GroupLasso as a transformer

A sample script to demonstrate how the group lasso estimators can be used for variable selection in a scikit-learn pipeline.

Setup

from group_lasso import GroupLasso
from sklearn.linear_model import Ridge
from sklearn.metrics import r2_score
from sklearn.pipeline import Pipeline
from utils import (
    get_groups_from_group_sizes,
    generate_group_lasso_coefficients,
)
import numpy as np
import matplotlib.pyplot as plt


np.random.seed(0)

Set dataset parameters

group_sizes = [np.random.randint(10, 20) for i in range(50)]
active_groups = [np.random.randint(2) for _ in group_sizes]
groups = get_groups_from_group_sizes(group_sizes)
num_coeffs = sum(group_sizes)
num_datapoints = 10000
noise_std = 20

Generate data matrix

X = np.random.standard_normal((num_datapoints, num_coeffs))

Generate coefficients

w = np.concatenate(
    [
        np.random.standard_normal(group_size) * is_active
        for group_size, is_active in zip(group_sizes, active_groups)
    ]
)
w = w.reshape(-1, 1)
true_coefficient_mask = w != 0
intercept = 2

Generate regression targets

y_true = X @ w + intercept
y = y_true + np.random.randn(*y_true.shape) * noise_std

View noisy data and compute maximum R^2

plt.figure()
plt.plot(y, y_true, ".")
plt.xlabel("Noisy targets")
plt.ylabel("Noise-free targets")
# Use noisy y as true because that is what we would have access
# to in a real-life setting.
R2_best = r2_score(y, y_true)

Generate pipeline and train it

pipe = Pipeline(
    memory=None,
    steps=[
        (
            "variable_selection",
            GroupLasso(
                groups=groups,
                group_reg=1.3,
                subsampling_scheme=1,
                supress_warning=True,
            ),
        ),
        ("regressor", Ridge(alpha=0.1)),
    ],
)
pipe.fit(X, y)

Traceback (most recent call last):
  File "/home/yngvem/anaconda3/lib/python3.7/site-packages/sphinx_gallery/gen_rst.py", line 440, in _memory_usage
    out = func()
  File "/home/yngvem/anaconda3/lib/python3.7/site-packages/sphinx_gallery/gen_rst.py", line 425, in __call__
    exec(self.code, self.globals)
  File "/home/yngvem/Programming/morro/group-lasso/examples/example_group_lasso_pipeline.py", line 90, in <module>
    supress_warning=True,
TypeError: __init__() got an unexpected keyword argument 'supress_warning'

Extract results and compute performance metrics

# Extract from pipeline
yhat = pipe.predict(X)
sparsity_mask = pipe["variable_selection"].sparsity_mask
coef = pipe["regressor"].coef_.T

# Construct full coefficient vector
w_hat = np.zeros_like(w)
w_hat[sparsity_mask] = coef

R2 = r2_score(y, yhat)
true_R2 = r2_score(y_true, yhat)

Print performance metrics

print(f"Number variables: {len(sparsity_mask)}")
print(f"Number of chosen variables: {sparsity_mask.sum()}")
print(f"R^2: {R2}, best possible R^2 = {R2_best}")
print(f"R^2 compared to noise-free data: {R2}")

Visualise regression coefficients

for i in range(w.shape[1]):
    plt.figure()
    plt.plot(w[:, i], ".", label="True weights")
    plt.plot(w_hat[:, i], ".", label="Estimated weights")

plt.figure()
plt.plot([w.min(), w.max()], [coef.min(), coef.max()], "gray")
plt.scatter(w, w_hat, s=10)
plt.ylabel("Learned coefficients")
plt.xlabel("True coefficients")
plt.show()