Using ceres for penalized spline regression

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Arrigo Benedetti

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May 6, 2023, 3:12:59 PM5/6/23
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I wonder if I could model a penalized spline (P-Spline) regression
problem with ceres. For penalized splines, the cost function has an
extra regularization term of the form

lambda*norm(D*x)

where D is a matrix operator applied to the spline coefficient vector
x that computes, say, its second order divided differences. lambda
controls the smoothness of the final fit. The question is: can ceres
model this term?

Thanks

-Arrigo

Dmitriy Korchemkin

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May 6, 2023, 3:26:19 PM5/6/23
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I think one option is to add residual block r = D * x and use it with loss function L(||r||^2) = lambda * sqrt(||r||^2).

Arrigo Benedetti

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May 8, 2023, 1:55:54 PM5/8/23
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Good idea, thanks!
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