---
abstract: 'We propose a new sparse regression method called the [*component lasso*]{}, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then applies the lasso to each subproblem separately, obtaining a coefficient vector for each one. Finally, it uses non-negative least squares to recombine the different vectors into a single solution. This step is useful in selecting and reweighting components that are correlated with the response. Simulated and real data examples show that the component lasso can outperform standard regression methods such as the lasso and elastic net, achieving a lower mean squared error as well as better support recovery. The modular structure also lends itself naturally to parallel computation.'
author:
- Nadine Hussami and Robert Tibshirani
bibliography:
- 'tibs.bib'
date:
- |
    Department of Electrical Engineering and\
    Departments of Health Research and Policy, and Statistics,\
    Stanford University, Stanford CA.;\
    nadinehu@stanford.edu; tibs@stanford.edu
- November 2013
title: A Component Lasso
---

[**Keywords.**]{} Lasso, elastic net, graphical lasso, sparsity, connected components, $\ell_1$-minimization, non-negative least squares, grouping effect.

Introduction {#sec:intro}
============

Suppose that we have a response vector $y\in\R^n$, a matrix $X \in \R^{n\times p}$ of predictor 