Sparse, flexible and efficient modeling using L1 regularization

Abstract

We consider the generic regularized optimization problem ŵ(λ) = arg minw, Σk=1m L(yk, x kTw) + λJ(w). We derive a general characterization of the properties of (loss L, penalty J) pairs which give piecewise linear coefficient paths. Such pairs allow us to efficiently generate the full regularized coefficient paths. We illustrate how we can use our results to build robust, efficient and adaptable modeling tools. © Springer-Verlag Berlin Heidelberg 2006.