83 lines
2.3 KiB
Python
83 lines
2.3 KiB
Python
|
"""
|
||
|
|
=============================================
|
||
|
|
Joint feature selection with multi-task Lasso
|
||
|
|
=============================================
|
||
|
|
|
||
|
|
The multi-task lasso allows to fit multiple regression problems
|
||
|
|
jointly enforcing the selected features to be the same across
|
||
|
|
tasks. This example simulates sequential measurements, each task
|
||
|
|
is a time instant, and the relevant features vary in amplitude
|
||
|
|
over time while being the same. The multi-task lasso imposes that
|
||
|
|
features that are selected at one time point are select for all time
|
||
|
|
point. This makes feature selection by the Lasso more stable.
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
|
||
|
|
# License: BSD 3 clause
|
||
|
|
|
||
|
|
# %%
|
||
|
|
# Generate data
|
||
|
|
# -------------
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
|
||
|
|
rng = np.random.RandomState(42)
|
||
|
|
|
||
|
|
# Generate some 2D coefficients with sine waves with random frequency and phase
|
||
|
|
n_samples, n_features, n_tasks = 100, 30, 40
|
||
|
|
n_relevant_features = 5
|
||
|
|
coef = np.zeros((n_tasks, n_features))
|
||
|
|
times = np.linspace(0, 2 * np.pi, n_tasks)
|
||
|
|
for k in range(n_relevant_features):
|
||
|
|
coef[:, k] = np.sin((1.0 + rng.randn(1)) * times + 3 * rng.randn(1))
|
||
|
|
|
||
|
|
X = rng.randn(n_samples, n_features)
|
||
|
|
Y = np.dot(X, coef.T) + rng.randn(n_samples, n_tasks)
|
||
|
|
|
||
|
|
# %%
|
||
|
|
# Fit models
|
||
|
|
# ----------
|
||
|
|
|
||
|
|
from sklearn.linear_model import Lasso, MultiTaskLasso
|
||
|
|
|
||
|
|
coef_lasso_ = np.array([Lasso(alpha=0.5).fit(X, y).coef_ for y in Y.T])
|
||
|
|
coef_multi_task_lasso_ = MultiTaskLasso(alpha=1.0).fit(X, Y).coef_
|
||
|
|
|
||
|
|
# %%
|
||
|
|
# Plot support and time series
|
||
|
|
# ----------------------------
|
||
|
|
|
||
|
|
import matplotlib.pyplot as plt
|
||
|
|
|
||
|
|
fig = plt.figure(figsize=(8, 5))
|
||
|
|
plt.subplot(1, 2, 1)
|
||
|
|
plt.spy(coef_lasso_)
|
||
|
|
plt.xlabel("Feature")
|
||
|
|
plt.ylabel("Time (or Task)")
|
||
|
|
plt.text(10, 5, "Lasso")
|
||
|
|
plt.subplot(1, 2, 2)
|
||
|
|
plt.spy(coef_multi_task_lasso_)
|
||
|
|
plt.xlabel("Feature")
|
||
|
|
plt.ylabel("Time (or Task)")
|
||
|
|
plt.text(10, 5, "MultiTaskLasso")
|
||
|
|
fig.suptitle("Coefficient non-zero location")
|
||
|
|
|
||
|
|
feature_to_plot = 0
|
||
|
|
plt.figure()
|
||
|
|
lw = 2
|
||
|
|
plt.plot(coef[:, feature_to_plot], color="seagreen", linewidth=lw, label="Ground truth")
|
||
|
|
plt.plot(
|
||
|
|
coef_lasso_[:, feature_to_plot], color="cornflowerblue", linewidth=lw, label="Lasso"
|
||
|
|
)
|
||
|
|
plt.plot(
|
||
|
|
coef_multi_task_lasso_[:, feature_to_plot],
|
||
|
|
color="gold",
|
||
|
|
linewidth=lw,
|
||
|
|
label="MultiTaskLasso",
|
||
|
|
)
|
||
|
|
plt.legend(loc="upper center")
|
||
|
|
plt.axis("tight")
|
||
|
|
plt.ylim([-1.1, 1.1])
|
||
|
|
plt.show()
|