Using ceres for penalized spline regression

[Arrigo Benedetti]

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]

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]

Good idea, thanks!