机器学习08DAY

线性回归

波士顿房价预测案例#

步骤

• 导入数据
• 数据分割
• 数据标准化
• 正规方程预测
• 梯度下降预测

# 导入模块
import pandas as pd # 导入数据
from sklearn.model_selection import train_test_split # 数据分割
from sklearn.preprocessing import StandardScaler # 数据标准化
from sklearn.linear_model import LinearRegression, SGDRegressor, Ridge # 正规方程，梯度下降, 岭回归
from sklearn.metrics import mean_squared_error # 均方差
import numpy as np

# 读取Boston房价数据
boston = pd.read_csv("./boston_house_prices.csv")
y = boston["MEDV"] # MEDV为离散型目标值
x = boston.drop(["MEDV"],axis=1) # 其他数据为特征值

x

	CRIM	ZN	INDUS	CHAS	NOX	RM	AGE	DIS	RAD	TAX	PTRATIO	B	LSTAT
0	0.00632	18.0	2.31	0	0.538	6.575	65.2	4.0900	1	296	15.3	396.90	4.98
1	0.02731	0.0	7.07	0	0.469	6.421	78.9	4.9671	2	242	17.8	396.90	9.14
2	0.02729	0.0	7.07	0	0.469	7.185	61.1	4.9671	2	242	17.8	392.83	4.03
3	0.03237	0.0	2.18	0	0.458	6.998	45.8	6.0622	3	222	18.7	394.63	2.94
4	0.06905	0.0	2.18	0	0.458	7.147	54.2	6.0622	3	222	18.7	396.90	5.33
...	...	...	...	...	...	...	...	...	...	...	...	...	...
501	0.06263	0.0	11.93	0	0.573	6.593	69.1	2.4786	1	273	21.0	391.99	9.67
502	0.04527	0.0	11.93	0	0.573	6.120	76.7	2.2875	1	273	21.0	396.90	9.08
503	0.06076	0.0	11.93	0	0.573	6.976	91.0	2.1675	1	273	21.0	396.90	5.64
504	0.10959	0.0	11.93	0	0.573	6.794	89.3	2.3889	1	273	21.0	393.45	6.48
505	0.04741	0.0	11.93	0	0.573	6.030	80.8	2.5050	1	273	21.0	396.90	7.88

506 rows × 13 columns

# 数据标准化需要传入二维数组，所以需要改变目标值的形状
y = np.array(y).reshape(-1, 1)

# 划分测试集和训练集
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.25)

# 特征值标准化
std_x = StandardScaler().fit(x_train)
x_train = std_x.transform(x_train)
x_test = std_x.transform(x_test)

# 因为特征值标准化后，传入模型的系数会增大，所以目标值也需要进行标准化
std_y = StandardScaler().fit(y_train)
y_train = std_y.transform(y_train)
y_test = std_y.transform(y_test)

# 实例化线性回归
lr = LinearRegression()
# 传入测试集训练模型
lr.fit(x_train,y_train)

LinearRegression()

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# 查看线性回归的回归系数
lr.coef_

array([[-0.11432612,  0.12922939,  0.05168773,  0.0306429 , -0.27800333,
         0.26465189,  0.02894241, -0.34962992,  0.31569604, -0.24717234,
        -0.26784233,  0.11032066, -0.41354896]])

# 线性回归预测测试集的目标值，std_y.inverse_transform：返回标准化之前的值（反标准化）
y_lr_predict = std_y.inverse_transform(lr.predict(x_test))
y_lr_predict

array([[16.88302519],
       [25.67464426],
       [24.11685261],
       [23.56287231],
       [33.21442377],
       [17.44428398],
       [25.08538719],
       [14.36188824],
       [23.8507796 ],
       [33.90875038],
       [30.19255243],
       [13.30811675],
       [28.60383216],
       [34.6094617 ],
       [27.32666762],
       [24.88310221],
       [21.97377504],
       [14.36080511],
       [15.19834144],
       [18.91688837],
       [14.39284881],
       [37.4279415 ],
       [28.85628069],
       [23.47343089],
       [30.65979144],
       [20.77177982],
       [21.29899429],
       [13.81410752],
       [24.36591359],
       [26.91067836],
       [19.39456288],
       [32.1620506 ],
       [19.55908532],
       [24.32677646],
       [31.64841534],
       [30.24445789],
       [32.6601561 ],
       [25.45770231],
       [24.36812628],
       [24.89892187],
       [39.51204317],
       [18.25845589],
       [30.78050699],
       [32.2023306 ],
       [43.40712056],
       [25.5830554 ],
       [24.18175285],
       [22.22948918],
       [16.30284868],
       [27.20443307],
       [ 4.3558633 ],
       [18.24971547],
       [17.84402513],
       [14.26170574],
       [13.64455453],
       [34.67825232],
       [ 8.26805278],
       [23.65092602],
       [ 6.3965518 ],
       [21.25451713],
       [15.71560149],
       [29.29210802],
       [29.4266973 ],
       [19.91658528],
       [14.95841515],
       [20.88449625],
       [28.59263417],
       [23.78937845],
       [23.4489951 ],
       [11.0440392 ],
       [19.4491492 ],
       [15.48416226],
       [18.68260651],
       [24.20199734],
       [15.78191346],
       [14.11243619],
       [22.94901405],
       [24.02549373],
       [21.11185284],
       [28.57665473],
       [ 7.45548609],
       [22.77052456],
       [ 3.44149312],
       [15.93067248],
       [25.72200382],
       [22.56825235],
       [32.70873719],
       [17.86289514],
       [24.49691931],
       [35.25395986],
       [26.98360999],
       [17.51000169],
       [28.08531514],
       [21.15268973],
       [24.73138251],
       [-4.82364972],
       [21.34031184],
       [21.89560028],
       [16.35765837],
       [35.32764197],
       [40.95997005],
       [23.59853443],
       [19.92593809],
       [34.43871021],
       [21.37340243],
       [20.48191389],
       [23.77537201],
       [28.67150943],
       [40.73850694],
       [29.38542779],
       [21.25032737],
       [22.15530128],
       [31.1447006 ],
       [17.18008197],
       [38.09276107],
       [18.17714902],
       [26.01850231],
       [13.73181577],
       [12.47399654],
       [27.01659936],
       [18.62962667],
       [11.26915964],
       [19.48824649],
       [23.64510406],
       [18.88328087],
       [19.49037977],
       [13.58238162]])

# 线性回归预测的均方差（损失值）
loss_lr = mean_squared_error(std_y.inverse_transform(y_test), y_lr_predict)
loss_lr

27.89401984711536

# 实例化梯度下降回归
sgd = SGDRegressor()
sgd.fit(x_train, y_train)

D:\DeveloperTools\Anaconda\lib\site-packages\sklearn\utils\validation.py:1143: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  y = column_or_1d(y, warn=True)

SGDRegressor()

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# 查看梯度下降回归的回归系数
sgd.coef_

array([-0.09761234,  0.08895746, -0.02421963,  0.02879482, -0.17976106,
        0.30861884, -0.00250273, -0.27224473,  0.12435245, -0.0780263 ,
       -0.24480836,  0.12012805, -0.38888841])

# 梯度下降回归预测测试集的目标值，std_y.inverse_transform：返回标准化之前的值（反标准化）
y_sgd_predict = std_y.inverse_transform(sgd.predict(x_test).reshape(-1,1))
y_sgd_predict

array([[15.21420286],
       [24.63693863],
       [24.39828101],
       [24.13982716],
       [32.78620978],
       [17.93179618],
       [26.15279053],
       [14.48966421],
       [23.47566531],
       [33.17239509],
       [31.84452891],
       [12.45562282],
       [27.95300787],
       [33.80241039],
       [28.49956651],
       [24.66480492],
       [22.36941513],
       [12.77314567],
       [16.19679874],
       [19.55497851],
       [16.56475828],
       [37.33119072],
       [28.7775393 ],
       [20.96986273],
       [30.61621249],
       [21.02209026],
       [21.7295418 ],
       [12.81210827],
       [24.5110437 ],
       [26.43938704],
       [18.35264658],
       [32.65009183],
       [18.43526582],
       [23.00618081],
       [31.7400822 ],
       [29.04743561],
       [33.05208407],
       [25.74448792],
       [24.50083552],
       [25.60223044],
       [39.54513459],
       [17.1185942 ],
       [31.03740088],
       [31.08938082],
       [43.05539907],
       [25.73953331],
       [24.94663261],
       [22.54125585],
       [18.28413619],
       [26.10355346],
       [ 6.00742562],
       [17.91294014],
       [18.30811745],
       [12.44053594],
       [12.80928627],
       [35.3744289 ],
       [ 9.09787342],
       [22.93659674],
       [ 5.43064498],
       [21.74836536],
       [14.35146387],
       [29.01003788],
       [29.08635743],
       [22.73088123],
       [14.63525207],
       [21.85792442],
       [27.65781677],
       [23.792957  ],
       [24.6814747 ],
       [10.92976509],
       [19.83990001],
       [15.96966791],
       [18.14900105],
       [25.20832651],
       [13.27422495],
       [14.30232772],
       [23.11242467],
       [25.77201334],
       [19.68444307],
       [28.57611678],
       [ 7.63364889],
       [20.4696819 ],
       [ 2.27690801],
       [16.55235057],
       [25.58622675],
       [22.77961526],
       [32.47346299],
       [17.77241159],
       [22.97811939],
       [36.08937688],
       [26.73491284],
       [18.29474336],
       [29.46454709],
       [21.71750293],
       [26.04970043],
       [-5.49919448],
       [22.22155065],
       [22.98441588],
       [15.12536374],
       [35.73982924],
       [40.87874356],
       [23.690842  ],
       [20.5993433 ],
       [35.69123855],
       [20.68804356],
       [20.94190843],
       [26.02227126],
       [31.17410177],
       [40.95630421],
       [29.90544672],
       [23.50763821],
       [22.27432439],
       [29.64014839],
       [16.78407484],
       [38.12893576],
       [17.69781499],
       [25.22891716],
       [14.21875615],
       [12.55974345],
       [26.99891265],
       [17.65595579],
       [ 8.4159419 ],
       [19.90142312],
       [22.80759632],
       [19.16843753],
       [19.42995139],
       [14.04081021]])

# 梯度下降回归预测的均方差（损失值）
loss_sgd = mean_squared_error(std_y.inverse_transform(y_test), y_sgd_predict)
loss_sgd

28.05592202385498

# 实例化岭回归 param:alpha(正则化力度)
rd = Ridge(alpha=1.0)

# 传入训练集 训练模型
rd.fit(x_train,y_train)

Ridge()

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# 查看岭回归的回归系数
rd.coef_

array([[-0.11307323,  0.12670886,  0.0472335 ,  0.03097279, -0.27277927,
         0.26649452,  0.02738887, -0.34543899,  0.30352311, -0.23553989,
        -0.26624461,  0.11041044, -0.4112231 ]])

# 岭回归预测测试集的目标值，std_y.inverse_transform：返回标准化之前的值（反标准化）
y_rd_predict = std_y.inverse_transform(rd.predict(x_test))
y_rd_predict

array([[16.81586993],
       [25.62225283],
       [24.13239652],
       [23.60178301],
       [33.17482664],
       [17.47603707],
       [25.12448624],
       [14.3927178 ],
       [23.82242142],
       [33.83569284],
       [30.25910195],
       [13.28992719],
       [28.54601232],
       [34.54914571],
       [27.36491618],
       [24.87707782],
       [22.00096365],
       [14.31750595],
       [15.26655896],
       [18.95164011],
       [14.52104908],
       [37.38819398],
       [28.82792081],
       [23.3211182 ],
       [30.6343198 ],
       [20.80233876],
       [21.31839148],
       [13.79005679],
       [24.3590396 ],
       [26.87702832],
       [19.35529157],
       [32.16020072],
       [19.52355909],
       [24.26581358],
       [31.63175652],
       [30.17323569],
       [32.66670796],
       [25.47912641],
       [24.36217689],
       [24.91701584],
       [39.47302165],
       [18.22458912],
       [30.75058024],
       [32.14915944],
       [43.35075081],
       [25.58142763],
       [24.22487493],
       [22.23864659],
       [16.45656221],
       [27.14231857],
       [ 4.52270441],
       [18.23427535],
       [17.87417222],
       [14.1986027 ],
       [13.62643288],
       [34.69768313],
       [ 8.34275415],
       [23.6132958 ],
       [ 6.38923846],
       [21.27558839],
       [15.66185343],
       [29.25676316],
       [29.39607496],
       [20.06328838],
       [14.96702673],
       [20.93444425],
       [28.53639958],
       [23.76724172],
       [23.49637722],
       [11.0745397 ],
       [19.48381901],
       [15.51875938],
       [18.65960692],
       [24.24100427],
       [15.64918598],
       [14.14894164],
       [22.94337728],
       [24.09499988],
       [21.05268108],
       [28.55429725],
       [ 7.51316118],
       [22.62833775],
       [ 3.43124359],
       [15.98036192],
       [25.70480807],
       [22.57033657],
       [32.66624286],
       [17.87124766],
       [24.43818932],
       [35.27111772],
       [26.94613641],
       [17.56269425],
       [28.14078364],
       [21.18918514],
       [24.78403264],
       [-4.78164143],
       [21.36553975],
       [21.94334785],
       [16.31804996],
       [35.31337498],
       [40.90768652],
       [23.60641046],
       [19.94431495],
       [34.4813584 ],
       [21.35327276],
       [20.51324011],
       [23.90175952],
       [28.77241981],
       [40.73752328],
       [29.39270623],
       [21.38182702],
       [22.15806225],
       [31.07297608],
       [17.17452852],
       [38.05954909],
       [18.16913598],
       [25.97549364],
       [13.78567603],
       [12.51045123],
       [26.99932827],
       [18.59193795],
       [11.15468796],
       [19.52228306],
       [23.60713735],
       [18.8861402 ],
       [19.4947593 ],
       [13.61341828]])

# 岭回归预测的均方差（损失值）
loss_rd = mean_squared_error(std_y.inverse_transform(y_test), y_rd_predict)
loss_rd

27.836735080339313