CondenseNet with exclusive lasso regularization

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...

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...

Exclusive Lasso for Multi-task Feature Selection

We propose a novel group regularization which we call exclusive lasso. Unlike the group lasso regularizer that assumes covarying variables in groups, the proposed exclusive lasso regularizer models the scenario when variables in the same group compete with each other. Analysis is presented to illustrate the properties of the proposed regularizer. We present a framework of kernel based multi-tas...

The Group-Lasso: `1,∞ Regularization versus `1,2 Regularization

The `1,∞ norm and the `1,2 norm are well known tools for joint regularization in Group-Lasso methods. While the `1,2 version has been studied in detail, there are still open questions regarding the uniqueness of solutions and the efficiency of algorithms for the `1,∞ variant. For the latter, we characterize the conditions for uniqueness of solutions, we present a simple test for uniqueness, and...

Generalized Lasso Regularization for Regression Models