On Fri, Feb 15, 2013 at 01:28:43PM +0100, Charles-Pierre Astolfi wrote:
> Just choose the alpha (from a fixed set) that minimizes the RMSE of
> the prediction of the last time step (or the last n time steps with
> exponential decay). Maybe I'm mistaken but there's no easy way to do
> that with LassoLarsCV.

In my opinion, I am not sure that you want an interpolator that
interpolate the model parameters for specific alphas. You may want to
compute the RMSE at the knots of the path, because I think that this is
where they will be the minimum that you are looking for.

If for some reason you need to interpolate to specific alphas, it might
be a good strategy to compute the square norm of residuals, and
interpolate this (this square norm will also be linear between the
knots). This is basically the mechanism behind LassoLarsCV. I believe
that something like sklearn.linear_model.least_angle._lars_path_residues
might help you achieve what you want. Note that it is a private function;
in other words we are not garanteeing that it will not change, and that
it's API will remain the same. This is on purpose, see below.

Your answer comforts me with my opinion that we _do not want_ to provide
the function that you are asking for. It is much easier to write such
function (just a simple matter of using scipy.interpolate.interp1d) than
to use it wisely. I don't believe that the difficulty is in writing this
function, and I believe that anybody who has the need for it, also has
specificities related to this need, and can/should code it himself. Most
importantly, I don't want to add yet another function to the already very
rich codebase of scikit-learn's linear models because I worry about the
maintenance issues, and the multiplication of entry points that make
things harder to grasp for users.

Now, that said, I think that we could do a better job pushing users
towards the solution that you are proposing, which is a good one. I will
improve the docstring of lasso_path to suggest this solution to users. 

Thanks a lot for your feedback,

Gaƫl

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