from sklearn.linear_model import Ridge, RidgeCV
from sklearn.model_selection import cross_val_score
import numpy as np

# ── Ridge adds L2 penalty to OLS ─────────────────────
# Minimises: Σ(y - ŷ)² + α * Σβᵢ²
# α (alpha): regularisation strength
#   α = 0: same as linear regression (no regularisation)
#   α → ∞: all coefficients shrink toward zero
# Effect: coefficients shrink proportionally (none become exactly zero)
# Best for: multicollinear features, more features than samples

alphas = [0.01, 0.1, 1.0, 10, 100, 1000]

# Manual grid search with cross-validation
results = []
for alpha in alphas:
    pipe = Pipeline([("scaler", StandardScaler()),
                     ("model", Ridge(alpha=alpha))])
    cv_r2 = cross_val_score(pipe, X_train, y_train, cv=5, scoring="r2")
    results.append({"alpha": alpha, "r2_mean": cv_r2.mean(), "r2_std": cv_r2.std()})

import pandas as pd
results_df = pd.DataFrame(results)
print(results_df)
best_alpha = results_df.loc[results_df["r2_mean"].idxmax(), "alpha"]
print(f"Best alpha: {best_alpha}")

# Built-in CV (faster)
alphas_to_try = np.logspace(-3, 4, 50)  # log-spaced from 0.001 to 10,000
ridge_cv = RidgeCV(alphas=alphas_to_try, cv=5, scoring="r2")
ridge_cv.fit(StandardScaler().fit_transform(X_train), y_train)
print(f"RidgeCV best alpha: {ridge_cv.alpha_:.4f}")
print(f"RidgeCV R²: {ridge_cv.score(StandardScaler().fit_transform(X_test), y_test):.4f}")

# ── Visualise coefficient shrinkage ──────────────────
fig, ax = plt.subplots(figsize=(10, 5))
coefs = []
for alpha in np.logspace(-3, 4, 100):
    r = Ridge(alpha=alpha)
    r.fit(StandardScaler().fit_transform(X_train), y_train)
    coefs.append(r.coef_)
coefs = np.array(coefs)
for i, name in enumerate(X.columns):
    ax.plot(np.logspace(-3, 4, 100), coefs[:, i], label=name)
ax.set_xscale("log")
ax.set(xlabel="Alpha (log scale)", ylabel="Coefficient Value",
       title="Ridge: Coefficient Shrinkage")
ax.axvline(best_alpha, color="red", linestyle="--", label="Best alpha")
ax.legend()
plt.tight_layout()

from sklearn.metrics import (mean_absolute_error, mean_squared_error,
                             root_mean_squared_error, r2_score,
                             mean_absolute_percentage_error)
import numpy as np

y_true = y_test
y_pred = pipeline.predict(X_test)

# ── MAE: Mean Absolute Error ──────────────────────────
# Average absolute difference. Same units as target.
# Robust to outliers (vs MSE/RMSE which square errors)
# Easy to explain: "on average, predictions are off by $X"
mae = mean_absolute_error(y_true, y_pred)
print(f"MAE:  ${mae:,.0f}")

# ── MSE: Mean Squared Error ───────────────────────────
# Squares errors → large errors penalised more heavily
# NOT in target units (hard to interpret directly)
# Used as training loss (differentiable)
mse = mean_squared_error(y_true, y_pred)
print(f"MSE:  ${mse:,.0f}")

# ── RMSE: Root Mean Squared Error ────────────────────
# sqrt(MSE) — back in target units
# Most common metric for regression
# More sensitive to large errors than MAE
rmse = root_mean_squared_error(y_true, y_pred)
print(f"RMSE: ${rmse:,.0f}")

# ── R²: Coefficient of Determination ─────────────────
# Proportion of variance explained: R² = 1 - SS_res/SS_tot
# R² = 1.0: perfect prediction
# R² = 0.0: as good as predicting the mean (useless model)
# R² < 0.0: WORSE than predicting the mean (seriously bad)
r2 = r2_score(y_true, y_pred)
print(f"R²:   {r2:.4f}")

# ── MAPE: Mean Absolute Percentage Error ─────────────
# Percentage error. Intuitive but problematic near zero.
# "Predictions are X% off on average"
mape = mean_absolute_percentage_error(y_true, y_pred)
print(f"MAPE: {mape:.2%}")

# ── When to use each ──────────────────────────────────
print("""
MAE:  Use when outliers exist and you want robust metric
      Use to communicate to stakeholders ("off by $X")
RMSE: Use when large errors are unacceptable (safety, medical)
      Standard metric for Kaggle regression competitions
R²:   Use to compare models on same dataset
      Useful relative metric: 0.85 >> 0.70
MAPE: Use for business reporting when % errors matter
      AVOID when target can be near zero
""")