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angvasilop / optimal_k

Optimizing k in k-fold cross validation
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"Perhaps asymptotically" #6

Open gjm112 opened 1 year ago

gjm112 commented 1 year ago

I would leave this phrase out entirely. Without a theorem or something it's complete speculation, right?

angvasilop commented 1 year ago

It is not necessarily speculation. "Perhaps asymptotically" means that the as n increases, k*_optimal will 1) keep decreasing but 2) never reach zero. In general, k can never be 0 (there is no such thing as 0-fold cross validation) so (2) has to be true, and sqrt(2n) (see e-mail with attachment) does decrease to zero asymptotically, so (1) is also true if Bx + C + D/x + E/x^2 is an acceptable model.