Fig. 18.1

[szcf-weiya]

original note: https://esl.hohoweiya.xyz/notes/HighDim/sim18_1/index.html

the figure has not been well reproduced,

here is a shortcoming to separate the note into the webpage

• the inserted code is copied instead of referring, hence it is not proper for continuous integration

now try to put the procedure for reproducing figures into the issues

[szcf-weiya]

after rewriting the testing error, the pattern of p = 20 can be reproduced,

p = 100 cannot completely be reproduced, but if adjust the minimum lambda, then it can also be reproduced,

however, the decreasing trend of p = 1000 can not be well reproduced except that sometimes the mean is indeed decreasing

[szcf-weiya]

tried different ways to calculate SNR

• empirical from Xbeta
• use var(Xbeta) formula, as also used in https://cran.r-project.org/web/packages/bestridge/vignettes/An-introduction-to-bestridge.html
  
• treat x individually, as in https://esl.hohoweiya.xyz/03-Linear-Methods-for-Regression/3.3-Subset-Selection/index.html
  

but the patterns are similar.

[szcf-weiya]

tried different SNR levels with the approach beta Sigma beta, it seems that a low SNR tends to reproduce the decreasing pattern.

[szcf-weiya]

also tried different lambdas given SNR = 2, but no changes

julia> run(p = 1000, nrep=100, λs = [0.001, 5000, 10000], snr = 2)

[szcf-weiya]

larger p does not reproduce, either.

julia> run(p = 5000, nrep=100, λs = [0.001, 100, 1000], snr = 2)