5 research outputs found
Efficient Smoothed Concomitant Lasso Estimation for High Dimensional Regression
In high dimensional settings, sparse structures are crucial for efficiency,
both in term of memory, computation and performance. It is customary to
consider penalty to enforce sparsity in such scenarios. Sparsity
enforcing methods, the Lasso being a canonical example, are popular candidates
to address high dimension. For efficiency, they rely on tuning a parameter
trading data fitting versus sparsity. For the Lasso theory to hold this tuning
parameter should be proportional to the noise level, yet the latter is often
unknown in practice. A possible remedy is to jointly optimize over the
regression parameter as well as over the noise level. This has been considered
under several names in the literature: Scaled-Lasso, Square-root Lasso,
Concomitant Lasso estimation for instance, and could be of interest for
confidence sets or uncertainty quantification. In this work, after illustrating
numerical difficulties for the Smoothed Concomitant Lasso formulation, we
propose a modification we coined Smoothed Concomitant Lasso, aimed at
increasing numerical stability. We propose an efficient and accurate solver
leading to a computational cost no more expansive than the one for the Lasso.
We leverage on standard ingredients behind the success of fast Lasso solvers: a
coordinate descent algorithm, combined with safe screening rules to achieve
speed efficiency, by eliminating early irrelevant features
A generic coordinate descent solver for nonsmooth convex optimization
International audienceWe present a generic coordinate descent solver for the minimization of a nonsmooth convex objective with structure. The method can deal in particular with problems with linear constraints. The implementation makes use of efficient residual updates and automatically determines which dual variables should be duplicated. A list of basic functional atoms is pre-compiled for efficiency and a modelling language in Python allows the user to combine them at run time. So, the algorithm can be used to solve a large variety of problems including Lasso, sparse multinomial logistic regression, linear and quadratic programs