add example for webpage,add cv to api

Author: floriankozikowski

doc/api.rst

@@ -18,6 +18,7 @@ Estimators
    :toctree: generated/
 
    GeneralizedLinearEstimator
+   GeneralizedLinearEstimatorCV
    CoxEstimator
    ElasticNet
    GroupLasso

examples/plot_generalized_linear_estimator_cv.py

@@ -1,28 +1,138 @@
 """
 ===================================
-Cross Validation for Generalized Linear Estimator
+Cross-Validation for Generalized Linear Models
 ===================================
+
+This example shows how to use cross-validation to automatically select
+the optimal regularization parameter for generalized linear models.
 """
+
+# Author: Florian Kozikowski
+
 import numpy as np
-from sklearn.datasets import make_regression
+import matplotlib.pyplot as plt
+
+from skglm.utils.data import make_correlated_data
 from skglm.cv import GeneralizedLinearEstimatorCV
+from skglm.estimators import GeneralizedLinearEstimator
 from skglm.datafits import Quadratic
 from skglm.penalties import L1_plus_L2
 from skglm.solvers import AndersonCD
 
+# %%
+# Generate correlated data with sparse ground truth
+# --------------------------------------------------
+X, y, true_coef = make_correlated_data(
+    n_samples=150, n_features=300, random_state=42
+)
 
-X, y = make_regression(n_samples=100, n_features=20, noise=0.1, random_state=42)
-
+# %%
+# Fit model using cross-validation
+# --------------------------------
+# The CV estimator automatically finds the best regularization strength
 estimator = GeneralizedLinearEstimatorCV(
     datafit=Quadratic(),
     penalty=L1_plus_L2(alpha=1.0, l1_ratio=0.5),
-    solver=AndersonCD(max_iter=50, tol=1e-4),
-    cv=6,
+    solver=AndersonCD(max_iter=100),
+    cv=5,
+    n_alphas=50,
 )
 estimator.fit(X, y)
 
 print(f"Best alpha: {estimator.alpha_:.3f}")
-print(f"L1 ratio: {estimator.penalty.l1_ratio:.3f}")
-print(f"Number of non-zero coefficients: {np.sum(estimator.coef_ != 0)}")
+n_nonzero = np.sum(estimator.coef_ != 0)
+n_true_nonzero = np.sum(true_coef != 0)
+print(f"Non-zero coefficients: {n_nonzero} (true: {n_true_nonzero})")
+
+# %%
+# Visualize the cross-validation path
+# -----------------------------------
+# Plot shows how CV balances model complexity with prediction performance
+
+# Get mean CV scores
+mean_scores = np.mean(estimator.scores_path_, axis=1)
+std_scores = np.std(estimator.scores_path_, axis=1)
+best_idx = np.argmax(mean_scores)
+best_alpha = estimator.alphas_[best_idx]
+
+# Compute coefficient paths
+coef_paths = []
+for alpha in estimator.alphas_:
+    est_temp = GeneralizedLinearEstimator(
+        datafit=Quadratic(),
+        penalty=L1_plus_L2(alpha=alpha, l1_ratio=0.5),
+        solver=AndersonCD(max_iter=100)
+    )
+    est_temp.fit(X, y)
+    coef_paths.append(est_temp.coef_)
+coef_paths = np.array(coef_paths)
+
+fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(8, 10), sharex=True)
+
+ax1.semilogx(estimator.alphas_, -mean_scores, 'b-', linewidth=2, label='MSE')
+ax1.fill_between(estimator.alphas_,
+                 -mean_scores - std_scores,
+                 -mean_scores + std_scores,
+                 alpha=0.2, label='±1 std. dev.')
+ax1.axvline(best_alpha, color='red', linestyle='--',
+            label=f'Best alpha = {best_alpha:.2e}')
+ax1.set_ylabel('MSE')
+ax1.set_title('Cross-Validation Score vs. Regularization')
+ax1.legend(loc='best')
+ax1.grid(True, alpha=0.3)
+ax1.set_xlabel('alpha')
+
+for j in range(coef_paths.shape[1]):
+    ax2.semilogx(estimator.alphas_, coef_paths[:, j], lw=1, alpha=0.3)
+ax2.axvline(best_alpha, color='red', linestyle='--')
+ax2.set_xlabel('alpha')
+ax2.set_ylabel('Coefficient value')
+ax2.set_title('Regularization Path of Coefficients')
+ax2.grid(True, alpha=0.3)
+
+plt.tight_layout()
+plt.show()
+
+# %% [markdown]
+# Top panel: Mean CV MSE shows U-shape, minimized at chosen alpha for optimal
+# bias-variance tradeoff.
+#
+# Bottom panel: At this alpha, most coefficients are shrunk (many near zero),
+# highlighting a sparse subset of key predictors.
+
+
+# %%
+# Visualize distance to true coefficients
+# ----------------------------------------
+# Compute how well different regularization strengths recover the true coefficients
+
+distances = []
+for alpha in estimator.alphas_:
+    est_temp = GeneralizedLinearEstimator(
+        datafit=Quadratic(),
+        penalty=L1_plus_L2(alpha=alpha, l1_ratio=0.5),
+        solver=AndersonCD(max_iter=100)
+    )
+    est_temp.fit(X, y)
+    distances.append(np.linalg.norm(est_temp.coef_ - true_coef, ord=1))
+
+plt.figure(figsize=(8, 5))
+plt.loglog(estimator.alphas_, distances, 'b-', linewidth=2)
+plt.axvline(estimator.alpha_, color='red', linestyle='--',
+            label=f'CV-selected alpha = {estimator.alpha_:.3f}')
+plt.xlabel('Alpha (regularization strength)')
+plt.ylabel('L1 distance to true coefficients')
+plt.title('Recovery of True Coefficients')
+plt.legend()
+plt.grid(True, alpha=0.3)
+plt.show()
+
+print(
+    f"Distance at CV-selected alpha: "
+    f"{np.linalg.norm(estimator.coef_ - true_coef, ord=1):.3f}")
 
-# TODO: add plot, test with other penalties and datafits
+# %% [markdown]
+# The U-shaped curve shows two failure modes: small alpha doesn't induce
+# enough sparsity (keeping noisy/irrelevant features), while large alpha
+# overshrinks all coefficients including the true signals. Cross-validation
+# finds a good balance without needing access to the ground truth.

skglm/__init__.py

@@ -4,3 +4,4 @@
     Lasso, WeightedLasso, ElasticNet, MCPRegression, MultiTaskLasso, LinearSVC,
     SparseLogisticRegression, GeneralizedLinearEstimator, CoxEstimator, GroupLasso,
 )
+from .cv import GeneralizedLinearEstimatorCV  # noqa F401