Tractatus Elastico-Plasticus: Mechanical Models in Nonparametric Regression

Ivan Mizera
Abstract
A common motif in the expositions of spline-based methods in statistical smoothing or numerical interpolation is an allusion to mechanical analogies - motivated possibly by a desire to provide some explanation why the resulting shapes ought to be regarded as .natural.. After a review of some of the more classical models coming from the theory of elasticity of solid bodies, corresponding to l2 regularization, we will show that the less common, nevertheless completely analogous version of plasticity theory allows to underpin, in a similar way, nowadays very actual framework of l1 regularization . in particular, penalties based on total variation. The talk is non-technical and should be accessible to a broader audience.