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ENH: gam like penalized (orthogonal, fractional) polynomials #5498

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josef-pkt opened this issue Feb 14, 2019 · 1 comment
Open

ENH: gam like penalized (orthogonal, fractional) polynomials #5498

josef-pkt opened this issue Feb 14, 2019 · 1 comment

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@josef-pkt
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Now that GAM is in master, we could use polynomial, especially, orthogonal polynomials with a similar structure.
It would also be a good case for extending and generalizing the supporting code, e.g. exog_extra or multi-column terms in predict, partial predict, diagnostic plots

If we use numpy polynomials (instead of scipy as in my early cases), then we should also be able to get second derivatives to penalized IMSE (integrated mean squared error), similar to GAM B-splines.
In my previous penalized polynomial cases, the penalization matrix (prior cov) was "made up", i.e. somewhat arbitrary increase of penality with order/power of polynomial term.

The cubic splines have code for transforming the data to a standard range, e.g. [-1, 1] interval.

@josef-pkt
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old issue #602 nonparametric regression
#3215 density estimation orthopoly

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