文章目錄

• • 一、 觀察波士頓房價數(shù)據(jù)并加載數(shù)據(jù)集
  • • 1、加載數(shù)據(jù)集
  • 二、 特征選擇
  • 三、 模型選擇
  • 四、 模型訓(xùn)練和測試
  • • 1、 訓(xùn)練模型
    • 2、打印線性方程參數(shù)
    • 3、模型預(yù)測
    • 4、 計算mae、mse
    • 5、 畫出學(xué)習(xí)曲線
  • 五、 模型性能評估和優(yōu)化
  • • 1、 模型優(yōu)化，考慮用二項式和三項式優(yōu)化
    • 2、 劃分?jǐn)?shù)據(jù)集函數(shù)
    • 3、定義MAE、MSE函數(shù)
    • 4、定義多項式模型函數(shù)
    • 5、 訓(xùn)練模型
    • 6、 定義畫出學(xué)習(xí)曲線的函數(shù)
    • 7、定義1、2、3次多項式
    • 8、劃分?jǐn)?shù)據(jù)集
    • 9、訓(xùn)練模型，并打印train score
    • 10、畫出學(xué)習(xí)曲線
  • 六、 結(jié)論與分析

一、 觀察波士頓房價數(shù)據(jù)并加載數(shù)據(jù)集

1、加載數(shù)據(jù)集

from sklearn.datasets import load_boston import pandas as pd import matplotlib.pyplot as plt import numpy as npboston=load_boston() df=pd.DataFrame(boston.data,columns=boston.feature_names) df['target']=boston.target

數(shù)據(jù)集共506條，包含有13個與房價相關(guān)的特征，分別是：

name釋義

CRIM	城鎮(zhèn)人均犯罪率
ZN	住宅用地所占比例
INDUS	城鎮(zhèn)中非住宅用地所占比例
CHAS	虛擬變量,用于回歸分析
NOX	環(huán)保指數(shù)
RM	每棟住宅的房間數(shù)
AGE	1940 年以前建成的自住單位的比例
DIS	距離 5 個波士頓的就業(yè)中心的加權(quán)距離
RAD	距離高速公路的便利指數(shù)
TAX	每一萬美元的不動產(chǎn)稅率
PTRATIO	城鎮(zhèn)中的教師學(xué)生比例
B	城鎮(zhèn)中的黑人比例
LSTAT	地區(qū)中有多少房東屬于低收入人群

2、查看數(shù)據(jù)項

#查看數(shù)據(jù)項 df.head()

二、 特征選擇

1、 畫出各數(shù)據(jù)項和房價的散點圖
2、 根據(jù)散點圖粗略選擇CRIM, RM, LSTAT三個特征值

features=df[['RM','CRIM', 'LSTAT']] target=df['target']

三、 模型選擇

利用多元線性回歸模型，其中自變量為數(shù)據(jù)集中的 feature_names 的維度（13維度），因變量為數(shù)據(jù)集中的 target 維度（房價）

#數(shù)據(jù)集劃分 split_num=int(len(features)*0.8) X_train=features[:split_num] Y_train=target[:split_num] X_test=features[split_num:] Y_test=target[split_num:]

設(shè)置標(biāo)簽字段，切分?jǐn)?shù)據(jù)集：訓(xùn)練集80%，測試集20%

四、 模型訓(xùn)練和測試

1、 訓(xùn)練模型

split_num=int(len(features)*0.8) X_train=features[:split_num] Y_train=target[:split_num] X_test=features[split_num:] Y_test=target[split_num:]

2、打印線性方程參數(shù)

print(model.coef_,model.intercept_)

3、模型預(yù)測

preds=model.predict(X_test)

4、 計算mae、mse

def mae_value(y_true,y_pred):n=len(y_true)mae=sum(np.abs(y_true-y_pred))/n return maedef mse_value(y_true,y_pred):n=len(y_true)mse=sum(np.square(y_true-y_pred))/n return msemae=mae_value(Y_test.values,preds) mse=mse_value(Y_test.values,preds) print("MAE",mae) print("MSE",mse)

5、 畫出學(xué)習(xí)曲線

from sklearn.model_selection import learning_curve from sklearn.model_selection import ShuffleSplit import matplotlib.pyplot as plt import numpy as np def plot_learning_curve(plt,estimator,title,X,y,ylim=None,cv=None,n_jobs=1,train_sizes=np.linspace(.1,1.0,5)):plt.title(title)if ylim is not None:plt.ylim(ylim)plt.xlabel("Training examples")plt.ylabel("Score")train_sizes,train_scores,test_scores=learning_curve(estimator,X,y,cv=cv,n_jobs=n_jobs,train_sizes=train_sizes)train_scores_mean=np.mean(train_scores,axis=1)train_scores_std=np.std(train_scores,axis=1)test_scores_mean=np.mean(test_scores,axis=1)test_scores_std=np.std(test_scores,axis=1)plt.grid()plt.fill_between(train_sizes,train_scores_mean-train_scores_std,train_scores_mean+train_scores_std,alpha=0.1,color="r")plt.fill_between(train_sizes,test_scores_mean-test_scores_std,test_scores_mean+test_scores_std,alpha=0.1,color="g")plt.plot(train_sizes,train_scores_mean,'o--',color="r",label="Training scores")plt.plot(train_sizes,test_scores_mean,'o-',color="g",label="Cross-validation score")plt.legend(loc="best")return pltcv=ShuffleSplit(n_splits=10,test_size=0.2,random_state=0) plt.figure(figsize=(10,6)) plot_learning_curve(plt,model,"Learn Curve for LinearRegression",features,target,ylim=None,cv=cv) plt.show()

五、 模型性能評估和優(yōu)化

1、 模型優(yōu)化，考慮用二項式和三項式優(yōu)化

import matplotlib.pyplot as plt import numpy as np from sklearn.datasets import load_boston from sklearn.model_selection import train_test_split from sklearn.linear_model import LinearRegression from sklearn.preprocessing import PolynomialFeatures from sklearn.pipeline import Pipeline from sklearn.model_selection import ShuffleSplit from sklearn.model_selection import learning_curve

2、 劃分?jǐn)?shù)據(jù)集函數(shù)

def split_data():boston = load_boston()x = boston.datay = boston.targetprint(boston.feature_names)x_train, x_test, y_train, y_test = train_test_split(x, y, test_size = 0.2,random_state=2)return (x, y, x_train, x_test, y_train, y_test)

3、定義MAE、MSE函數(shù)

def mae_value(y_true,y_pred):n=len(y_true)mae=sum(np.abs(y_true-y_pred))/nreturn maedef mse_value(y_true,y_pred):n=len(y_true)mse=sum(np.square(y_true-y_pred))/n return mse

4、定義多項式模型函數(shù)

def polynomial_regression(degree=1):polynomial_features = PolynomialFeatures(degree=degree, include_bias=False)#模型開啟數(shù)據(jù)歸一化linear_regression_model = LinearRegression(normalize=True)model = Pipeline([("polynomial_features", polynomial_features),("linear_regression", linear_regression_model)])return model

5、 訓(xùn)練模型

def train_model(x_train, x_test, y_train, y_test, degrees): res = []for degree in degrees:model = polynomial_regression(degree)model.fit(x_train, y_train)train_score = model.score(x_train, y_train)test_score = model.score(x_test, y_test)res.append({"model": model, "degree": degree, "train_score": train_score, "test_score": test_score})preds=model.predict(x_test)mae=mae_value(y_test,preds)mse=mse_value(y_test,preds)print(" degree: " ,degree, " MAE:",mae," MSE",mse)for r in res:print("degree: {}; train score: {}; test_score: {}".format(r["degree"], r["train_score"], r["test_score"]))return res

6、 定義畫出學(xué)習(xí)曲線的函數(shù)

def plot_learning_curve(plt,estimator,title,X,y,ylim=None,cv=None,n_jobs=1,train_sizes=np.linspace(.1,1.0,5)):plt.title(title)if ylim is not None:plt.ylim(ylim)plt.xlabel("Training examples")plt.ylabel("Score")train_sizes,train_scores,test_scores=learning_curve(estimator,X,y,cv=cv,n_jobs=n_jobs,train_sizes=train_sizes)train_scores_mean=np.mean(train_scores,axis=1)train_scores_std=np.std(train_scores,axis=1)test_scores_mean=np.mean(test_scores,axis=1)test_scores_std=np.std(test_scores,axis=1)plt.grid()plt.fill_between(train_sizes,train_scores_mean-train_scores_std,train_scores_mean+train_scores_std,alpha=0.1,color="r")plt.fill_between(train_sizes,test_scores_mean-test_scores_std,test_scores_mean+test_scores_std,alpha=0.1,color="g")plt.plot(train_sizes,train_scores_mean,'o--',color="r",label="Training scores")plt.plot(train_sizes,test_scores_mean,'o-',color="g",label="Cross-validation score")plt.legend(loc="best")return plt

7、定義1、2、3次多項式

degrees = [1,2,3]

8、劃分?jǐn)?shù)據(jù)集

x, y, x_train, x_test, y_train, y_test = split_data()

9、訓(xùn)練模型，并打印train score

res = train_model(x_train, x_test, y_train, y_test, degrees)

10、畫出學(xué)習(xí)曲線

cv = ShuffleSplit(n_splits=10, test_size=0.2, random_state=0) plt.figure(figsize=(10, 6))for index, data in enumerate(res):plot_learning_curve(plt, data["model"], "degree %d"%data["degree"], x, y, cv=cv) plt.show()

六、 結(jié)論與分析

通過對波士頓房價數(shù)據(jù)的分析預(yù)測練習(xí)，運用多元回歸模型（一共十三個維度），前期訓(xùn)練量不足導(dǎo)致擬合程度不理想。經(jīng)過模型的參數(shù)優(yōu)化，采用了全部特征值，結(jié)果顯示一次多項式訓(xùn)練準(zhǔn)確度72%，測試準(zhǔn)確度76%。二次多項式訓(xùn)練準(zhǔn)確度92%，測試準(zhǔn)確度89%，mae=2.36, mse=8.67。綜上所述，采用二次多項式回歸方法優(yōu)化效果較好。

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