Polynomial Regression Model

Posted on 2025/04/19, 3:03 PM By admin22

3つの変数から導かれる結果について、多項式回帰モデルを使って見える化をしてみました。
target_functionは対象の任意の関数とします。

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib import animation
from mpl_toolkits.mplot3d import Axes3D
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
from sklearn.model_selection import train_test_split

# --- 任意の非線形関数 ---
def target_function(x1, x2, x3):
    #return 2 * x1**2 - 3 * x2 + 1.5 * x3**2 + 4 * x1 * x3 + np.random.normal(0, 2, size=x1.shape)
    return 2 * x1**3 - 3 * x2**3 + 1.5 * x3 + 4 * x1 * x3**2 + 2000*np.random.rand(x1.shape[0]) - 1000

# --- データ生成 ---
np.random.seed(42)
n_samples = 200
x1 = np.random.uniform(0, 10, n_samples)
x2 = np.random.uniform(0, 10, n_samples)
x3 = np.random.uniform(0, 10, n_samples)
y = target_function(x1, x2, x3)


df = pd.DataFrame({'x1': x1, 'x2': x2, 'x3': x3, 'y': y})
X = df[['x1', 'x2', 'x3']]
y = df['y']

# --- 特徴量変換と学習 ---
poly = PolynomialFeatures(degree=3, include_bias=False)
X_poly = poly.fit_transform(X)

X_train, X_test, y_train, y_test = train_test_split(X_poly, y, test_size=0.2, random_state=42)
model = LinearRegression().fit(X_train, y_train)

# --- 評価 ---
y_pred = model.predict(X_test)
mse = mean_squared_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)


print(f"x1の範囲: {x1.min():.2f} 〜 {x1.max():.2f}")
print(f"x1の標準偏差: {x1.std():.2f}")
print(f"x2の範囲: {x2.min():.2f} 〜 {x2.max():.2f}")
print(f"x2の標準偏差: {x2.std():.2f}")
print(f"x3の範囲: {x3.min():.2f} 〜 {x3.max():.2f}")
print(f"x3の標準偏差: {x3.std():.2f}")
print(f"yの範囲: {y.min():.2f} 〜 {y.max():.2f}")
print(f"yの標準偏差: {y.std():.2f}")

print(f"📊 モデル評価")
print(f"  - MSE: {mse:.3f}")
print(f"  - R² : {r2:.3f}")

# --- 3D アニメーション ---
fig = plt.figure(figsize=(10, 7))
ax = fig.add_subplot(111, projection='3d')

grid_x1, grid_x2 = np.meshgrid(np.linspace(0, 10, 30), np.linspace(0, 10, 30))

def update(frame):
    ax.clear()
    fixed_x3 = frame
    grid_x3 = np.full_like(grid_x1, fixed_x3)

    # グリッド点 → DataFrameに変換（列名つけるのが重要）
    grid_points = np.c_[grid_x1.ravel(), grid_x2.ravel(), grid_x3.ravel()]
    grid_df = pd.DataFrame(grid_points, columns=['x1', 'x2', 'x3'])

    # モデル予測
    grid_poly = poly.transform(grid_df)
    grid_y = model.predict(grid_poly).reshape(grid_x1.shape)

    # 回帰面
    ax.plot_surface(grid_x1, grid_x2, grid_y, color='orange', alpha=0.6)

    # 実データ（x3 ≈ frame）
    mask = np.isclose(df['x3'], fixed_x3, atol=0.5)
    ax.scatter(df.loc[mask, 'x1'], df.loc[mask, 'x2'], df.loc[mask, 'y'],
               color='blue', alpha=0.5)

    # 軸・表示
    ax.set_xlabel('x1')
    ax.set_ylabel('x2')
    ax.set_zlabel('y')
    ax.set_title(f'Polynomial Regression Surface (x3={fixed_x3:.1f})')
    ax.set_zlim(y.min(), y.max())

ani = animation.FuncAnimation(fig, update, frames=np.linspace(0, 9, 10), interval=1000)
plt.show()

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

from matplotlib import animation

from mpl_toolkits.mplot3d import Axes3D

from sklearn.preprocessing import PolynomialFeatures

from sklearn.linear_model import LinearRegression

from sklearn.metrics import mean_squared_error, r2_score

from sklearn.model_selection import train_test_split

# --- 任意の非線形関数 ---

def target_function(x1, x2, x3):

#return 2 * x1**2 - 3 * x2 + 1.5 * x3**2 + 4 * x1 * x3 + np.random.normal(0, 2, size=x1.shape)

return 2 * x1**3 - 3 * x2**3 + 1.5 * x3 + 4 * x1 * x3**2 + 2000*np.random.rand(x1.shape[0]) - 1000

# --- データ生成 ---

np.random.seed(42)

n_samples = 200

x1 = np.random.uniform(0, 10, n_samples)

x2 = np.random.uniform(0, 10, n_samples)

x3 = np.random.uniform(0, 10, n_samples)

y = target_function(x1, x2, x3)

df = pd.DataFrame({'x1': x1, 'x2': x2, 'x3': x3, 'y': y})

X = df[['x1', 'x2', 'x3']]

y = df['y']

# --- 特徴量変換と学習 ---

poly = PolynomialFeatures(degree=3, include_bias=False)

X_poly = poly.fit_transform(X)

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

model = LinearRegression().fit(X_train, y_train)

# --- 評価 ---

y_pred = model.predict(X_test)

mse = mean_squared_error(y_test, y_pred)

r2 = r2_score(y_test, y_pred)

print(f"x1の範囲: {x1.min():.2f} 〜 {x1.max():.2f}")

print(f"x1の標準偏差: {x1.std():.2f}")

print(f"x2の範囲: {x2.min():.2f} 〜 {x2.max():.2f}")

print(f"x2の標準偏差: {x2.std():.2f}")

print(f"x3の範囲: {x3.min():.2f} 〜 {x3.max():.2f}")

print(f"x3の標準偏差: {x3.std():.2f}")

print(f"yの範囲: {y.min():.2f} 〜 {y.max():.2f}")

print(f"yの標準偏差: {y.std():.2f}")

print(f"📊 モデル評価")

print(f" - MSE: {mse:.3f}")

print(f" - R² : {r2:.3f}")

# --- 3D アニメーション ---

fig = plt.figure(figsize=(10, 7))

ax = fig.add_subplot(111, projection='3d')

grid_x1, grid_x2 = np.meshgrid(np.linspace(0, 10, 30), np.linspace(0, 10, 30))

def update(frame):

ax.clear()

fixed_x3 = frame

grid_x3 = np.full_like(grid_x1, fixed_x3)

# グリッド点 → DataFrameに変換（列名つけるのが重要）

grid_points = np.c_[grid_x1.ravel(), grid_x2.ravel(), grid_x3.ravel()]

grid_df = pd.DataFrame(grid_points, columns=['x1', 'x2', 'x3'])

# モデル予測

grid_poly = poly.transform(grid_df)

grid_y = model.predict(grid_poly).reshape(grid_x1.shape)

# 回帰面

ax.plot_surface(grid_x1, grid_x2, grid_y, color='orange', alpha=0.6)

# 実データ（x3 ≈ frame）

mask = np.isclose(df['x3'], fixed_x3, atol=0.5)

ax.scatter(df.loc[mask, 'x1'], df.loc[mask, 'x2'], df.loc[mask, 'y'],

color='blue', alpha=0.5)

# 軸・表示

ax.set_xlabel('x1')

ax.set_ylabel('x2')

ax.set_zlabel('y')

ax.set_title(f'Polynomial Regression Surface (x3={fixed_x3:.1f})')

ax.set_zlim(y.min(), y.max())

ani = animation.FuncAnimation(fig, update, frames=np.linspace(0, 9, 10), interval=1000)

plt.show()

3次元では、2つの変数までしか扱えませんので、x3を固定化しますが、アニメーションによりx3を動かしてみました。

PolynomialFeaturesのdegreeを1にした場合

以上、ChatGPTとの対話から作成しました。
まずシンプルな動作できる形をAIで作っておいて、あとは手作業で作り込んでいくという、こういうコーディングの仕方は、本当に便利です。

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