[READY] FIX - more than one iteration done when fitting with alpha > alpha_max

[Badr-MOUFAD]

closes #252

We get such behavior because of how we construct a dual feasible vector.

Indeed, when alpha > alpha_max (let say alpha = m * alpha_max where m > 1) , we start the solver at theta = m * y / n_samples, wich is feasible yet not optimal.

...

This proceeds as follows:

• [x] fix bug
• [x] add unit testing

[mathurinm]

In homotopy we should avoid computing alpha_max when we can (it is costly) Instead we should just avoid rescaling if the point is already feasible.

If we fit with alpha > alpha_max, then the first dual pt is y, the dual norm is alpha_max < alpha and so we should not rescale it.

[Badr-MOUFAD]

I do agree with your suggestion.

However, implementing it (mine also) will imply making big changes to the code as we don't always compute alpha_max (depends on whether it was passed or not), and computing it varies according to the solved the problem.

Given these new insights, shall we perform these changes to fix this [non-harmful] bug?

[mathurinm]

In homotopy.py, L296 and L305, we compute the dual norm of X.T theta and automatically rescale by it. We should L305 rescale only if it is greater than alpha. Otherwise, the point is feasible, no need to rescale.

There is no extra cost and the code modification is minor

[codecov-commenter]

Codecov Report

Merging #257 (580cc14) into main (75e3a4c) will increase coverage by 0.09%. The diff coverage is 100.00%.

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@@            Coverage Diff             @@
##             main     #257      +/-   ##
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+ Coverage   88.44%   88.53%   +0.09%     
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  Files          15       15              
  Lines        1134     1143       +9     
  Branches      136      136              
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+ Hits         1003     1012       +9     
  Misses        101      101              
  Partials       30       30              

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unittests	∅ <ø> (∅)

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Impacted Files	Coverage Δ
celer/homotopy.py	86.89% <100.00%> (ø)
celer/tests/test_lasso.py	100.00% <100.00%> (ø)

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[Badr-MOUFAD]

@mathurinm, I will let you check with reproduce.py that this solves the bug.