In this example, a sparse regression example is
built, noise is added, then the truth is hidden. This model has
200 variables ot choose from  190 are simply noise (drawn from
N(0,1)) and the other 10 drive the response vector, y. We use SparseLab
tools to undercover the true sparse model.
The following plots show the true model, in red,
and the estimated model in blue. The Forward Stepwise Algorithm
was used to recover the model coefficients in the first plot; in
the second plot Forward Stepwise was use, but with a cutoff dictated
by False Discovery Rates; the third plot used Matching Pursuit,
and the final plot used Orthogonal Matching Pursuit to recover the
underlying model. It's easy to visually compare the algorithms in
this setting.
All these tools are included in SparseLab, along
with the code that generated this example (it is also linked to
above). If one were so inclined, it is very easy to change the parameters
(such as number of variable, observations, noise level, algorithm
used) but simply modifying the script.
