Input selection in ARX model estimation using group lasso regularization

Regularization Parameter Selection in the Group Lasso

This article discusses the problem of choosing a regularization parameter in the group Lasso proposed by Yuan and Lin (2006), an l1-regularization approach for producing a block-wise sparse model that has been attracted a lot of interests in statistics, machine learning, and data mining. It is important to choose an appropriate regularization parameter from a set of candidate values, because it...

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...

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...

Learning interactions through hierarchical group-lasso regularization

We introduce a method for learning pairwise interactions 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 then show how we can accommodate continuous variables a...

Model Clustering via Group Lasso