代碼實現
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()
使用學習曲線
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個元素
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))
# 繪制性能變化
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() # 增加圖例
plt.show()
# 訓練數據及上誤差主鍵升高；一開始快，后年變慢 穩定；
# 測試數據集上，誤差從大變小。測試誤差還是比訓練高，可以理解。
函數提煉
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)
使用多項式回歸的學習曲線
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階的學習學習曲線
poly20_reg = PolynomialRegression(degree=20)
plot_learning_curve(poly20_reg, X_train, X_test, y_train, y_test)
在相對穩定的情況下，測試和訓練數據的 RMSE 間距依然是比較大的。這種通常是過擬合的情況，泛化能力不夠。