学习曲线(Learning Curve)

代码实现

代码实现

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(666)
x = np.random.uniform(-3.0, 3.0, size=100)
X = x.reshape(-1, 1)
y = 0.5 * x**2 + x + 2 + np.random.normal(0, 1, size=100)

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

使用学习曲线

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=10)
 
X_train.shape
# (75, 1)

from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error

train_score = []
test_score = []
for i in range(1, 76):
    lin_reg = LinearRegression()
    lin_reg.fit(X_train[:i], y_train[:i])  # 每次取前n个元素
    
    y_train_predict = lin_reg.predict(X_train[:i])
    train_score.append(mean_squared_error(y_train[:i], y_train_predict))
    
    y_test_predict = lin_reg.predict(X_test)
    test_score.append(mean_squared_error(y_test, y_test_predict))

# 绘制性能变化
plt.plot([i for i in range(1, 76)], np.sqrt(train_score), label="train") 
plt.plot([i for i in range(1, 76)], np.sqrt(test_score), label="test")
plt.legend() # 增加图例
plt.show()
# 训练数据及上误差主键升高；一开始快，后年变慢 稳定；
# 测试数据集上，误差从大变小。测试误差还是比训练高，可以理解。

函数提炼

def plot_learning_curve(algo, X_train, X_test, y_train, y_test):
    train_score = []
    test_score = []
    for i in range(1, len(X_train)+1):
        algo.fit(X_train[:i], y_train[:i])
    
        y_train_predict = algo.predict(X_train[:i])
        train_score.append(mean_squared_error(y_train[:i], y_train_predict))
    
        y_test_predict = algo.predict(X_test)
        test_score.append(mean_squared_error(y_test, y_test_predict))
        
    plt.plot([i for i in range(1, len(X_train)+1)], 
                               np.sqrt(train_score), label="train")
    plt.plot([i for i in range(1, len(X_train)+1)], 
                               np.sqrt(test_score), label="test")
    plt.legend()
    plt.axis([0, len(X_train)+1, 0, 4])
    plt.show()
    
plot_learning_curve(LinearRegression(), X_train, X_test, y_train, y_test)

使用多项式回归的学习曲线

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

def PolynomialRegression(degree):
    return Pipeline([
        ("poly", PolynomialFeatures(degree=degree)),
        ("std_scaler", StandardScaler()),
        ("lin_reg", LinearRegression())
    ])

poly2_reg = PolynomialRegression(degree=2)
plot_learning_curve(poly2_reg, X_train, X_test, y_train, y_test)

最佳

20阶的学习学习曲线

poly20_reg = PolynomialRegression(degree=20)
plot_learning_curve(poly20_reg, X_train, X_test, y_train, y_test)

在相对稳定的情况下，测试和训练数据的 RMSE 间距依然是比较大的。这种通常是过拟合的情况，泛化能力不够。