Sum-of-Norm regularization in estimation problems
Abstract:
Regularization has long been used in estimation problem to curb the flexibility of models, and to provide reliable and numerically sound estimates. During the past 15 years the power of l-1 regularization has been especially appreciated, mainly due to the introduction of efficient convex programming techniques. l-1 regularization favors solutions which has many elements exactly equal to zero, and has been very successful in, for example, regresssor selection (LASSO) and compressed sensing.
This presentation shows how the related sum-of-norm regularization works well for some system identification and estimation-related problems compared to conventional techniques. We apply it to segmentation of ARX- models, identification of hybrid piecewise affine models, to state smoothing with abrupt disturbances and to path generation.