Learning and Estimation Applications of an Online Homotopy Algorithm for a Generalization of the LASSO

The LASSO is a widely used shrinkage and selection method for linear regression. We propose a generalization of the LASSO in which the l1 penalty is applied on a linear transformation of the regression parameters, allowing to input prior information on the structure of the problem and to improve interpretability of the results. We also study time varying system with an l1-penalty on the variations of the state, leading to estimates that exhibit few “jumps”. We propose a homotopy algorithm that updates the solution as additional measurements are available. The algorithm takes advantage of the sparsity of the solution for computational efficiency and is promising for mining large datasets. The algorithm is implemented on three experimental data sets representing applications to traffic estimation from sparsely sampled probe vehicles, flow estimation in tidal channels and text analysis of on-line news.