【初心者向け】ディープラーニングと回帰分析、何が違う？グラフでわかりやすく解説

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score
from sklearn.model_selection import train_test_split
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense

# ---------------------------------------------
# データ生成関数（1次 or 2次）
# ---------------------------------------------
def generate_data(func='linear', n_samples=1000, noise_std=5.0):
    np.random.seed(0)
    X = np.random.uniform(-10, 10, size=(n_samples, 1))
    
    if func == 'linear':
        y = 3 * X[:, 0] + 5 + np.random.normal(0, noise_std, n_samples)
    elif func == 'quadratic':
        y = 0.5 * X[:, 0]**2 - 2 * X[:, 0] + 3 + np.random.normal(0, noise_std, n_samples)
        y = -y + 80  # 上に凸で視覚的に分かりやすく
    else:
        raise ValueError("func must be 'linear' or 'quadratic'")
    
    return X, y

# ---------------------------------------------
# 重回帰モデルで学習
# ---------------------------------------------
def run_linear_regression(X_train, y_train, X_test):
    model = LinearRegression()
    model.fit(X_train, y_train)
    y_pred = model.predict(X_test)
    return y_pred

# ---------------------------------------------
# ディープラーニングモデルで学習
# ---------------------------------------------
def run_deep_learning(X_train, y_train, X_test):
    model = Sequential([
        Dense(64, activation='relu', input_shape=(1,)),
        Dense(64, activation='relu'),
        Dense(1)
    ])
    model.compile(optimizer='adam', loss='mse')
    model.fit(X_train, y_train, epochs=100, verbose=0)
    y_pred = model.predict(X_test).flatten()
    return y_pred

# ---------------------------------------------
# 評価とプロット（予測値 + 残差）
# ---------------------------------------------
def evaluate_and_plot(X_test, y_test, y_pred_lr, y_pred_dl, title):
    print(f"\n--- {title} ---")
    print("Linear Regression R²:", r2_score(y_test, y_pred_lr))
    print("Deep Learning     R²:", r2_score(y_test, y_pred_dl))

    # 1. 予測結果の散布図
    plt.figure(figsize=(12, 5))
    plt.subplot(1, 2, 1)
    plt.scatter(X_test, y_test, label='True', color='black', s=20)
    plt.scatter(X_test, y_pred_lr, label='Linear Regression', color='blue', alpha=0.6)
    plt.scatter(X_test, y_pred_dl, label='Deep Learning', color='red', alpha=0.6)
    plt.title(f"{title}（予測散布図）")
    plt.xlabel('X')
    plt.ylabel('y')
    plt.legend()
    plt.grid(True)

    # 2. 残差プロット
    residuals_lr = y_test - y_pred_lr
    residuals_dl = y_test - y_pred_dl

    plt.subplot(1, 2, 2)
    plt.scatter(y_pred_lr, residuals_lr, color='blue', alpha=0.6, label='Linear Regression')
    plt.scatter(y_pred_dl, residuals_dl, color='red', alpha=0.6, label='Deep Learning')
    plt.axhline(0, color='gray', linestyle='--')
    plt.title(f"{title}（残差プロット）")
    plt.xlabel('予測値')
    plt.ylabel('残差（実測値 - 予測値）')
    plt.legend()
    plt.grid(True)

    plt.tight_layout()
    plt.show()

# ---------------------------------------------
# メイン実行部（1次関数 & 2次関数）
# ---------------------------------------------
for func_type in ['linear', 'quadratic']:
    X, y = generate_data(func=func_type)
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

    y_pred_lr = run_linear_regression(X_train, y_train, X_test)
    y_pred_dl = run_deep_learning(X_train, y_train, X_test)

    evaluate_and_plot(X_test, y_test, y_pred_lr, y_pred_dl, f"関数タイプ: {func_type}")