リッジ回帰とラッソ回帰 | 正則化で過学習を抑える

import numpy as np
import matplotlib.pyplot as plt
import japanize_matplotlib
from sklearn.linear_model import Lasso, LassoCV, LinearRegression, Ridge, RidgeCV
from sklearn.model_selection import cross_val_score
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler

# パラメータ
n_samples = 200
n_features = 10
n_informative = 3
rng = np.random.default_rng(42)

# 真の重み（スパース）
coef = np.zeros(n_features)
coef[:n_informative] = rng.normal(loc=3.0, scale=1.0, size=n_informative)

# 説明変数と目的変数を生成
X = rng.normal(size=(n_samples, n_features))
y = X @ coef + rng.normal(scale=5.0, size=n_samples)

# 各モデルを作成・学習
# with_mean=False にしているのは疎行列対応の書き方の名残かも
linear = make_pipeline(
    StandardScaler(with_mean=False),
    LinearRegression()
).fit(X, y)

ridge = make_pipeline(
    StandardScaler(with_mean=False),
    RidgeCV(alphas=np.logspace(-3, 3, 13), cv=5)
).fit(X, y)

lasso = make_pipeline(
    StandardScaler(with_mean=False),
    LassoCV(alphas=np.logspace(-3, 1, 9), cv=5, max_iter=50_000)
).fit(X, y)

models = {
    "Linear": linear,
    "Ridge": ridge,
    "Lasso": lasso,
}

# 係数の比較可視化
indices = np.arange(n_features)
width = 0.25
plt.figure(figsize=(10, 4))
plt.bar(indices - width, np.abs(linear[-1].coef_), width=width, label="Linear")
plt.bar(indices,         np.abs(ridge[-1].coef_),  width=width, label="Ridge")
plt.bar(indices + width, np.abs(lasso[-1].coef_),  width=width, label="Lasso")
plt.xlabel("特徴量インデックス")
plt.ylabel("|係数|")
plt.legend()
plt.grid(alpha=0.3)
plt.tight_layout()
plt.show()

# 汎化性能のスコア
for name, model in models.items():
    scores = cross_val_score(model, X, y, cv=5, scoring="r2")
    print(f"{name:>6}: R^2 = {scores.mean():.3f} ± {scores.std():.3f}")