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

import matplotlib.pyplot as plt
import numpy as np
from sklearn.linear_model import Ridge
from sklearn.metrics import r2_score
from sklearn.pipeline import Pipeline

from group_lasso import GroupLasso

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 = np.concatenate(
    [size * [i] for i, size in enumerate(group_sizes)]
).reshape(-1, 1)
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)
example group lasso pipeline

Generate pipeline and train it

pipe = Pipeline(
    memory=None,
    steps=[
        (
            "variable_selection",
            GroupLasso(
                groups=groups,
                group_reg=5,
                l1_reg=0,
                scale_reg="inverse_group_size",
                subsampling_scheme=1,
                supress_warning=True,
            ),
        ),
        ("regressor", Ridge(alpha=0.1)),
    ],
)
pipe.fit(X, y)

Out:

/home/docs/checkouts/readthedocs.org/user_builds/group-lasso/envs/latest/lib/python3.7/site-packages/group_lasso-1.5.0-py3.7.egg/group_lasso/_fista.py:119: ConvergenceWarning: The FISTA iterations did not converge to a sufficient minimum.
You used subsampling then this is expected, otherwise, try increasing the number of iterations or decreasing the tolerance.

Pipeline(steps=[('variable_selection',
                 GroupLasso(group_reg=5,
                            groups=array([[ 0],
       [ 0],
       [ 0],
       [ 0],
       [ 0],
       [ 0],
       [ 0],
       [ 0],
       [ 0],
       [ 0],
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       [ 5]...
       [46],
       [46],
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       [49],
       [49],
       [49],
       [49],
       [49],
       [49],
       [49],
       [49],
       [49],
       [49]]),
                            l1_reg=0, scale_reg='inverse_group_size',
                            subsampling_scheme=1, supress_warning=True)),
                ('regressor', Ridge(alpha=0.1))])

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)

# 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}")

Out:

Number variables: 720
Number of chosen variables: 313
R^2: 0.46373947136901283, best possible R^2 = 0.46262785225190173

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()
  • example group lasso pipeline
  • example group lasso pipeline

Total running time of the script: ( 0 minutes 4.421 seconds)

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