flexIC: Minimal, Runnable Demo

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Kevin E. Wells, PhD

2025-06-26

1 Simulate marginals

n <- 200; k <- 5
Sigma <- matrix(0.6, k, k); diag(Sigma) <- 1
X0  <- mvtnorm::rmvnorm(n, sigma = Sigma)
R_star <- cor(X0, method = "spearman")

2 IC vs flexIC

out_ic   <- flexIC(X0, R_star, eps = "none")
out_flex <- flexIC(X0, R_star, eps = 0.02, max_iter = 50)
X_ic     <- out_ic
X_flex   <- out_flex

3 Maximum rank-error

err_ic   <- max(abs(cor(X_ic  , method = "spearman") - R_star))
err_flex <- max(abs(cor(X_flex, method = "spearman") - R_star))

data.frame(
  method         = c("IC (eps = 'none')", "flexIC (eps = 0.02)"),
  max_rank_error = c(err_ic, err_flex)
)
#>                method max_rank_error
#> 1   IC (eps = 'none')     0.09301133
#> 2 flexIC (eps = 0.02)     0.04386710

4 Speed benchmark

microbenchmark(
  IC     = flexIC(X0, R_star, eps = "none"),
  flexIC = flexIC(X0, R_star, eps = 0.02, max_iter = 50),
  times  = 100L
)
#> Unit: microseconds
#>    expr    min       lq      mean   median       uq     max neval cld
#>      IC  751.7   844.40  1021.888   903.95   931.85  6931.9   100  a 
#>  flexIC 4392.6 17940.95 19571.516 19111.20 19721.50 34530.2   100   b

5 Optional: Visual check

if (requireNamespace("ggplot2", quietly = TRUE)) {
  flexIC::plot_marginals_grid(X0, X_flex, bins = 30)
}
#> Showing first 4 of 5 variables.

6 Session info

sessionInfo()
#> R version 4.4.2 (2024-10-31 ucrt)
#> Platform: x86_64-w64-mingw32/x64
#> Running under: Windows 11 x64 (build 22631)
#> 
#> Matrix products: default
#> 
#> 
#> locale:
#> [1] LC_COLLATE=C                          
#> [2] LC_CTYPE=English_United States.utf8   
#> [3] LC_MONETARY=English_United States.utf8
#> [4] LC_NUMERIC=C                          
#> [5] LC_TIME=English_United States.utf8    
#> 
#> time zone: America/Chicago
#> tzcode source: internal
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] microbenchmark_1.5.0 mvtnorm_1.3-3        flexIC_0.1.4        
#> 
#> loaded via a namespace (and not attached):
#>  [1] Matrix_1.7-1      gtable_0.3.6      jsonlite_1.8.9    dplyr_1.1.4      
#>  [5] compiler_4.4.2    tidyselect_1.2.1  jquerylib_0.1.4   splines_4.4.2    
#>  [9] scales_1.3.0      yaml_2.3.10       fastmap_1.2.0     lattice_0.22-6   
#> [13] TH.data_1.1-2     ggplot2_3.5.2     R6_2.5.1          labeling_0.4.3   
#> [17] generics_0.1.3    knitr_1.49        MASS_7.3-61       tibble_3.2.1     
#> [21] munsell_0.5.1     bslib_0.8.0       pillar_1.10.1     rlang_1.1.4      
#> [25] multcomp_1.4-26   cachem_1.1.0      xfun_0.50         sass_0.4.9       
#> [29] cli_3.6.3         withr_3.0.2       magrittr_2.0.3    digest_0.6.37    
#> [33] grid_4.4.2        rstudioapi_0.17.1 sandwich_3.1-1    lifecycle_1.0.4  
#> [37] vctrs_0.6.5       evaluate_1.0.3    glue_1.8.0        farver_2.1.2     
#> [41] codetools_0.2-20  zoo_1.8-12        survival_3.7-0    colorspace_2.1-1 
#> [45] rmarkdown_2.29    tools_4.4.2       pkgconfig_2.0.3   htmltools_0.5.8.1

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