Παλινδρόμηση Μερικών Ελαχίστων Τετραγώνων (PLS)

from __future__ import annotations

import japanize_matplotlib
import matplotlib.pyplot as plt
import numpy as np
from sklearn.cross_decomposition import PLSRegression
from sklearn.datasets import load_linnerud
from sklearn.model_selection import KFold, cross_val_score
from sklearn.pipeline import Pipeline
from sklearn.preprocessing import StandardScaler

def evaluate_pls_latent_factors(
    cv_splits: int = 5,
    xlabel: str = "Number of latent factors",
    ylabel: str = "CV MSE (lower is better)",
    label_best: str = "best={k}",
    title: str | None = None,
) -> dict[str, object]:
    """Cross-validate PLS regression for different latent factor counts.

    Args:
        cv_splits: Number of folds for cross-validation.
        xlabel: Label for the number-of-factors axis.
        ylabel: Label for the cross-validation error axis.
        label_best: Format string for the best-factor annotation.
        title: Optional plot title.

    Returns:
        Dictionary with the selected factor count, CV score, and loadings.
    """
    japanize_matplotlib.japanize()
    data = load_linnerud()
    X = data["data"]
    y = data["target"][:, 0]

    max_components = min(X.shape[1], 6)
    components = np.arange(1, max_components + 1)
    cv = KFold(n_splits=cv_splits, shuffle=True, random_state=0)

    scores = []
    pipelines = []
    for k in components:
        model = Pipeline([
            ("scale", StandardScaler()),
            ("pls", PLSRegression(n_components=int(k))),
        ])
        cv_score = cross_val_score(
            model,
            X,
            y,
            cv=cv,
            scoring="neg_mean_squared_error",
        ).mean()
        scores.append(cv_score)
        pipelines.append(model)

    scores_arr = np.array(scores)
    best_idx = int(np.argmax(scores_arr))
    best_k = int(components[best_idx])
    best_mse = float(-scores_arr[best_idx])

    best_model = pipelines[best_idx].fit(X, y)
    x_loadings = best_model["pls"].x_loadings_
    y_loadings = best_model["pls"].y_loadings_

    fig, ax = plt.subplots(figsize=(8, 4))
    ax.plot(components, -scores_arr, marker="o")
    ax.axvline(best_k, color="red", linestyle="--", label=label_best.format(k=best_k))
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)
    if title:
        ax.set_title(title)
    ax.legend()
    fig.tight_layout()
    plt.show()

    return {
        "best_k": best_k,
        "best_mse": best_mse,
        "x_loadings": x_loadings,
        "y_loadings": y_loadings,
    }

metrics = evaluate_pls_latent_factors()
print(f"Best number of latent factors: {metrics['best_k']}")
print(f"Best CV MSE: {metrics['best_mse']:.3f}")
print("X loadings:
", metrics['x_loadings'])
print("Y loadings:
", metrics['y_loadings'])