Generalized LASSO with under-determined regularization matrices

Generalized LASSO with under-determined regularization matrices

This paper studies the intrinsic connection between a generalized LASSO and a basic LASSO formulation. The former is the extended version of the latter by introducing a regularization matrix to the coefficients. We show that when the regularization matrix is even- or under-determined with full rank conditions, the generalized LASSO can be transformed into the LASSO form via the Lagrangian frame...

Generalized Lasso Regularization for Regression Models

Adaptive multi-penalty regularization based on a generalized Lasso path

For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of problems of unmixing type where signal and noise are additively mixed, is one of such examples. In this paper, we propose a novel algorithmic framework for a...

Regularization with the Smooth-Lasso procedure

We consider the linear regression problem. We propose the S-Lasso procedure to estimate the unknown regression parameters. This estimator enjoys sparsity of the representation while taking into account correlation between successive covariates (or predictors). The study covers the case when p ≫ n, i.e. the number of covariates is much larger than the number of observations. In the theoretical p...

Posterior regularization and attribute assessment of under-determined linear mappings

Linear mappings are omnipresent in data processing analysis ranging from regression to distance metric learning. The interpretation of coefficients from under-determined mappings raises an unexpected challenge when the original modeling goal does not impose regularization. Therefore, a general posterior regularization strategy is presented for inducing unique results, and additional sensitivity...