I'm interested in knowing what "solving LASSO" entails, ie, how is your regularization/constraint parameter chosen? It seems like it would be a pretty crucial component of your results, unless you are solving SPGL1 to completion, but then you would be solving bpdn?
To what I responded:
Hello Tim,
Thanks for asking this question. I guess you are asking what paramrter \tau I am using (in the spgl1 sense)?
My known solution is an instance of zeros and ones. I also know the sparsity of the "unknown" vector beforehand, so I know what the \tau parameter should be. So in essence, I am really showing the best DT transition since I know the exact \tau parameter when I ask SPGL1 to solve my problem. Does that answer your question ?
Cheers,
Igor.
Tim then responded with:
Ah yes, so this is an "oracle" lasso solution. That makes sense now, thanks!
Ps: the implications of this on really large systems that experience numerical roundoff errors is very scary!
Tim is really nice, he diplomatically calls it an "oracle",
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