Choice of size_weight option for the StabilizedRegression function

[fumi-github]

Thank you for the wonderful program.

In section 4.3 of your manuscript
https://arxiv.org/abs/1911.01850
you write:
Firstly, only sample random sets up to a certain size. If one has an idea about how many variables are required to get a stable set (this can often be checked empirically), it empirically seemed to help to sample more sets with this size and less sets with different sizes.

Could you elaborate on "this can often be checked empirically"

In my data, I tried size_weight = seq(1, sw) for various sw.
As sw increases, median(pval_stab) also seemed to increase, and there was no obvious threshold.

I would appreciate any suggestion.
Fumi

[fumi-github]

Sorry again.
I noticed in Appendix B:
Sub-sampling: Set a fixed maximal set size, that allows for an accurate OLS fit given the sample size. Then, randomly draw sets with at most this maximal size.

The following scan of set size (= number of variables) didn't show clear threshold in my data:

library(glmnet)
cvob = cv.glmnet(x = X, y = Y)
plot(cvob)

[NiklasPfister]

Hi Fumi! Thanks for your interest in the method and sorry for the late response.

There is no one fits them all for selecting this parameter. Generally, I would recommend trying multiple values and then check how much this affects the results. To get a rough idea of how many variables you need for a reasonable prediction you could do a cross-validation with lasso and check how many variables are selected. Then select a number slightly bigger than this.