Note
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GroupLasso for logistic regression¶
A sample script for group lasso regression
Setup¶
import matplotlib.pyplot as plt
import numpy as np
from group_lasso import LogisticGroupLasso
np.random.seed(0)
LogisticGroupLasso.LOG_LOSSES = True
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)])
num_coeffs = sum(group_sizes)
num_datapoints = 10000
noise_std = 1
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
p = 1 / (1 + np.exp(-y))
p_true = 1 / (1 + np.exp(-y_true))
c = np.random.binomial(1, p_true)
View noisy data and compute maximum accuracy¶
plt.figure()
plt.plot(p, p_true, ".")
plt.xlabel("Noisy probabilities")
plt.ylabel("Noise-free probabilities")
# Use noisy y as true because that is what we would have access
# to in a real-life setting.
best_accuracy = ((p_true > 0.5) == c).mean()
Generate estimator and train it¶
gl = LogisticGroupLasso(
groups=groups,
group_reg=0.05,
l1_reg=0,
scale_reg="inverse_group_size",
subsampling_scheme=1,
supress_warning=True,
)
gl.fit(X, c)
Extract results and compute performance metrics¶
# Extract info from estimator
pred_c = gl.predict(X)
sparsity_mask = gl.sparsity_mask_
w_hat = gl.coef_
# Compute performance metrics
accuracy = (pred_c == c).mean()
# Print results
print(f"Number variables: {len(sparsity_mask)}")
print(f"Number of chosen variables: {sparsity_mask.sum()}")
print(f"Accuracy: {accuracy}, best possible accuracy = {best_accuracy}")
Visualise regression coefficients¶
coef = gl.coef_[:, 1] - gl.coef_[:, 0]
plt.figure()
plt.plot(w / np.linalg.norm(w), ".", label="True weights")
plt.plot(
coef / np.linalg.norm(coef), ".", label="Estimated weights",
)
plt.figure()
plt.plot([w.min(), w.max()], [coef.min(), coef.max()], "gray")
plt.scatter(w, coef, s=10)
plt.ylabel("Learned coefficients")
plt.xlabel("True coefficients")
plt.figure()
plt.plot(gl.losses_)
plt.show()
Total running time of the script: ( 0 minutes 0.000 seconds)