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
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| 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)
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LinearRegression()
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LinearRegression
LinearRegression()
# 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
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# 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)
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SGDRegressor()
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SGDRegressor
SGDRegressor()
# 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
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# 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)
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#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label { background-color: rgba(212, 235, 255, 1) }
#sk-container-id-3 input.sk-hidden--visually { border: 0; clip: rect(1px, 1px, 1px, 1px); height: 1px; margin: -1px; overflow: hidden; padding: 0; position: absolute; width: 1px }
#sk-container-id-3 div.sk-estimator { font-family: monospace; background-color: rgba(240, 248, 255, 1); border: 1px dotted rgba(0, 0, 0, 1); border-radius: 0.25em; box-sizing: border-box; margin-bottom: 0.5em }
#sk-container-id-3 div.sk-estimator:hover { background-color: rgba(212, 235, 255, 1) }
#sk-container-id-3 div.sk-parallel-item::after { content: ""; width: 100%; border-bottom: 1px solid rgba(128, 128, 128, 1); flex-grow: 1 }
#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label { background-color: rgba(212, 235, 255, 1) }
#sk-container-id-3 div.sk-serial::before { content: ""; position: absolute; border-left: 1px solid rgba(128, 128, 128, 1); box-sizing: border-box; top: 0; bottom: 0; left: 50%; z-index: 0 }
#sk-container-id-3 div.sk-serial { display: flex; flex-direction: column; align-items: center; background-color: rgba(255, 255, 255, 1); padding-right: 0.2em; padding-left: 0.2em; position: relative }
#sk-container-id-3 div.sk-item { position: relative; z-index: 1 }
#sk-container-id-3 div.sk-parallel { display: flex; align-items: stretch; justify-content: center; background-color: rgba(255, 255, 255, 1); position: relative }
#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before { content: ""; position: absolute; border-left: 1px solid rgba(128, 128, 128, 1); box-sizing: border-box; top: 0; bottom: 0; left: 50%; z-index: -1 }
#sk-container-id-3 div.sk-parallel-item { display: flex; flex-direction: column; z-index: 1; position: relative; background-color: rgba(255, 255, 255, 1) }
#sk-container-id-3 div.sk-parallel-item:first-child::after { align-self: flex-end; width: 50% }
#sk-container-id-3 div.sk-parallel-item:last-child::after { align-self: flex-start; width: 50% }
#sk-container-id-3 div.sk-parallel-item:only-child::after { width: 0 }
#sk-container-id-3 div.sk-dashed-wrapped { border: 1px dashed rgba(128, 128, 128, 1); margin: 0 0.4em 0.5em; box-sizing: border-box; padding-bottom: 0.4em; background-color: rgba(255, 255, 255, 1) }
#sk-container-id-3 div.sk-label label { font-family: monospace; font-weight: bold; display: inline-block; line-height: 1.2em }
#sk-container-id-3 div.sk-label-container { text-align: center }
#sk-container-id-3 div.sk-container { display: inline-block !important; position: relative }
#sk-container-id-3 div.sk-text-repr-fallback { display: none }
Ridge()
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Ridge
Ridge()
# 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
