def test_ridge():
"""
Ridge from sklearn is the same as the R package penalised
but differs from glmnet, whose regularisation on beta_0 seems
to be different as compared to penalized R package and sklearn package.
glmnet and ElasticNet gives different results and different from
Ridge and penalized
"""
R_code_penalized = """
library(penalized)
x = matrix(c(0,1,2,3,0,1,2,4), ncol=2)
coefficients(
penalized(c(0,1,2,4), x, lambda1=0,lambda2=1, standardize=F))
0.04615385 0.40000000 0.63076923
"""
ridge = linear_model.Ridge(alpha=1)
alae(ridge.fit(X, Y).coef_, np.array([0.4, 0.63076923]), places=6)
alae([ridge.fit(X, Y).intercept_], [0.04615384615384599], places=10)
def test_ridge():
"""
Ridge from sklearn is the same as the R package penalised
but differs from glmnet, whose regularisation on beta_0 seems
to be different as compared to penalized R package and sklearn package.
glmnet and ElasticNet gives different results and different from
Ridge and penalized
"""
R_code_penalized = """
library(penalized)
x = matrix(c(0,1,2,3,0,1,2,4), ncol=2)
coefficients(
penalized(c(0,1,2,4), x, lambda1=0,lambda2=1, standardize=F))
0.04615385 0.40000000 0.63076923
"""
ridge = linear_model.Ridge(alpha=1)
alae(ridge.fit(X, Y).coef_ , np.array([0.4, 0.63076923]), places=6)
alae([ridge.fit(X, Y).intercept_], [0.04615384615384599], places=10)
def test_lasso():
"""
Lasso, ElasticNet (using l1_ratio=1) and glmnet (alpha=1) gives the same
results.
scikit-learn Lasso documentation::
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
In glmnet::
lambda * [ (1-alpha)/2||beta||_2^2 + alpha||beta||_1. ]
so if we set alpha = 1, the first term (ridge) disappears
Using the penalised function, we get different results...that is
intercept is 0.2 and coeff are [0 (0.8857143)
"""
R_code_glmnet = """
fit = glmnet(x, c(0,1,2,4), alpha=1, lambda=1, standardize=F)
c(fit$a0, fit$beta)
$s0
[1] 0.8
V1 = ( ., V2 0.5428571)
"""
lasso = linear_model.Lasso(alpha=1)
alae(lasso.fit(X, Y).coef_, np.array([0., 0.54285714]), places=6)
alae([lasso.fit(X, Y).intercept_], [0.8], places=10)
# The code using ElasticNet class is
en = linear_model.ElasticNet(l1_ratio=1, alpha=1)
en.fit(X, Y)
alae([0.8], [en.intercept_], places=6)
alae(en.coef_, np.array([0., 0.54285714]), places=6)
def test_lasso():
"""
Lasso, ElasticNet (using l1_ratio=1) and glmnet (alpha=1) gives the same
results.
scikit-learn Lasso documentation::
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
In glmnet::
lambda * [ (1-alpha)/2||beta||_2^2 + alpha||beta||_1. ]
so if we set alpha = 1, the first term (ridge) disappears
Using the penalised function, we get different results...that is
intercept is 0.2 and coeff are [0 (0.8857143)
"""
R_code_glmnet = """
fit = glmnet(x, c(0,1,2,4), alpha=1, lambda=1, standardize=F)
c(fit$a0, fit$beta)
$s0
[1] 0.8
V1 = ( ., V2 0.5428571)
"""
lasso = linear_model.Lasso(alpha=1)
alae(lasso.fit(X, Y).coef_ , np.array([0., 0.54285714]), places=6)
alae([lasso.fit(X, Y).intercept_], [0.8], places=10)
# The code using ElasticNet class is
en = linear_model.ElasticNet(l1_ratio=1, alpha=1)
en.fit(X, Y)
alae([0.8], [en.intercept_], places=6)
alae(en.coef_, np.array([ 0. , 0.54285714]), places=6)
