Solved – Difference between smoothing spline and penalised spline

Question

I have read many documents, and I am confused about the difference between smoothing splines and penalised splines.

Are those two the same?

Can someone please suggest any good document which can explain these concepts clearly to me?

Answer 1

There are sometimes some variations in how people use the terminology but usually a smoothing spline has a knot at every x-point while a penalized spline does not.

Penalized splines use a reduced knot set -- not necessarily at data points, somewhat akin to regression splines in that aspect.

Penalized splines and smoothing splines are otherwise similar in that they both include a smoothing term (roughness penalty) and a fit term (lack of fit penalty).