lasso_complexity
Matthew Stephens
2021-05-26
Last updated: 2021-05-26
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Knit directory: misc/analysis/
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Introduction
I was suprised to hear that lasso complexity for full solution path is O(np min(n,p)). I always thought it was O(np) per iteration and did not think about how the number of iterations required might increase with n and p. I wanted to do a quick simulation check.
library("glmnet")Warning: package 'glmnet' was built under R version 3.6.2Loading required package: MatrixLoaded glmnet 4.1n_seq = c(100, 200, 500, 1000, 2000, 5000, 10000)
p = 10000
nmax = 10000
X = matrix(rnorm(nmax*p),nrow=nmax)
b = rnorm(p)
time = c()
for(n in n_seq){
y = X[1:n,] %*% b + rnorm(n)
time = c(time,system.time(fit <- glmnet(X[1:n,],y))[1]) # user time
#print(time)
}
plot(log(n_seq),log(time), main = "log-time vs log(n)")
slope = (log(time)[7]-log(time)[1])/(log(n_seq)[7]-log(n_seq)[1])
print(slope)user.self
1.256022
sessionInfo()R version 3.6.0 (2019-04-26)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS 10.16
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/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] glmnet_4.1 Matrix_1.2-18
loaded via a namespace (and not attached):
[1] Rcpp_1.0.6 pillar_1.4.6 compiler_3.6.0 later_1.1.0.1
[5] git2r_0.27.1 workflowr_1.6.2 iterators_1.0.12 tools_3.6.0
[9] digest_0.6.27 evaluate_0.14 lifecycle_1.0.0 tibble_3.0.4
[13] lattice_0.20-41 pkgconfig_2.0.3 rlang_0.4.10 foreach_1.5.0
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[29] rmarkdown_2.3 magrittr_2.0.1 whisker_0.4 backports_1.1.10
[33] promises_1.1.1 codetools_0.2-16 ellipsis_0.3.1 htmltools_0.5.0
[37] splines_3.6.0 shape_1.4.4 httpuv_1.5.4 stringi_1.4.6
[41] crayon_1.3.4