Standardizing X different in Python Lasso and R glmnet?

Question

I was trying to get the same result fitting lasso using Python's scikit-learn and R's glmnet. A helpful link

If I specify "normalize =True" in Python and "standardize = T" in R, they gave me the same result.

Python:

from sklearn.linear_model import Lasso
X = np.array([[1, 1, 2], [3, 4, 2], [6, 5, 2], [5, 5, 3]])
y = np.array([1, 0, 0, 1])
reg = Lasso(alpha =0.01, fit_intercept = True, normalize =True)
reg.fit(X, y)
np.hstack((reg.intercept_, reg.coef_))

Out[95]: array([-0.89607695,  0.        , -0.24743375,  1.03286824])

R:

reg_glmnet = glmnet(X, y, alpha = 1, lambda = 0.02,standardize = T)
coef(reg_glmnet)

4 x 1 sparse Matrix of class "dgCMatrix"
                    s0
(Intercept) -0.8960770
V1           .        
V2          -0.2474338
V3           1.0328682

However, if I don't want to standardize variables and set normalize =False and standardize = F, they gave me quite different results.

Python:

from sklearn.linear_model import Lasso
Z = np.array([[1, 1, 2], [3, 4, 2], [6, 5, 2], [5, 5, 3]])
y = np.array([1, 0, 0, 1])
reg = Lasso(alpha =0.01, fit_intercept = True, normalize =False)
reg.fit(Z, y)
np.hstack((reg.intercept_, reg.coef_))

Out[96]: array([-0.88      ,  0.09384212, -0.36159299,  1.05958478])

R:

reg_glmnet = glmnet(X, y, alpha = 1, lambda = 0.02,standardize = F)
coef(reg_glmnet)

4 x 1 sparse Matrix of class "dgCMatrix"
                     s0
(Intercept) -0.76000000
V1           0.04441697
V2          -0.29415542
V3           0.97623074

What's the difference between "normalize" in Python's Lasso and "standardize" in R's glmnet?

Answer 1

Currently, with regard to the normalize parameter the docs state "If you wish to standardize, please use StandardScaler before calling fit on an estimator with normalize=False .''

So evidently normalize and standardize are not the same with sklearn.linear_model.Lasso . Having read the StandardScaler docs I fail to understand the difference, but the fact that there is one is implied by the provided description of the normalize parameter.