翻译——2_Linear Regression and Support Vector Regression

上篇 1_Project Overview, Data Wrangling and Exploratory Analysis

使用不同的机器学习方法进行预测

线性回归

在这本笔记本中，将训练一个线性回归模型来预测基于历史能源数据、几个天气变量、一天中的小时、一周中的一天、周末和假期的电源能耗。

为了做到这一点，我们将把模型设定为从2012-01-01到2014-10-31的每日和每小时的能源和天气数据。

%matplotlib inline 
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
pd.options.display.mpl_style = 'default'

from sklearn.linear_model import LinearRegression
dailyElectricity = pd.read_excel('Data/dailyElectricityWithFeatures.xlsx')
dailyElectricity = dailyElectricity.drop('startDay', 1).drop('endDay', 1)

dailyChilledWater = pd.read_excel('Data/dailyChilledWaterWithFeatures.xlsx')
dailyChilledWater = dailyChilledWater.drop('startDay', 1).drop('endDay', 1)

dailySteam = pd.read_excel('Data/dailySteamWithFeatures.xlsx')
dailySteam = dailySteam.drop('startDay', 1).drop('endDay', 1)

hourlyElectricity = pd.read_excel('Data/hourlyElectricityWithFeatures.xlsx')
hourlyElectricity = hourlyElectricity.drop('startTime', 1).drop('endTime', 1)

hourlyChilledWater = pd.read_excel('Data/hourlyChilledWaterWithFeatures.xlsx')
hourlyChilledWater = hourlyChilledWater.drop('startTime', 1).drop('endTime', 1)

hourlySteam = pd.read_excel('Data/hourlySteamWithFeatures.xlsx')
hourlySteam = hourlySteam.drop('startTime', 1).drop('endTime', 1)

#显示出dataframe
dailyElectricity.head()

	electricity-kWh	RH-%	T-C	Tdew-C	pressure-mbar	solarRadiation-W/m2	windDirection	windSpeed-m/s	humidityRatio-kg/kg	coolingDegrees	heatingDegrees	dehumidification	occupancy
2012-01-01	2800.244977	76.652174	7.173913	3.073913	1004.956522	95.260870	236.086957	4.118361	0.004796	0.086957	7.826087	0	0.0
2012-01-02	3168.974047	55.958333	5.833333	-2.937500	994.625000	87.333333	253.750000	5.914357	0.003415	0.000000	9.166667	0	0.3
2012-01-03	5194.533376	42.500000	-3.208333	-12.975000	1002.125000	95.708333	302.916667	6.250005	0.001327	0.000000	18.208333	0	0.3
2012-01-04	5354.861935	41.541667	-7.083333	-16.958333	1008.250000	98.750000	286.666667	5.127319	0.000890	0.000000	22.083333	0	0.3
2012-01-05	5496.223993	46.916667	-0.583333	-9.866667	1002.041667	90.750000	258.333333	5.162041	0.001746	0.000000	15.583333	0	0.3

每日预测

向dataframe添加新特征:工作日、一年中的一天和一周。

def addDailyTimeFeatures(df):
    df['weekday'] = df.index.weekday
    df['day'] = df.index.dayofyear
    df['week'] = df.index.weekofyear
    return df
    
dailyElectricity = addDailyTimeFeatures(dailyElectricity)
dailyChilledWater = addDailyTimeFeatures(dailyChilledWater)
dailySteam = addDailyTimeFeatures(dailySteam)

每日电力预测

df_elect = dailyElectricity[['weekday', 'day', 'week', 
                             'occupancy', 'electricity-kWh']]

elect_train = pd.DataFrame(data=df_elect, 
                           index=np.arange('2012-01', '2013-07', 
                                           dtype='datetime64[D]')).dropna()
elect_test = pd.DataFrame(data=df_elect, 
                          index=np.arange('2013-07', '2014-11', 
                                          dtype='datetime64[D]')).dropna()

XX_elect_train = elect_train.drop('electricity-kWh', 
                                  axis = 1).reset_index().drop('index', axis = 1)
XX_elect_test = elect_test.drop('electricity-kWh', 
                                axis = 1).reset_index().drop('index', axis = 1)

YY_elect_train = elect_train['electricity-kWh']
YY_elect_test = elect_test['electricity-kWh']

lr_elect = LinearRegression()
lr_elect.fit(XX_elect_train,YY_elect_train)

y_lr = lr_elect.predict(XX_elect_test)

print "The test score R2: ", lr_elect.score(XX_elect_test, YY_elect_test)

print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_elect_train.columns, lr_elect.coef_), 
             columns = ['elect_features', 'linearRegr_Coefficients'])

The test score R2:  0.608937488563
The Linear Regression coefficients are

	elect_features	linearRegr_Coefficients
0	weekday	-125.392163
1	day	0.550121
2	week	-11.553215
3	occupancy	2830.298384

#Plot observed and Predicted electricity value 
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_elect_test.index, YY_elect_test, label='Observed', color='k')
plt.plot(XX_elect_test.index, y_lr, label='Predicted', color='g')
plt.legend(loc='upper right')

# 图观察与线性回归预测使用。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_elect_test, YY_elect_test, c='k')
plt.scatter(YY_elect_test, y_lr, c='g')
plt.xlabel('Observed Elec. Usage (kWh)')
plt.ylabel("Predicted Elec. Usage (kWh): $hat{Y}_i$")
plt.title("Energy vs Predicted Elec.: $Y_i$ vs $hat{Y}_i$")

每日冷水预报

chilledw_train = pd.DataFrame(data=dailyChilledWater, index=np.arange('2012-01', '2013-07', dtype='datetime64[D]')).dropna()
chilledw_test = pd.DataFrame(data=dailyChilledWater, index=np.arange('2013-07', '2014-11', dtype='datetime64[D]')).dropna()

XX_chilledw_train = chilledw_train.drop('chilledWater-TonDays', axis = 1).reset_index().drop('index', axis = 1)
XX_chilledw_test = chilledw_test.drop('chilledWater-TonDays', axis = 1).reset_index().drop('index', axis = 1)

YY_chilledw_train = chilledw_train['chilledWater-TonDays']
YY_chilledw_test = chilledw_test['chilledWater-TonDays']

lr_chilledw = LinearRegression()
lr_chilledw.fit(XX_chilledw_train,YY_chilledw_train)

print "The test score R2: ", lr_chilledw.score(XX_chilledw_test, YY_chilledw_test)

print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_chilledw_train.columns, lr_chilledw.coef_), columns = ['chilledw_features', 'linearRegr_Coefficients'])

The test score R2:  0.830709188732
The Linear Regression coefficients are

	chilledw_features	linearRegr_Coefficients
0	RH-%	0.464299
1	T-C	6.062113
2	Tdew-C	-2.486768
3	pressure-mbar	-0.095268
4	solarRadiation-W/m2	0.042885
5	windDirection	-0.025036
6	windSpeed-m/s	-1.166902
7	humidityRatio-kg/kg	1673.166705
8	coolingDegrees	2.853128
9	heatingDegrees	4.421394
10	dehumidification	2999.125771
11	occupancy	0.571356
12	weekday	-2.461900
13	day	-0.010718
14	week	0.122757

# 实测和预测的电量值
y_lr = lr_chilledw.predict(XX_chilledw_test)
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_chilledw_test.index, YY_chilledw_test, label='Observed', color='k')
plt.plot(XX_chilledw_test.index, y_lr, label='Predicted', color='r')
plt.legend(loc='upper right')

# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_chilledw_test, YY_chilledw_test, c='k')
plt.scatter(YY_chilledw_test, y_lr, c='r')
plt.xlabel('Observed Chilled Water Usage (TonDays)')
plt.ylabel("Predicted Chilled Water Usage (TonDays): $hat{Y}_i$")
plt.title("Observed vs Predicted Chilled Water: $Y_i$ vs $hat{Y}_i$")

每日热水预测

steam_train = pd.DataFrame(data=dailySteam, index=np.arange('2012-01', '2013-07', dtype='datetime64[D]')).dropna()
steam_test = pd.DataFrame(data=dailySteam, index=np.arange('2013-07', '2014-11', dtype='datetime64[D]')).dropna()

XX_steam_train = steam_train.drop('steam-LBS', axis = 1).reset_index().drop('index', axis = 1)
XX_steam_test = steam_test.drop('steam-LBS', axis = 1).reset_index().drop('index', axis = 1)

YY_steam_train = steam_train['steam-LBS']
YY_steam_test = steam_test['steam-LBS']

lr_steam = LinearRegression()
lr_steam.fit(XX_steam_train,YY_steam_train)

print "The test score R2: ", lr_steam.score(XX_steam_test, YY_steam_test)

print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_steam_train.columns, lr_steam.coef_), columns = ['steam_features', 'linearRegr_Coefficients'])

The test score R2:  0.942276415896
The Linear Regression coefficients are

	steam_features	linearRegr_Coefficients
0	RH-%	66.535470
1	T-C	458.096751
2	Tdew-C	-951.521615
3	pressure-mbar	-30.891470
4	solarRadiation-W/m2	-18.446292
5	windDirection	-7.828922
6	windSpeed-m/s	251.824413
7	humidityRatio-kg/kg	857001.445663
8	coolingDegrees	-99.989152
9	heatingDegrees	1794.351286
10	dehumidification	-482120.622688
11	occupancy	3150.501909
12	weekday	-531.583401
13	day	-1.499061
14	week	-43.000664

# 实测和预测的电量值
y_lr = lr_steam.predict(XX_steam_test)
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_steam_test.index, YY_steam_test, label='Observed', color='k')
plt.plot(XX_steam_test.index, y_lr, label='Predicted', color='g')
plt.legend(loc='upper right')

# 绘制实际使用量与预测使用量。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_steam_test, YY_steam_test, c='k')
plt.scatter(YY_steam_test, y_lr, c='g')
plt.xlabel('Observed Steam Usage (LBS)')
plt.ylabel("Predicted Steam Usage (LBS): $hat{Y}_i$")
plt.title("Observed vs Predicted Steam: $Y_i$ vs $hat{Y}_i$")

每小时预测

向dataframe添加新特征:小时、工作日、年中的一天和周。

def addHourlyTimeFeatures(df):
    df['hour'] = df.index.hour
    df['weekday'] = df.index.weekday
    df['day'] = df.index.dayofyear
    df['week'] = df.index.weekofyear    
    return df

hourlyElectricity = addHourlyTimeFeatures(hourlyElectricity)

每小时电力预测

df_hourlyelect = hourlyElectricity[['hour', 'weekday', 'day', 'week', 'cosHour', 
                                                      'occupancy', 'electricity-kWh']]

hourlyelect_train = pd.DataFrame(data=df_hourlyelect, index=np.arange('2014-01-01 00:00:00', '2014-10-01 00:00:00', dtype='datetime64[h]')).dropna()
hourlyelect_test = pd.DataFrame(data=df_hourlyelect, index=np.arange('2014-10-01 00:00:00', '2014-11-01 00:00:00', dtype='datetime64[h]')).dropna()

XX_hourlyelect_train = hourlyelect_train.drop('electricity-kWh', axis = 1).reset_index().drop('index', axis = 1)
XX_hourlyelect_test = hourlyelect_test.drop('electricity-kWh', axis = 1).reset_index().drop('index', axis = 1)

YY_hourlyelect_train = hourlyelect_train['electricity-kWh']
YY_hourlyelect_test = hourlyelect_test['electricity-kWh']

lr_hourlyelect = LinearRegression()
lr_hourlyelect.fit(XX_hourlyelect_train,YY_hourlyelect_train)

y_hourlyelect_lr = lr_hourlyelect.predict(XX_hourlyelect_test)

print "The test score R2: ", lr_hourlyelect.score(XX_hourlyelect_test, YY_hourlyelect_test)

print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_hourlyelect_train.columns, lr_hourlyelect.coef_), columns = ['hourlyelect_features', 'linearRegr_Coefficients'])

The test score R2:  0.714713369958
The Linear Regression coefficients are

	hourlyelect_features	linearRegr_Coefficients
0	hour	-0.287362
1	weekday	-6.995868
2	day	-0.309981
3	week	0.955127
4	cosHour	-81.049080
5	occupancy	114.803110

# 实测和预测的电量值
fig = plt.figure(figsize=(25,7))
plt.scatter(XX_hourlyelect_test.index, YY_hourlyelect_test, label='Observed', color='k')
plt.plot(XX_hourlyelect_test.index, y_hourlyelect_lr, label='Predicted', color='r')
plt.legend(loc='upper right')

#Plot Observed vs. Predicted usage.
fig = plt.figure(figsize=(6,6))
plt.plot(YY_hourlyelect_test, YY_hourlyelect_test, c='k')
plt.scatter(YY_hourlyelect_test, y_hourlyelect_lr, c='r')
plt.xlabel('Observed Elec. Usage (kWh)')
plt.ylabel("Predicted Elec. Usage (kWh): $hat{Y}_i$")
plt.title("Energy vs Predicted Elec.: $Y_i$ vs $hat{Y}_i$")

每小时冷水预报

hourlychilledw_train = pd.DataFrame(data=hourlyChilledWater, 
                                    index=np.arange('2014-01-01 00:00:00', 
                                                    '2014-09-01 00:00:00', 
                                                    dtype='datetime64[h]')).dropna()
hourlychilledw_test = pd.DataFrame(data=hourlyChilledWater, 
                                   index=np.arange('2014-09-01 00:00:00', 
                                                   '2014-11-01 00:00:00', 
                                                   dtype='datetime64[h]')).dropna()

XX_hourlychilledw_train = 
		hourlychilledw_train.drop('chilledWater-TonDays', 
                          		  axis = 1).reset_index().drop('index', axis = 1)
XX_hourlychilledw_test = 
		hourlychilledw_test.drop('chilledWater-TonDays', 
                                 axis = 1).reset_index().drop('index', axis = 1)

YY_hourlychilledw_train = hourlychilledw_train['chilledWater-TonDays']
YY_hourlychilledw_test = hourlychilledw_test['chilledWater-TonDays']

lr_hourlychilledw = LinearRegression()
lr_hourlychilledw.fit(XX_hourlychilledw_train,YY_hourlychilledw_train)

y_hourlychilledw_lr = lr_hourlychilledw.predict(XX_hourlychilledw_test)

print "The test score R2: ", lr_hourlychilledw.score(XX_hourlychilledw_test, YY_hourlychilledw_test)

print "The Linear Regression coefficients are"
pd.DataFrame(zip(XX_hourlychilledw_train.columns, 
                 lr_hourlychilledw.coef_), 
             columns = ['hourlychilledw_features', 'linearRegr_Coefficients'])

The test score R2:  0.709930521875
The Linear Regression coefficients are

	hourlychilledw_features	linearRegr_Coefficients
0	RH-%	-0.028198
1	T-C	0.459533
2	Tdew-C	0.166999
3	pressure-mbar	-0.007099
4	solarRadiation-W/m2	0.001003
5	windDirection	-0.000382
6	windSpeed-m/s	0.004837
7	humidityRatio-kg/kg	-91.425425
8	coolingDegrees	-0.172407
9	heatingDegrees	0.603195
10	dehumidification	226.397306
11	occupancy	0.483000
12	cosHour	-0.562715

#Plot Observed and Predicted electricity value 
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_hourlychilledw_test.index,
            YY_hourlychilledw_test, 
            label='Observed', 
            color='k')
plt.plot(XX_hourlychilledw_test.index, 
         y_hourlychilledw_lr, 
         label='Predicted', 
         color='g')
plt.legend(loc='upper right')

# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_hourlychilledw_test, YY_hourlychilledw_test, c='k')
plt.scatter(YY_hourlychilledw_test, y_hourlychilledw_lr, c='g')
plt.xlabel('Observed Chilled Water Usage (TonDays)')
plt.ylabel("Predicted Chilled Water Usage (TonDays): $hat{Y}_i$")
plt.title("Observed vs Predicted Chilled Water: $Y_i$ vs $hat{Y}_i$")

每小时热水预测

hourlysteam_train = pd.DataFrame(data=hourlySteam, 
                                 index=np.arange('2012-01-01 00:00:00', 
                                                 '2014-02-01 00:00:00', 
                                                 dtype='datetime64[h]')).dropna()
hourlysteam_test = pd.DataFrame(data=hourlySteam, 
                                index=np.arange('2014-02-01 00:00:00', 
                                                '2014-11-01 00:00:00', 
                                                dtype='datetime64[h]')).dropna()

XX_hourlysteam_train = 
		hourlysteam_train.drop('steam-LBS', 
                              axis = 1).reset_index().drop('index', axis = 1)
XX_hourlysteam_test = 
		hourlysteam_test.drop('steam-LBS', 
                              axis = 1).reset_index().drop('index', axis = 1)

YY_hourlysteam_train = hourlysteam_train['steam-LBS']
YY_hourlysteam_test = hourlysteam_test['steam-LBS']

lr_hourlysteam = LinearRegression()
lr_hourlysteam.fit(XX_hourlysteam_train,YY_hourlysteam_train)

y_hourlysteam_lr = lr_hourlysteam.predict(XX_hourlysteam_test)

print "The test score R2: ", lr_hourlysteam.score(XX_hourlysteam_test, 
                                                  YY_hourlysteam_test)

print "The coefficients Linear Regression are"
pd.DataFrame(zip(XX_hourlysteam_train.columns, 
                 lr_hourlysteam.coef_), 
             columns = ['hourlysteam_features', 'linearRegr_Coefficients'])

The test score R2:  0.764295430491
The coefficients Linear Regression are

	hourlysteam_features	linearRegr_Coefficients
0	RH-%	5.367666
1	T-C	8.577206
2	Tdew-C	-54.743326
3	pressure-mbar	-0.279591
4	solarRadiation-W/m2	0.138138
5	windDirection	0.041451
6	windSpeed-m/s	13.943372
7	humidityRatio-kg/kg	75847.104324
8	coolingDegrees	-31.597421
9	heatingDegrees	57.903822
10	dehumidification	-8088.312347
11	occupancy	131.534596
12	cosHour	-343.896782

# 图观测值和预测值
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_hourlysteam_test.index, 
            YY_hourlysteam_test, 
            label='Observed', 
            color='k')
plt.plot(XX_hourlysteam_test.index, y_hourlysteam_lr, label='Predicted', color='r')
plt.legend(loc='upper right')

#Plot Observed vs. Predicted usage.
fig = plt.figure(figsize=(6,6))
plt.plot(YY_hourlysteam_test, YY_hourlysteam_test, c='k')
plt.scatter(YY_hourlysteam_test, y_hourlysteam_lr, c='r')
plt.xlabel('Observed Steam Usage (LBS)')
plt.ylabel("Predicted Steam Usage (LBS): $hat{Y}_i$")
plt.title("Observed vs Predicted Steam: $Y_i$ vs $hat{Y}_i$")

支持向量回归和交叉验证

在这本笔记本中，将训练一个支持向量回归(SVR)模型来预测基于历史能源数据、几个天气变量、一天中的小时、一周中的一天、周末和假期的能源能耗。

为了做到这一点，我们将模型与2012年01月01日至2014年10月31日的每日和每小时的能源和天气数据进行拟合，并计算预测的平均残差平方。

在设计期间，我们使用交叉验证来微调SVR参数。由于SVR需要太多的时间来计算，在最后的笔记本中，将设置参数为交叉验证找到的最优值。仍然会显示作为交叉验证输入的参数范围。

%matplotlib inline 
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.svm import SVR
from sklearn.grid_search import GridSearchCV
from sklearn import cross_validation
from sklearn import grid_search

pd.options.display.mpl_style = 'default'

dailyElectricity = pd.read_excel('Data/dailyElectricityWithFeatures.xlsx')
dailyElectricity = dailyElectricity.drop('startDay', 1).drop('endDay', 1)

dailyChilledWater = pd.read_excel('Data/dailyChilledWaterWithFeatures.xlsx')
dailyChilledWater = dailyChilledWater.drop('startDay', 1).drop('endDay', 1)

dailySteam = pd.read_excel('Data/dailySteamWithFeatures.xlsx')
dailySteam = dailySteam.drop('startDay', 1).drop('endDay', 1)

hourlyElectricity = pd.read_excel('Data/hourlyElectricityWithFeatures.xlsx')
hourlyElectricity = hourlyElectricity.drop('startTime', 1).drop('endTime', 1)

hourlyChilledWater = pd.read_excel('Data/hourlyChilledWaterWithFeatures.xlsx')
hourlyChilledWater = hourlyChilledWater.drop('startTime', 1).drop('endTime', 1)

hourlySteam = pd.read_excel('Data/hourlySteamWithFeatures.xlsx')
hourlySteam = hourlySteam.drop('startTime', 1).drop('endTime', 1)

#显示dataframe
dailyElectricity.head()

	electricity-kWh	RH-%	T-C	Tdew-C	pressure-mbar	solarRadiation-W/m2	windDirection	windSpeed-m/s	humidityRatio-kg/kg	coolingDegrees	heatingDegrees	dehumidification	occupancy
2012-01-01	2800.244977	76.652174	7.173913	3.073913	1004.956522	95.260870	236.086957	4.118361	0.004796	0.086957	7.826087	0	0.0
2012-01-02	3168.974047	55.958333	5.833333	-2.937500	994.625000	87.333333	253.750000	5.914357	0.003415	0.000000	9.166667	0	0.3
2012-01-03	5194.533376	42.500000	-3.208333	-12.975000	1002.125000	95.708333	302.916667	6.250005	0.001327	0.000000	18.208333	0	0.3
2012-01-04	5354.861935	41.541667	-7.083333	-16.958333	1008.250000	98.750000	286.666667	5.127319	0.000890	0.000000	22.083333	0	0.3
2012-01-05	5496.223993	46.916667	-0.583333	-9.866667	1002.041667	90.750000	258.333333	5.162041	0.001746	0.000000	15.583333	0	0.3

每日预测

向dataframe添加新特征:工作日、一年中的一天和一周。

def addDailyTimeFeatures(df):
    df['weekday'] = df.index.weekday
    df['day'] = df.index.dayofyear
    df['week'] = df.index.weekofyear
    return df
    
dailyElectricity = addDailyTimeFeatures(dailyElectricity)
dailyChilledWater = addDailyTimeFeatures(dailyChilledWater)
dailySteam = addDailyTimeFeatures(dailySteam)

每日电力预测

df_elect = dailyElectricity[['weekday', 'day', 'week', 
                             'occupancy', 'electricity-kWh']]

elect_train = pd.DataFrame(data=df_elect, 
                           index=np.arange('2012-01', '2013-07', 
                                           dtype='datetime64[D]')).dropna()
elect_test = pd.DataFrame(data=df_elect, 
                          index=np.arange('2013-07', '2014-11', 
                                          dtype='datetime64[D]')).dropna()

XX_elect_train = elect_train.drop('electricity-kWh', 
                                  axis = 1).reset_index().drop('index', axis = 1)
XX_elect_test = elect_test.drop('electricity-kWh', 
                                axis = 1).reset_index().drop('index', axis = 1)

YY_elect_train = elect_train['electricity-kWh']
YY_elect_test = elect_test['electricity-kWh']

# 输入参数范围交叉验证
gamma_range = [0.01, 0.001, 0.0001]
epsilon_range = [x * 0.1 for x in range(0, 2)]
C_range = range(1, 2500, 500)

# 为了加快速度，首先找到C和gamma的最佳解析器，然后在方法调用中直接设置它们
tuned_parameters = [{
    'kernel': ['rbf', 'linear'],
#    'C': C_range,
#    'gamma': gamma_range,
    'epsilon': epsilon_range}]

# 使用交叉验证搜索最佳参数。
svr_elect = GridSearchCV(SVR(C=2000, gamma=0.01), param_grid = tuned_parameters, verbose = 0)

# 选择合适的回归模型
y_elect = svr_elect.fit(XX_elect_train, YY_elect_train).predict(XX_elect_test)

print 'Optimum parameters C=2000 and gamma=0.01 for SVR'
print 'Optimum parameters epsilon and kernel for SVR: ', svr_elect.best_params_

print "The test score R2 for SVR: ", svr_elect.score(XX_elect_test, YY_elect_test)

print("SVR mean squared error: %.2f"
      % np.mean((YY_elect_test - svr_elect.predict(XX_elect_test)) ** 2))

Optimum parameters C=2000 and gamma=0.01 for SVR
Optimum parameters epsilon and kernel for SVR:  {'epsilon': 0.1, 'kernel': 'rbf'}
The test score R2 for RBF:  0.691753544427
RBF mean squared error: 391582.21

# 在测试期间观测和预测的电力需求的时间序列。
fig = plt.figure(figsize=(15,7))
plt.scatter(XX_elect_test.index, YY_elect_test, c='k', label='Observed')
plt.plot(XX_elect_test.index, y_elect, c='r', label='Predicted')
plt.xlabel('data')
plt.ylabel('target')
plt.title('Support Vector Regression')
plt.legend()
plt.show()

# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.scatter(YY_elect_test, YY_elect_test, c='k')
plt.scatter(YY_elect_test, y_elect, c='r')
plt.xlabel('Observed Elec. Usage (kWh)')
plt.ylabel("Predicted Elec. Usage (kWh): $hat{Y}_i$")
plt.title("Energy vs Predicted Energy: $Y_i$ vs $hat{Y}_i$")

每日冷水预测

chilledw_train = pd.DataFrame(data=dailyChilledWater, 
                              index=np.arange('2012-01', '2013-07', 
                                              dtype='datetime64[D]')).dropna()
chilledw_test = pd.DataFrame(data=dailyChilledWater, 
                             index=np.arange('2013-07', '2014-11', 
                                             dtype='datetime64[D]')).dropna()

XX_chilledw_train = 
		chilledw_train.drop('chilledWater-TonDays', 
                            axis = 1).reset_index().drop('index', axis = 1)
XX_chilledw_test = 
		chilledw_test.drop('chilledWater-TonDays', 
                           axis = 1).reset_index().drop('index', axis = 1)

YY_chilledw_train = chilledw_train['chilledWater-TonDays']
YY_chilledw_test = chilledw_test['chilledWater-TonDays']

# SVR回归器的最优参数
gamma_range = [0.1, 0.01, 0.001, 0.0001]
epsilon_range = [x * 0.1 for x in range(0, 3)]
C_range = range(1, 5, 2)

tuned_parameters = [{
    'kernel': ['rbf', 'linear'],
#    'C': C_range,
#    'gamma': gamma_range,
    'epsilon': epsilon_range}]

svr_chilledw = GridSearchCV(SVR(C=3, gamma=0.0001), param_grid = tuned_parameters, verbose = 0)

y_chilledw = svr_chilledw.fit(XX_chilledw_train, YY_chilledw_train).predict(XX_chilledw_test)

print 'Optimum parameters C=3 and gamma=0.1 for SVR'
print 'Optimum epsilon and kernel: ', svr_chilledw.best_params_

print "The test score R2 for SVR: ", svr_chilledw.score(XX_chilledw_test, YY_chilledw_test)

print("SVR mean squared error: %.2f"
      % np.mean((YY_chilledw_test - svr_chilledw.predict(XX_chilledw_test)) ** 2))

Optimum parameters C=3 and gamma=0.1 for SVR
Optimum epsilon and kernel:  {'epsilon': 0.1, 'kernel': 'linear'}
The test score R2 for SVR:  0.764904375769
SVR mean squared error: 443.92

# 使用SVR绘制观察和预测的冷水值
fig = plt.figure(figsize=(15,10))
plt.scatter(XX_chilledw_test.index, YY_chilledw_test, c='k', label='Observed')
plt.plot(XX_chilledw_test.index, y_chilledw, c='g', label='Predicted')
plt.xlabel('data')
plt.ylabel('target')
plt.title('Support Vector Regression')
plt.legend()
plt.show()

# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.scatter(YY_chilledw_test, YY_chilledw_test, c='k')
plt.scatter(YY_chilledw_test, y_chilledw, c='g')
plt.xlabel('Observed Chilled Water Usage (TonDays)')
plt.ylabel("Predicted Chilled Water Usage (TonDays): $hat{Y}_i$")
plt.title("Observed vs Predicted Energy: $Y_i$ vs $hat{Y}_i$")

每日热水预测

steam_train = pd.DataFrame(data=dailySteam, 
                           index=np.arange('2012-01', '2013-07', 
                                           dtype='datetime64[D]')).dropna()
steam_test = pd.DataFrame(data=dailySteam, 
                          index=np.arange('2013-07', '2014-11', 
                                          dtype='datetime64[D]')).dropna()

XX_steam_train = steam_train.drop('steam-LBS', 
                                  axis = 1).reset_index().drop('index', axis = 1)
XX_steam_test = steam_test.drop('steam-LBS', 
                                axis = 1).reset_index().drop('index', axis = 1)

YY_steam_train = steam_train['steam-LBS']
YY_steam_test = steam_test['steam-LBS']

gamma_range = [0.1, 0.01, 0.001, 0.0001]
epsilon_range = [x * 0.1 for x in range(0, 3)]
C_range = range(1, 500, 50)

tuned_parameters = [{
    'kernel': ['rbf', 'linear'],
#    'C': C_range,
    'gamma': gamma_range,
    'epsilon': epsilon_range}]

svr_steam = GridSearchCV(SVR(C=50), param_grid = tuned_parameters, verbose = 0)

y_steam = svr_steam.fit(XX_steam_train, YY_steam_train).predict(XX_steam_test)

print 'Optimum parameters C=50 for SVR'
print 'Optimum epsilon, gamma and kernel: ', svr_steam.best_params_

print "The test score R2 for SVR: ", svr_steam.score(XX_steam_test, YY_steam_test)

print("SVR mean squared error: %.2f"
      % np.mean((YY_steam_test - svr_steam.predict(XX_steam_test)) ** 2))

Optimum parameters C=50 for SVR
Optimum epsilon, gamma and kernel:  {'epsilon': 0.2, 'gamma': 0.1, 'kernel': 'linear'}
The test score R2 for SVR:  0.938467924325
SVR mean squared error: 20632451.77

# 图观测值和预测值 
fig,ax = plt.subplots(1, 1,figsize=(20,10))
plt.scatter(XX_steam_test.index, YY_steam_test, c='k', label='Observed')
plt.plot(XX_steam_test.index, y_steam, c='r', label='Predicted')
plt.xlabel('data')
plt.ylabel('target')
plt.title('Support Vector Regression')
plt.legend()
plt.show()

# 图观测值和预测值
fig = plt.figure(figsize=(6,6))
plt.scatter(YY_steam_test, YY_steam_test, c='k')
plt.scatter(YY_steam_test, y_steam, c='r')
plt.xlabel('Observed Steam Usage (LBS)')
plt.ylabel("Predicted Steam Usage (LBS): $hat{Y}_i$")
plt.title("Observed vs Predicted Energy: $Y_i$ vs $hat{Y}_i$")

每小时预测

每小时电力预测

向dataframe添加新特征:小时、工作日、年中的一天和周。

def addHourlyTimeFeatures(df):
    df['hour'] = df.index.hour
    df['weekday'] = df.index.weekday
    df['day'] = df.index.dayofyear
    df['week'] = df.index.weekofyear    
    return df

hourlyElectricity = addHourlyTimeFeatures(hourlyElectricity)

df_hourlyelect = hourlyElectricity[['hour', 'weekday', 'day', 'week', 
                                    'cosHour', 'occupancy', 'electricity-kWh']]

hourlyelect_train = pd.DataFrame(data=df_hourlyelect, 
                                 index=np.arange('2014-01-01 00:00:00', 
                                                 '2014-10-01 00:00:00', 
                                                 dtype='datetime64[h]')).dropna()
hourlyelect_test = pd.DataFrame(data=df_hourlyelect, 
                                index=np.arange('2014-10-01 00:00:00', 
                                                '2014-11-01 00:00:00', 
                                                dtype='datetime64[h]')).dropna()

XX_hourlyelect_train = 
		hourlyelect_train.drop('electricity-kWh', 
                               axis = 1).reset_index().drop('index', axis = 1)
XX_hourlyelect_test = 
		hourlyelect_test.drop('electricity-kWh', 
                              axis = 1).reset_index().drop('index', axis = 1)

YY_hourlyelect_train = hourlyelect_train['electricity-kWh']
YY_hourlyelect_test = hourlyelect_test['electricity-kWh']

gamma_range = [0.01, 0.001, 0.0001]
epsilon_range = [x * 0.1 for x in range(0, 2)]
C_range = range(1, 5, 1)

tuned_parameters = [{
    'kernel': ['rbf', 'linear'],
#    'C': C_range,
#    'gamma': gamma_range,
    'epsilon': epsilon_range}]

svr_hourlyelect = GridSearchCV(SVR(C=1, gamma=0.01), param_grid = tuned_parameters, verbose = 0)

y_hourlyelect = svr_hourlyelect.fit(XX_hourlyelect_train, YY_hourlyelect_train).predict(XX_hourlyelect_test)

print 'Optimum parameters C=1 and gamma=0.01 for SVR'
print 'Optimum epsilon and kernel for SVR: ', svr_hourlyelect.best_params_

print "The test score R2: ", svr_hourlyelect.score(XX_hourlyelect_test, YY_hourlyelect_test)

print("SVR mean squared error: %.2f"
      % np.mean((YY_hourlyelect_test - 
                 svr_hourlyelect.predict(XX_hourlyelect_test)) ** 2))

Optimum parameters C=1 and gamma=0.01 for SVR
Optimum epsilon and kernel for SVR:  {'epsilon': 0.1, 'kernel': 'linear'}
The test score R2:  0.747282383852
SVR mean squared error: 1561.24

# 实测和预测的电量值
fig = plt.figure(figsize=(20,10))
plt.scatter(XX_hourlyelect_test.index, 
            YY_hourlyelect_test, 
            label='Observed', 
            color='k')
plt.plot(XX_hourlyelect_test.index, y_hourlyelect, label='Predicted', color='g')
plt.legend(loc='upper right')

# 观察到的和预测的使用情况。
fig = plt.figure(figsize=(6,6))
plt.plot(YY_hourlyelect_test, YY_hourlyelect_test, c='k')
plt.scatter(YY_hourlyelect_test, y_hourlyelect, c='g')
plt.xlabel('Observed Elec. Usage (kWh)')
plt.ylabel("Predicted Elec. Usage (kWh): $hat{Y}_i$")
plt.title("Observed vs Predicted Elec.: $Y_i$ vs $hat{Y}_i$")

下篇3_Gaussian Process Regression