``LogisticGroupLasso`` is not equivalent to ``scikit-learn`` ``LogisticRegression`` with groups of size 1

[Badr-MOUFAD]

Problem

LogisticGroupLasso doesn't give the same regression coefficient as scikit-learn LogisticRegression when fitted on groups with size 1.

Expected behavior

Group logistic regression with groups of size one should be equivalent to logistic regression.

Script to reproduce

(click to expend)

import numpy as np
from sklearn.linear_model import LogisticRegression
from group_lasso import LogisticGroupLasso


n_samples, n_features = 20, 60

# generate dummy data
rng = np.random.RandomState(123)
X = rng.randn(n_samples, n_features)
y = np.sign(rng.randn(n_samples))

# max regularization parameter
alpha_max = np.linalg.norm(X.T @ y, ord=np.inf) / (2 * n_samples)
alpha =  0.1 * alpha_max 

# fit scikit-learn log reg 
sk_model = LogisticRegression(
    penalty='l1',
    C=1/(n_samples * alpha),  # scikit-learn uses an un-normalized loss
    fit_intercept=False, tol=1e-9, solver='liblinear'
).fit(X, y)
sk_coef = sk_model.coef_.flatten()

# group log reg
yn_model = LogisticGroupLasso(
    group_reg=alpha,
    groups=np.arange(n_features),
    fit_intercept=False,
    subsampling_scheme=None,
    tol=1e-9,
    l1_reg=0.,
).fit(X, y)
coef_ = yn_model.coef_
yn_coef = coef_[:, 1]

np.testing.assert_allclose(yn_coef, sk_coef)

output

(click to expend)

AssertionError: 
Not equal to tolerance rtol=1e-07, atol=0

Mismatched elements: 10 / 60 (16.7%)
Max absolute difference: 0.96593495
Max relative difference: 1.
 x: array([ 0.      , -0.      , -0.010529,  0.      ,  0.      ,  0.43878 ,
        0.      ,  0.337345,  0.15179 , -0.      ,  0.066626,  0.      ,
       -0.      ,  0.      , -0.      ,  0.      ,  0.      , -0.      ,...
 y: array([ 0.      ,  0.      , -0.034694,  0.      ,  0.      ,  1.111946,
        0.      ,  0.840564,  0.309066,  0.      ,  0.15613 ,  0.      ,
        0.      ,  0.      ,  0.      ,  0.      ,  0.      ,  0.      ,...

[mathurinm]

Hi @yngvem, do you have any feedback on this?