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Quadratic Programming and Penalised Regressionby Andrew D. A. C. Smith
Quadratic programming is a versatile tool for calculating estimates in penalised regression. It can be used to produce estimates based on L1 roughness penalties, as in total variation denoising. In particular, it can calculate
estimates when the roughness penalty is the total variation of a derivative
of the estimate. Combining two roughness penalties, the total variation and
total variation of the third derivative, results in an estimate with continuous
second derivative but controls the number of spurious local extreme values. A
multiresolution criterion may be included in a quadratic program to achieve
local smoothing without having to specify smoothing parameters.
