Show Sidebar Hide Sidebar

# Lasso and Elastic Net for Sparse Signals in Scikit-learn

Estimates Lasso and Elastic-Net regression models on a manually generated sparse signal corrupted with an additive noise. Estimated coefficients are compared with the ground-truth.

#### New to Plotly?¶

Plotly's Python library is free and open source! Get started by downloading the client and reading the primer.
You can set up Plotly to work in online or offline mode, or in jupyter notebooks.
We also have a quick-reference cheatsheet (new!) to help you get started!

### Version¶

In :
import sklearn
sklearn.__version__

Out:
'0.18.1'

### Imports¶

This tutorial imports r2_score, Lasso and ElasticNet.

In :
print(__doc__)

import plotly.plotly as py
import plotly.graph_objs as go

import numpy as np
from sklearn.metrics import r2_score
from sklearn.linear_model import Lasso
from sklearn.linear_model import ElasticNet

Automatically created module for IPython interactive environment


### Calculations¶

Generate some sparse data to play with

In :
np.random.seed(42)

n_samples, n_features = 50, 200
X = np.random.randn(n_samples, n_features)
coef = 3 * np.random.randn(n_features)
inds = np.arange(n_features)
np.random.shuffle(inds)
coef[inds[10:]] = 0  # sparsify coef
y = np.dot(X, coef)

y += 0.01 * np.random.normal((n_samples,))

# Split data in train set and test set
n_samples = X.shape
X_train, y_train = X[:n_samples / 2], y[:n_samples / 2]
X_test, y_test = X[n_samples / 2:], y[n_samples / 2:]


### Lasso¶

In :
alpha = 0.1
lasso = Lasso(alpha=alpha)

y_pred_lasso = lasso.fit(X_train, y_train).predict(X_test)
r2_score_lasso = r2_score(y_test, y_pred_lasso)
print(lasso)
print("r^2 on test data : %f" % r2_score_lasso)

Lasso(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=1000,
normalize=False, positive=False, precompute=False, random_state=None,
selection='cyclic', tol=0.0001, warm_start=False)
r^2 on test data : 0.384710


### ElasticNet¶

In :
enet = ElasticNet(alpha=alpha, l1_ratio=0.7)

y_pred_enet = enet.fit(X_train, y_train).predict(X_test)
r2_score_enet = r2_score(y_test, y_pred_enet)
print(enet)
print("r^2 on test data : %f" % r2_score_enet)

ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.7,
max_iter=1000, normalize=False, positive=False, precompute=False,
random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
r^2 on test data : 0.240176


### Plot Results¶

In :
p1 = go.Scatter(y=enet.coef_,
mode='lines',
line=dict(color='lightgreen', width=2),
name='Elastic net coefficients')

p2 = go.Scatter(y=lasso.coef_,
mode='lines',
line=dict(color='gold', width=2),
name='Lasso coefficients')

p3 = go.Scatter(y=coef,
mode='lines',
line=dict(color='navy', dash='dash', width=2),
name='original coefficients')
layout = go.Layout(title = "Lasso R^2: %f, Elastic Net R^2: %f"
% (r2_score_lasso, r2_score_enet),
hovermode='closest')

fig = go.Figure(data=[p1, p2, p3], layout=layout)

In :
py.iplot(fig)

Out: 