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I am currently working on a method for adaptive knot placement in Spline regression. Following Osborne et.al. (1998), Yuan et.al. (2014) I am interested in using LASSO regression to select a subset of basis and then obtain by means of an algorithm a knot vector. My question regards the penalisation parameter $\lambda$, I've seen some authors that select the value for it according to the 10-fold CV, but I have some doubts regarding this. In this particular case we want to extract a signal, so I am not sure if the CV is the best method for selecting the penalisation, I mean, we are not going to extrapolate our results to a new set of data. In this case wouldn't it be better to use AIC criterium instead?

I am open to any suggestion, and I thank you in advance.

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    $\begingroup$ Maybe the procedure suggested in this paper could be useful in your case (ref. Visualization of Genomic Changes by Segmented Smoothing Using an L0 Penalty" - DOI: 10.1371/journal.pone.0038230) $\endgroup$ – Gi_F. Jan 31 at 11:53

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