We provide code for the homotopy algorithm introduced in

P. Garrigues and L. El Ghaoui, An Homotopy Algorithm for the Lasso with Online Observations, in Advances in Neural Information Processing Systems 21 (NIPS 2008).

You can check out the details in the paper available on my website. The notations are consistent with the notations in the paper.

We solve the l1-penalized least-square also known as Lasso or Basis Pursuit Denoising:

\min_\theta .5*\|X \theta - y\|_2^2 + \mu \|\theta\|_1

We provide the following algorithms to solve Lasso:

• An interior point method, requires cvxmod
• Lars
• Coordinate descent

In the online setting the solution is updated using the reclasso algorithm.

The function compare_algo compares RecLasso with Lasso and Coordinate Descent with warm start and reproduces the results in Figure 2.

The function adaptive_regularization illustrates the proposed algorithm to select the regularization parameter, and reproduces the results in Figure 3.