Hoofdstuk 29 — Supervised learning: regressie (LinearRegression, Ridge, Lasso)

Let op: De tekst is in het Nederlands; alle Python codevoorbeelden zijn in het Engels.

Doelen:

• Begrijpen van lineaire regressie en regularisatie (L2 Ridge, L1 Lasso).
• Train/test‑split, metriekkeuze (MSE, MAE, R^2) en feature scaling.

Installatie:

pip install scikit-learn numpy pandas

29.1 Data genereren of laden

import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split

rng = np.random.default_rng(0)
X = pd.DataFrame({
    'x1': rng.normal(size=300),
    'x2': rng.normal(size=300),
    'x3': rng.normal(size=300)
})
# Waarheid: y = 3*x1 - 2*x2 + noise; x3 is ruis
y = 3*X['x1'] - 2*X['x2'] + rng.normal(scale=0.5, size=300)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

29.2 Lineaire regressie

from sklearn.linear_model import LinearRegression

lin = LinearRegression()
lin.fit(X_train, y_train)
print('R^2 (train):', lin.score(X_train, y_train))
print('R^2 (test): ', lin.score(X_test, y_test))
print('Coefficients:', lin.coef_, 'Intercept:', lin.intercept_)

29.3 Ridge en Lasso

Regularisatie helpt overfitting voorkomen en kan stabiliteit verhogen.

from sklearn.linear_model import Ridge, Lasso
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline

ridge = Pipeline([
    ('scaler', StandardScaler()),
    ('model', Ridge(alpha=1.0, random_state=42))
]).fit(X_train, y_train)

lasso = Pipeline([
    ('scaler', StandardScaler()),
    ('model', Lasso(alpha=0.1, random_state=42, max_iter=10000))
]).fit(X_train, y_train)

print('Ridge R^2 (test):', ridge.score(X_test, y_test))
print('Lasso R^2 (test):', lasso.score(X_test, y_test))

29.4 Metrieken: MSE, MAE, R^2

from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score

pred = lin.predict(X_test)
print('MSE:', mean_squared_error(y_test, pred))
print('MAE:', mean_absolute_error(y_test, pred))
print('R^2:', r2_score(y_test, pred))

29.5 Feature selectie met Lasso

coef = lasso.named_steps['model'].coef_
print(coef)
# Coefs die exact 0 zijn, worden effectief verwijderd

29.6 Cross‑validation varianten

from sklearn.model_selection import cross_val_score
scores = cross_val_score(ridge, X, y, cv=5, scoring='r2')
print('CV R^2:', scores.mean())

29.7 Samenvatting

• LinearRegression voor basismodellen; Ridge/Lasso voor regularisatie.
• Schaal features bij Ridge/Lasso voor consistente regulering.
• Evalueer met passende regressiemetrieken en gebruik CV voor robuustheid.