Note
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Warm start to choose regularisation strength¶
Setup¶
import matplotlib.pyplot as plt
import numpy as np
from group_lasso import GroupLasso
np.random.seed(0)
GroupLasso.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)]
).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
Generate estimator and train it¶
num_regs = 10
regularisations = np.logspace(-0.5, 1.5, num_regs)
weights = np.empty((num_regs, w.shape[0],))
gl = GroupLasso(
groups=groups,
group_reg=5,
l1_reg=0,
frobenius_lipschitz=True,
scale_reg="inverse_group_size",
subsampling_scheme=1,
supress_warning=True,
n_iter=1000,
tol=1e-3,
warm_start=True, # Warm start to start each subsequent fit with previous weights
)
for i, group_reg in enumerate(regularisations[::-1]):
gl.group_reg = group_reg
gl.fit(X, y)
weights[-(i + 1)] = gl.sparsity_mask_.squeeze()
Visualise chosen covariate groups¶
plt.figure()
plt.pcolormesh(np.arange(w.shape[0]), regularisations, -weights, cmap="gray")
plt.yscale("log")
plt.xlabel("Covariate number")
plt.ylabel("Regularisation strength")
plt.title("Active groups are black and inactive groups are white")
plt.show()
Total running time of the script: ( 0 minutes 20.652 seconds)