine data

print(xtable(mise.hs.table,caption="Comparison of methods for denoising Poisson data for the ``Heavisine'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_hs",digits=2),type = "html")

Comparison of methods for denoising Poisson data for the ``Heavisine’’ test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.
	intensity (0.01,3)	intensity (1/8,8)	intensity (1/128,128)
SMASH	81.41	43.21	7.21
BMSM	85.29	44.22	7.35
Haar-Fisz	274.26	105.47	9.23

Bursts data

print(xtable(mise.bur.table,caption="Comparison of methods for denoising Poisson data for the ``Bursts'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_bur",digits=2),type = "html")

Comparison of methods for denoising Poisson data for the ``Bursts’’ test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.
	intensity (0.01,3)	intensity (1/8,8)	intensity (1/128,128)
SMASH	487.34	234.35	33.11
BMSM	706.04	301.86	34.42
Haar-Fisz	618.39	299.39	25.20

Clipped Blocks data

print(xtable(mise.cb.table,caption="Comparison of methods for denoising Poisson data for the ``Clipped Blocks'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_cb",digits=2),type = "html")

Comparison of methods for denoising Poisson data for the ``Clipped Blocks’’ test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.
	intensity (0.01,3)	intensity (1/8,8)	intensity (1/128,128)
SMASH	307.80	137.28	6.82
BMSM	355.15	143.09	6.91
Haar-Fisz	632.21	338.55	29.72

Bumps data

print(xtable(mise.b.table,caption="Comparison of methods for denoising Poisson data for the ``Bumps'' test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.",label="table:pois_b",digits=2),type = "html")

Comparison of methods for denoising Poisson data for the ``Bumps’’ test function for 3 different (min,max) intensities ((0.01,3), (1/8,8), (1/128,128)). Performance is measured using MISE over 100 independent datasets, with smaller values indicating better performance. Values colored in red indicates the smallest MISE amongst all methods for a given (min, max) intensity.
	intensity (0.01,3)	intensity (1/8,8)	intensity (1/128,128)
SMASH	2597.46	1194.62	141.21
BMSM	4036.77	1889.94	171.07
Haar-Fisz	3113.37	1658.74	184.66

Session information

sessionInfo()
# R version 3.4.3 (2017-11-30)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS High Sierra 10.13.6
# 
# Matrix products: default
# BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.4/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] xtable_1.8-2  cowplot_0.9.3 ggplot2_3.1.0
# 
# loaded via a namespace (and not attached):
#  [1] Rcpp_1.0.0        compiler_3.4.3    pillar_1.2.1     
#  [4] git2r_0.23.0      plyr_1.8.4        workflowr_1.1.1  
#  [7] bindr_0.1.1       R.methodsS3_1.7.1 R.utils_2.6.0    
# [10] tools_3.4.3       digest_0.6.17     evaluate_0.11    
# [13] tibble_1.4.2      gtable_0.2.0      pkgconfig_2.0.2  
# [16] rlang_0.2.2       yaml_2.2.0        bindrcpp_0.2.2   
# [19] withr_2.1.2       stringr_1.3.1     dplyr_0.7.6      
# [22] knitr_1.20        rprojroot_1.3-2   grid_3.4.3       
# [25] tidyselect_0.2.4  glue_1.3.0        R6_2.2.2         
# [28] rmarkdown_1.10    purrr_0.2.5       magrittr_1.5     
# [31] whisker_0.3-2     backports_1.1.2   scales_0.5.0     
# [34] htmltools_0.3.6   assertthat_0.2.0  colorspace_1.4-0 
# [37] stringi_1.2.4     lazyeval_0.2.1    munsell_0.4.3    
# [40] R.oo_1.21.0

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