Last updated: 2023-05-04

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Description:

Test for implementation of Poisson SER. The derivation can be found here: https://www.overleaf.com/read/rnftbwbsqrrg

source("/Users/nicholeyang/Downloads/survival-susie/code/vi_poisson.R")
sim.data = function(n, X, ss, sigma2, prior.prob){
  gamma = rmultinom(1, size = 1, prob = prior.prob)
  b = rnorm(1, 0, sqrt(sigma2))
  b.vec = b*gamma
  lambda = ss * exp( X%*% b.vec)
  y = unlist(lapply(lambda, function(x) rpois(1, lambda = x)))
  return(list(y = y, X = X, ss =ss, b.vec = b.vec))
}

Simulation 1

set.seed(1)
n = 20
p = 5
ss = rep(1, 20)
X = matrix(NA, nrow = n, ncol = p)
for (i in 1:p){
  X[, i] = rnorm(n)
}

dat = sim.data(n, X, ss, sigma2 = 1, prior.prob = rep(1/p, p))
dat$b.vec
#            [,1]
# [1,]  0.0000000
# [2,]  0.0000000
# [3,]  0.0000000
# [4,]  0.0000000
# [5,] -0.9109216
# initializations 
m.vec = rep(1, p)
v2.vec = rep(1, p)
alpha <- rep(1/p, p)
pi <- rep(1/p, p)

lower = c(-1e2, 1e-12)
upper = c(1e2, 1e4)

result <- update_q(X, dat$y, ss, m.vec, v2.vec, sigma2 = 1, pi, alpha, maxiter = 20, tol, lower, upper)
head(result$alpha)
head(result$m.vec)
head(result$v2.vec)
#            [,1]         [,2]         [,3]         [,4]      [,5]
# [1,] 0.20000000 0.2000000000 0.2000000000 0.2000000000 0.2000000
# [2,] 0.07292743 0.0001021124 0.0001111229 0.0001115133 0.9267478
# [3,] 0.07423784 0.0001078727 0.0001173151 0.0001178384 0.9254191
# [4,] 0.07434965 0.0001083748 0.0001178547 0.0001183898 0.9253057
# [5,] 0.07435923 0.0001084179 0.0001179010 0.0001184372 0.9252960
# [6,] 0.07435952 0.0001084192 0.0001179024 0.0001184386 0.9252957
#           [,1]        [,2]      [,3]      [,4]       [,5]
# [1,] 1.0000000  1.00000000 1.0000000 1.0000000  1.0000000
# [2,] 0.7625952 -0.10056749 0.1228895 0.1661023 -0.9296332
# [3,] 0.7590191 -0.09993402 0.1220551 0.1654071 -0.9249457
# [4,] 0.7587137 -0.09992108 0.1220375 0.1653811 -0.9245456
# [5,] 0.7587087 -0.09989792 0.1220037 0.1653811 -0.9245369
# [6,] 0.7587087 -0.09989725 0.1220010 0.1653811 -0.9245369
#            [,1]       [,2]       [,3]       [,4]       [,5]
# [1,] 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000
# [2,] 0.03477561 0.05737413 0.06205704 0.03551602 0.03737578
# [3,] 0.03475016 0.05698267 0.06160822 0.03537572 0.03735103
# [4,] 0.03475007 0.05695186 0.06156815 0.03536832 0.03735236
# [5,] 0.03474685 0.05694348 0.06155843 0.03536832 0.03734782
# [6,] 0.03474685 0.05694547 0.06156837 0.03536832 0.03734782
tail(result$alpha, n = 1)
tail(result$m.vec, n = 1)
tail(result$v2.vec, n = 1)
#             [,1]         [,2]         [,3]         [,4]      [,5]
# [20,] 0.07435952 0.0001084192 0.0001179024 0.0001184386 0.9252957
#            [,1]       [,2]      [,3]      [,4]       [,5]
# [20,] 0.7587087 -0.0998966 0.1219836 0.1653811 -0.9245369
#             [,1]       [,2]       [,3]       [,4]       [,5]
# [20,] 0.03474685 0.05694683 0.06156505 0.03536832 0.03734782
plot(result$elbo, xlab = "iter", ylab = "elbo")

Version Author Date
fc5ae54 yunqiyang0215 2023-05-04

Simulation 2

set.seed(3)
n = 200
p = 5
ss = rep(1, n)
X = matrix(NA, nrow = n, ncol = p)
for (i in 1:p){
  X[, i] = rnorm(n)
}

dat = sim.data(n, X, ss, sigma2 = 1, prior.prob = rep(1/p, p))
dat$b.vec
#            [,1]
# [1,]  0.0000000
# [2,]  0.0000000
# [3,]  0.0000000
# [4,] -0.9728448
# [5,]  0.0000000
# initializations 
m.vec = rep(1, p)
v2.vec = rep(1, p)
alpha <- rep(1/p, p)
pi <- rep(1/p, p)

lower = c(-1e2, 1e-12)
upper = c(1e2, 1e4)

result <- update_q(X, dat$y, ss, m.vec, v2.vec, sigma2 = 1, pi, alpha, maxiter = 20, tol, lower, upper)
head(result$alpha)
head(result$m.vec)
head(result$v2.vec)
#               [,1]          [,2]          [,3] [,4]          [,5]
# [1,]  2.000000e-01  2.000000e-01  2.000000e-01  0.2  2.000000e-01
# [2,] 2.573553e-100 4.966843e-100 3.413141e-100  1.0 8.244662e-100
# [3,] 2.558142e-100 4.937279e-100 3.392754e-100  1.0 8.195830e-100
# [4,] 2.558142e-100 4.937279e-100 3.392754e-100  1.0 8.195830e-100
# [5,] 2.558142e-100 4.937279e-100 3.392754e-100  1.0 8.195830e-100
# [6,] 2.558142e-100 4.937279e-100 3.392754e-100  1.0 8.195830e-100
#             [,1]        [,2]        [,3]      [,4]      [,5]
# [1,]  1.00000000  1.00000000  1.00000000  1.000000 1.0000000
# [2,] -0.05615829 -0.09768592 -0.07725215 -1.005268 0.1202053
# [3,] -0.05615829 -0.09768592 -0.07725215 -1.005268 0.1202053
# [4,] -0.05615829 -0.09768592 -0.07725215 -1.005268 0.1202053
# [5,] -0.05615829 -0.09768592 -0.07725215 -1.005268 0.1202053
# [6,] -0.05615829 -0.09768592 -0.07725215 -1.005268 0.1202053
#             [,1]        [,2]        [,3]        [,4]        [,5]
# [1,] 1.000000000 1.000000000 1.000000000 1.000000000 1.000000000
# [2,] 0.005221934 0.004810562 0.004911976 0.001547982 0.004865276
# [3,] 0.005221934 0.004810562 0.004911976 0.001547982 0.004865276
# [4,] 0.005221934 0.004810562 0.004911976 0.001547982 0.004865276
# [5,] 0.005221934 0.004810562 0.004911976 0.001547982 0.004865276
# [6,] 0.005221934 0.004810562 0.004911976 0.001547982 0.004865276
tail(result$alpha, n = 1)
tail(result$m.vec, n = 1)
tail(result$v2.vec, n = 1)
#                [,1]          [,2]          [,3] [,4]         [,5]
# [20,] 2.558142e-100 4.937279e-100 3.392754e-100    1 8.19583e-100
#              [,1]        [,2]        [,3]      [,4]      [,5]
# [20,] -0.05615829 -0.09768592 -0.07725215 -1.005268 0.1202053
#              [,1]        [,2]        [,3]        [,4]        [,5]
# [20,] 0.005221934 0.004810562 0.004911976 0.001547982 0.004865276
plot(result$elbo, xlab = "iter", ylab = "elbo")

Version Author Date
970761b yunqiyang0215 2023-05-04
fc5ae54 yunqiyang0215 2023-05-04

Simulation 3

set.seed(5)
n = 2e3
p = 5
ss = rep(1, n)
X = matrix(NA, nrow = n, ncol = p)
for (i in 1:p){
  X[, i] = rnorm(n)
}

dat = sim.data(n, X, ss, sigma2 = 1, prior.prob = rep(1/p, p))
dat$b.vec
#           [,1]
# [1,] 0.0000000
# [2,] 0.0000000
# [3,] 0.0000000
# [4,] 0.1007886
# [5,] 0.0000000
# initializations 
m.vec = rep(1, p)
v2.vec = rep(1, p)
alpha <- rep(1/p, p)
pi <- rep(1/p, p)

lower = c(-0.1, 0)
upper = c(10, 1e4)

result <- update_q(X, dat$y, ss, m.vec, v2.vec, sigma2 = 1, pi, alpha, maxiter = 1, tol, lower, upper)
head(result$alpha)
head(result$m.vec)
head(result$v2.vec)

tail(result$alpha, n = 1)
tail(result$m.vec, n = 1)
tail(result$v2.vec, n = 1)

plot(result$elbo, xlab = "iter", ylab = "elbo")

sessionInfo()
# R version 4.1.1 (2021-08-10)
# Platform: x86_64-apple-darwin20.6.0 (64-bit)
# Running under: macOS Monterey 12.0.1
# 
# Matrix products: default
# BLAS:   /usr/local/Cellar/openblas/0.3.18/lib/libopenblasp-r0.3.18.dylib
# LAPACK: /usr/local/Cellar/r/4.1.1_1/lib/R/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] workflowr_1.6.2
# 
# loaded via a namespace (and not attached):
#  [1] Rcpp_1.0.8.3     pillar_1.6.4     compiler_4.1.1   bslib_0.4.1     
#  [5] later_1.3.0      jquerylib_0.1.4  git2r_0.28.0     highr_0.9       
#  [9] tools_4.1.1      digest_0.6.28    jsonlite_1.7.2   evaluate_0.14   
# [13] lifecycle_1.0.1  tibble_3.1.5     pkgconfig_2.0.3  rlang_1.0.6     
# [17] cli_3.1.0        rstudioapi_0.13  yaml_2.2.1       xfun_0.27       
# [21] fastmap_1.1.0    stringr_1.4.0    knitr_1.36       fs_1.5.0        
# [25] vctrs_0.3.8      sass_0.4.4       rprojroot_2.0.2  glue_1.4.2      
# [29] R6_2.5.1         fansi_0.5.0      rmarkdown_2.11   whisker_0.4     
# [33] magrittr_2.0.1   promises_1.2.0.1 ellipsis_0.3.2   htmltools_0.5.2 
# [37] httpuv_1.6.3     utf8_1.2.2       stringi_1.7.5    cachem_1.0.6    
# [41] crayon_1.4.1