CDClassifier does not converge about lightning HOT 4 CLOSED

Coordinate descent is known to converge slowly for very loosely regularized problems (small alpha). alpha=0.01 doesn't seem small on first sight but it could be for that particular problem. One way to check is to plot test MSE as a function of alpha. The plot should have a bell shape (too regularized = underfit, loosely regularized = overfit). Perhaps alpha=0.01 will be in the overfit region.

That said the oscillating effect is a bit strange so this could be a bug. I would be curious how the scikit-learn or liblinear solvers behave on the same data.

Also, does the problem only occur with L2 regularization or also with L1 regularization?

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@mblondel I confirm, the solver terminates much quicker with L1 penalty, however, I can see some oscillation there too -- especially once I set tol very low:

In [23]: est = CDClassifier(C=10.0, alpha=1.0, random_state=0, penalty="l1", loss="log", verbose=3, max_iter=25, tol=0.000001)
In [24]: est.fit(bin_dense[:10000,:], bin_target[:10000])
Iteration 0
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Active size: 100
Violation sum ratio: 1.000000 (tol=0.000000)
Iteration 1
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Active size: 100
Violation sum ratio: 0.119174 (tol=0.000000)
Iteration 2
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Active size: 100
Violation sum ratio: 0.016049 (tol=0.000000)
Iteration 3
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Active size: 100
Violation sum ratio: 0.002891 (tol=0.000000)
Iteration 4
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Active size: 100
Violation sum ratio: 0.000715 (tol=0.000000)
Iteration 5
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Active size: 100
Violation sum ratio: 0.000306 (tol=0.000000)
Iteration 6
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Active size: 100
Violation sum ratio: 0.000166 (tol=0.000000)
Iteration 7
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Active size: 100
Violation sum ratio: 0.000043 (tol=0.000000)
Iteration 8
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Active size: 100
Violation sum ratio: 0.000030 (tol=0.000000)
Iteration 9
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Active size: 100
Violation sum ratio: 0.000013 (tol=0.000000)
Iteration 10
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Active size: 100
Violation sum ratio: 0.000008 (tol=0.000000)
Iteration 11
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Active size: 100
Violation sum ratio: 0.000008 (tol=0.000000)
Iteration 12
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Active size: 100
Violation sum ratio: 0.000011 (tol=0.000000)

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liblinear (sklearn LogisticRegression) w/ L2 penalty terminates after 4 iterations.

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I pushed b07bf03 which I believe should fix or improve the situation. The L2 solver now uses the same stopping criterion as other solvers. Also you can now use termination="violation_sum" or termination="violation_max". On my laptop, the solver now stops in ~5 iterations with tol=1e-3, ~10 iterations with tol=1e-4 and ~30 iterations with tol=1e-5.

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