岭回归

目录

• 岭回归实现
  • 使用岭回归

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模型正则化 Regularization

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岭回归实现

import numpy as np
import matplotlib.pyplot as plt
 
np.random.seed(42)
x = np.random.uniform(-3.0, 3.0, size=100)
X = x.reshape(-1, 1)
y = 0.5 * x + 3 + np.random.normal(0, 1, size=100)

plt.scatter(x, y)
plt.show()

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from sklearn.pipeline import Pipeline
from sklearn.preprocessing import PolynomialFeatures
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LinearRegression

def PolynomialRegression(degree):
    return Pipeline([
        ("poly", PolynomialFeatures(degree=degree)),
        ("std_scaler", StandardScaler()),
        ("lin_reg", LinearRegression())
    ])
 
from sklearn.model_selection import train_test_split

np.random.seed(666)
X_train, X_test, y_train, y_test = train_test_split(X, y)
 
from sklearn.metrics import mean_squared_error

poly_reg = PolynomialRegression(degree=20)
poly_reg.fit(X_train, y_train)

y_poly_predict = poly_reg.predict(X_test)
mean_squared_error(y_test, y_poly_predict)
# 167.94010867293571

X_plot = np.linspace(-3, 3, 100).reshape(100, 1)
y_plot = poly_reg.predict(X_plot)

plt.scatter(x, y)
plt.plot(X_plot[:,0], y_plot, color='r')
plt.axis([-3, 3, 0, 6])
plt.show()

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def plot_model(model):
    X_plot = np.linspace(-3, 3, 100).reshape(100, 1)
    y_plot = model.predict(X_plot)

    plt.scatter(x, y)
    plt.plot(X_plot[:,0], y_plot, color='r')
    plt.axis([-3, 3, 0, 6])
    plt.show()

plot_model(poly_reg)

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使用岭回归

from sklearn.linear_model import Ridge

def RidgeRegression(degree, alpha):
    return Pipeline([
        ("poly", PolynomialFeatures(degree=degree)),
        ("std_scaler", StandardScaler()),
        ("ridge_reg", Ridge(alpha=alpha))
    ])

ridge1_reg = RidgeRegression(20, 0.0001)
ridge1_reg.fit(X_train, y_train)

y1_predict = ridge1_reg.predict(X_test)
mean_squared_error(y_test, y1_predict)
# 1.3233492754051845

plot_model(ridge1_reg)

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ridge2_reg = RidgeRegression(20, 1)
ridge2_reg.fit(X_train, y_train)

y2_predict = ridge2_reg.predict(X_test)
mean_squared_error(y_test, y2_predict)
# 1.1888759304218448

plot_model(ridge2_reg)

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ridge3_reg = RidgeRegression(20, 100)
ridge3_reg.fit(X_train, y_train)

y3_predict = ridge3_reg.predict(X_test)
mean_squared_error(y_test, y3_predict)
# 1.3196456113086197
 
plot_model(ridge3_reg)

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ridge4_reg = RidgeRegression(20, 10000000)
ridge4_reg.fit(X_train, y_train)

y4_predict = ridge4_reg.predict(X_test)
mean_squared_error(y_test, y4_predict)
# 1.8408455590998372
 
plot_model(ridge4_reg)

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