This code is reproducing the "speed trials" experiment of [1] on the following methods:

- homotopy (a.k.a. LARS-LASSO) (Osborne / Efron et al. / simplification by Loth)
- iso-lambda descent (Loth)
- Cyclical coordinate descent (CCD) (Fu / ... / Friedman)

The homotopy computes the exact regularization path. The other methods being designed to solve for a specified value of the regularization parameter, they are run for min(n,p) successive values uniformly distributed between the null-solution and least-square solution parameters, using the solution of a step as a hot start for the next one. n is the number of samples and p the number of features. CCD having asymptotic convergence, a stopping criterion is needed, that was chosen to be
  max(|correlation|) - lambda < 0.05 * dlambda
where lambda is the regularization parameter, that is the supremum of features' correlation to the residual in the LASSO solution, and dlambda is the amount by which lambda is decreased at each step. Note that stopping when the least change of a coefficient is lower than some threshold, as in the 2010 article of Friedman et al., gives running times insensitive to features correlation, as opposed to what happens here and in [1]. However, the first criterion seems a more sensible choice, as the excess correlation is a better grounded measure of error.

The results of the homotopy here and in [1] are different to a great extent. One reason is that in [1], the implementations were either in R or in bugged C. The other may come from the care taken in simplifying the algorithm and implementing it efficiently (though no fancy optimization is used).

The random data are the same for each algorihtm.

The code compiles on Unix systems, but probably does not need much change if you really need to use another system.
To run the experiment, go to the Speed_trials directory, and type "make run". A file 'dat' is produced that lists the running times in sec (real time) averaged over 10 runs for each problem. 

- References -

1. Friedman, J., Hastie, T., Höfling, H., Tibshirani, R.: Pathwise coordinate optimization. Annals of Applied Statistics 1(2) (2007) 302–332