Hey Ariel,

On Sat, Sep 29, 2012 at 08:54:46AM -0700, Ariel Rokem wrote:
> Sure - here's a minimal example based on what I'm trying to do with this (data
> at the top, calculations at the bottom): 

> https://gist.github.com/3804428

I do believe that it's a convergence problem. I have updated your gist at
https://gist.github.com/3804487
to fit with more and more iterations, and when I run it I get:

In [1]: %run sklearn_EN_example.py
/home/varoquau/dev/scikit-learn/sklearn/linear_model/coordinate_descent.py:207:
UserWarning: Coordinate descent with alpha=0 may lead to unexpected
results and is discouraged.
  self.positive)
/home/varoquau/dev/scikit-learn/sklearn/linear_model/coordinate_descent.py:222:
UserWarning: Objective did not converge for target 0, you might want to
increase the number of iterations
  ' to increase the number of iterations')
With ElasticNet: 0.9785
With ElasticNet (1 refit): 0.9800
With ElasticNet (2 refit): 0.9809
With ElasticNet (3 refit): 0.9815
With ElasticNet (4 refit): 0.9819
With ElasticNet (5 refit): 0.9821
With ElasticNet (6 refit): 0.9823
With ElasticNet (7 refit): 0.9824
With ElasticNet (8 refit): 0.9825
With ElasticNet (9 refit): 0.9826
With ElasticNet (10 refit): 0.9827
With LinearRegression: 1.0000

So the conclusion are indeed that ElasticNet with alpha=0 does not
converge well, as we thought. Also, the code did warn you about the
problem.

The coordinate descent solver does not work well on unpenalized problem.
You should not use it. It's a fundemental flaw of the algorithm. One
algorithm cannot be well-suited for every usecase. The coordinate descent
solver used in the ElasticNet object is good for non-smooth problems (the
l1 penalty) with sparse solutions. While this is the normal setting for
Elastic Net, you are definitely not in this situation.

HTH,

Gaël

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