Seagull: lasso, group lasso and sparse-group lasso regularization for linear regression models via proximal gradient descent

A Sparse-group Lasso

For high dimensional supervised learning problems, often using problem specific assumptions can lead to greater accuracy. For problems with grouped covariates, which are believed to have sparse effects both on a group and within group level, we introduce a regularized model for linear regression with `1 and `2 penalties. We discuss the sparsity and other regularization properties of the optimal...

Learning interactions via hierarchical group-lasso regularization.

We introduce a method for learning pairwise interactions in a linear regression or logistic regression model in a manner that satisfies strong hierarchy: whenever an interaction is estimated to be nonzero, both its associated main effects are also included in the model. We motivate our approach by modeling pairwise interactions for categorical variables with arbitrary numbers of levels, and the...

Adaptive Lasso and group-Lasso for functional Poisson regression

High dimensional Poisson regression has become a standard framework for the analysis of massive counts datasets. In this work we estimate the intensity function of the Poisson regression model by using a dictionary approach, which generalizes the classical basis approach, combined with a Lasso or a group-Lasso procedure. Selection depends on penalty weights that need to be calibrated. Standard ...

Lasso Regularization Paths for NARMAX Models via Coordinate Descent

We propose a new algorithm for estimating NARMAX models with L1 regularization for models represented as a linear combination of basis functions. Due to the L1-norm penalty the Lasso estimation tends to produce some coefficients that are exactly zero and hence gives interpretable models. The novelty of the contribution is the inclusion of error regressors in the Lasso estimation (which yields a...

Generalized Lasso Regularization for Regression Models