隨書程式碼，閱讀筆記。

• 線性迴歸擬合正弦函式

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

n_dots = 200

X = np.linspace(-2 * np.pi, 2 * np.pi, n_dots)
Y = np.sin(X) + 0.2 * np.random.rand(n_dots) - 0.1
X = X.reshape(-1, 1)
Y = Y.reshape(-1, 1);


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

def polynomial_model(degree=1):
    polynomial_features = PolynomialFeatures(degree=degree,
                                             include_bias=False)
    linear_regression = LinearRegression(normalize=True)
    pipeline = Pipeline([("polynomial_features", polynomial_features),
                         ("linear_regression", linear_regression)])
    return pipeline


from sklearn.metrics import mean_squared_error

degrees = [2, 3, 5, 10]
results = []
for d in degrees:
    model = polynomial_model(degree=d)
    model.fit(X, Y)
    train_score = model.score(X, Y)
    mse = mean_squared_error(Y, model.predict(X))
    results.append({"model": model, "degree": d, "score": train_score, "mse": mse})
for r in results:
    print("degree: {}; train score: {}; mean squared error: {}".format(r["degree"], r["score"], r["mse"]))

:
from matplotlib.figure import SubplotParams

plt.figure(figsize=(12, 6), dpi=200, subplotpars=SubplotParams(hspace=0.3))
for i, r in enumerate(results):
    fig = plt.subplot(2, 2, i+1)
    plt.xlim(-8, 8)
    plt.title("LinearRegression degree={}".format(r["degree"]))
    plt.scatter(X, Y, s=5, c='b', alpha=0.5)
    plt.plot(X, r["model"].predict(X), 'r-')
 

• 預測房價

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

from sklearn.datasets import load_boston

boston = load_boston()
X = boston.data
y = boston.target
X.shape

boston.feature_names


from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=3)

import time
from sklearn.linear_model import LinearRegression

model = LinearRegression()

#model = LinearRegression(normalize=True) #歸一化，能加快演算法收斂速度，優化演算法訓練效率，無法提升演算法準確性

start = time.clock()
model.fit(X_train, y_train)

train_score = model.score(X_train, y_train)
cv_score = model.score(X_test, y_test)
print('elaspe: {0:.6f}; train_score: {1:0.6f}; cv_score: {2:.6f}'.format(time.clock()-start, train_score, cv_score))

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

def polynomial_model(degree=1):
    polynomial_features = PolynomialFeatures(degree=degree,
                                             include_bias=False)
    linear_regression = LinearRegression(normalize=True)
    pipeline = Pipeline([("polynomial_features", polynomial_features),
                         ("linear_regression", linear_regression)])
    return pipeline

model = polynomial_model(degree=2)

start = time.clock()
model.fit(X_train, y_train)

train_score = model.score(X_train, y_train)
cv_score = model.score(X_test, y_test)
print('elaspe: {0:.6f}; train_score: {1:0.6f}; cv_score: {2:.6f}'.format(time.clock()-start, train_score, cv_score))

#elaspe: 0.016412; train_score: 0.930547; cv_score: 0.860465

#畫出學習曲線
from common.utils import plot_learning_curve
from sklearn.model_selection import ShuffleSplit

cv = ShuffleSplit(n_splits=10, test_size=0.2, random_state=0)
plt.figure(figsize=(18, 4), dpi=200)
title = 'Learning Curves (degree={0})'
degrees = [1, 2, 3]

start = time.clock()
plt.figure(figsize=(18, 4), dpi=200)
for i in range(len(degrees)):
    plt.subplot(1, 3, i + 1)
    plot_learning_curve(plt, polynomial_model(degrees[i]), title.format(degrees[i]), X, y, ylim=(0.01, 1.01), cv=cv)

print('elaspe: {0:.6f}'.format(time.clock()-start))
 

多項式的階數對訓練模型效能影響很大，階數低，容易欠擬合，階數高，容易過擬合。