Recursive $\ell_{1,\infty}$ Group lasso

Recursive Least Squares (RLS) is a widely used method for adaptive filtering and prediction in signal processing and related fields. Its applications include: acoustic echo cancelation; wireless channel equalization; interference cancelation and data streaming predictors. In these applications a measurement stream is recursively fitted to a linear model, described by the coefficients of an FIR prediction filter, in such a way to minimize a weighted average of squared residual prediction errors. Compared to other adaptive filtering algorithms such as Least Mean Square (LMS) filters, RLS is popular because of its fast convergence and low steady-state error. In many applications it is natural to constrain the predictor coefficients to be sparse.