Active Set Algorithms for the LASSO
type: Dataset
description: This thesis disserts on the computation of the Least Absolute Shrinkage and Selection Operator (LASSO) and derivate problems, in regression analysis. This operator has drawn increasing attention since its introduction by Robert Tibshirani in 1996, for its ability to provide or recover sparse linear models from noisy observations, sparsity meaning that only a few of possibly many explaining variables are selected to appear in the model. The selection is a result of adding to the least-squares method a constraint or minimization on the sum of absolute values of the linear coeffcients, otherwise called the l1 norm of the coefficient vector. After recounting the motivations, principles and problematics of regression analysis, linear estimators, least-squares minimization, model selection, and regularization, the two equivalent formulations of the LASSO constrained or regularized are presented, that both define a non-trivial computation problem to associate an estimator to a set of observations and a selection parameter. A brief history of algorithms for solving these problems is given, as well as the two possible approaches for handling the non differentiability of the l1 norm, and the equivalence to a quadratic program is explained. The second part focuses on practical algorithms for solving the LASSO. An algorithm proposed in 2000 by Michael Osborne is reformulated. This reformulation consists in giving a general definition and explanation of the active set method, that generalizes the simplex algorithm to convex programming, then specifying it to the LASSO program, and separately addressing linear algebra optimizations. Although it describes the same algorithm in essence, the presentation given here aims at exhibiting clearly its mechanisms, and uses different variables. In addition to helping understand and use this algorithm that seemed to be underrated, the alternative view taken here brings light on the possibility and advantages, not foreseen by the authors, to …
issued: 2026-05-10T07:54:22.005998
language: en
modified: 2026-05-10T07:54:22.006002
contact point: Organization
  fn: CCSD
keyword: active-set-method
keyword: gradient-method-for-the-lasso
keyword: infoeu-reposemanticsdoctoralthesis
keyword: infoinfo-lgcomputer-science-csmachine-learning-cslg
keyword: lars
keyword: lasso-resolution
keyword: methode-de-gradient-pour-le-lasso
keyword: methode-densemble-actif
keyword: resolution-du-lasso
keyword: theses
landing page: https://theses.hal.science/tel-00845441

Active Set Algorithms for the LASSO
type: Distribution
format: HTML
issued: 2026-05-10T07:54:22.008054
modified: 2026-05-10T07:54:21.993501
access URL: https://theses.hal.science/tel-00845441

test_moissonnage_selune
type: Agent