集成学习案例二 (蒸汽量预测)
使用经脱敏后的锅炉传感器采集的数据(采集频率是分钟级别),进行蒸汽量的预测.
数据分成训练数据(train.txt)和测试数据(test.txt),其中字段”V0”-“V37”,这 38 个字段是作为特征变量,”target”作为目标变量。
评价指标:均方误差 MSE
import warnings
warnings.filterwarnings("ignore")
import matplotlib.pyplot as plt
import seaborn as sns
# 模型
import pandas as pd
import numpy as np
from scipy import stats
from sklearn.model_selection import train_test_split
from sklearn.model_selection import GridSearchCV, RepeatedKFold, cross_val_score,cross_val_predict,KFold
from sklearn.metrics import make_scorer,mean_squared_error
from sklearn.linear_model import LinearRegression, Lasso, Ridge, ElasticNet
from sklearn.svm import LinearSVR, SVR
from sklearn.neighbors import KNeighborsRegressor
from sklearn.ensemble import RandomForestRegressor, GradientBoostingRegressor,AdaBoostRegressor
from xgboost import XGBRegressor
from sklearn.preprocessing import PolynomialFeatures,MinMaxScaler,StandardScaler
加载数据
5 rows × 40 columns
import warnings
warnings.filterwarnings("ignore")
import matplotlib.pyplot as plt
import seaborn as sns
# 模型
import pandas as pd
import numpy as np
from scipy import stats
from sklearn.model_selection import train_test_split
from sklearn.model_selection import GridSearchCV, RepeatedKFold, cross_val_score,cross_val_predict,KFold
from sklearn.metrics import make_scorer,mean_squared_error
from sklearn.linear_model import LinearRegression, Lasso, Ridge, ElasticNet
from sklearn.svm import LinearSVR, SVR
from sklearn.neighbors import KNeighborsRegressor
from sklearn.ensemble import RandomForestRegressor, GradientBoostingRegressor,AdaBoostRegressor
from xgboost import XGBRegressor
from sklearn.preprocessing import PolynomialFeatures,MinMaxScaler,StandardScaler
data_train = pd.read_csv('train.txt',sep = '\t')
data_test = pd.read_csv('test.txt',sep = '\t')
#合并训练数据和测试数据
data_train["oringin"]="train"
data_test["oringin"]="test"
data_all=pd.concat([data_train,data_test],axis=0,ignore_index=True)
#显示前 5 条数据
data_all.head()
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使用 kdeplot(核密度估计图) 进行数据的初步分析,即 EDA。
for column in data_all.columns[0:-2]:
#核密度估计(kernel density estimation)是在概率论中用来估计未知的密度函数,属于非参数检验方法之一。通过核密度估计图可以比较直观的看出数据样本本身的分布特征。
g = sns.kdeplot(data_all[column][(data_all["oringin"] == "train")], color="Red", shade = True)
g = sns.kdeplot(data_all[column][(data_all["oringin"] == "test")], ax =g, color="Blue", shade= True)
g.set_xlabel(column)
g.set_ylabel("Frequency")
g = g.legend(["train","test"])
plt.show()
查看特征之间的相关性(相关程度)
data_train1=data_all[data_all["oringin"]=="train"].drop("oringin",axis=1)
plt.figure(figsize=(20, 16)) # 指定绘图对象宽度和高度
colnm = data_train1.columns.tolist() # 列表头
mcorr = data_train1[colnm].corr(method="spearman") # 相关系数矩阵,即给出了任意两个变量之间的相关系数
mask = np.zeros_like(mcorr, dtype=np.bool) # 构造与 mcorr 同维数矩阵 为 bool 型
mask[np.triu_indices_from(mask)] = True # 角分线右侧为 True
cmap = sns.diverging_palette(220, 10, as_cmap=True) # 返回 matplotlib colormap 对象,调色板
g = sns.heatmap(mcorr, mask=mask, cmap=cmap, square=True, annot=True, fmt='0.2f') # 热力图(看两两相似度)
plt.show()
进行降维操作,即将相关性的绝对值小于阈值的特征进行删除
threshold = 0.1
corr_matrix = data_train1.corr().abs()
drop_col=corr_matrix[corr_matrix["target"]<threshold].index
data_all.drop(drop_col,axis=1,inplace=True)进行归一化操作
V0 V1 V10 V12 V13 V15 V16 V18 V19
count 4813.000000 4813.000000 4813.000000 4813.000000 4813.000000 4813.000000 4813.000000 4813.000000 4813.000000 481
mean 0.694172 0.721357 0.348518 0.578507 0.612372 0.402251 0.679294 0.446542 0.519158 0.60
std 0.144198 0.131443 0.134882 0.105088 0.149835 0.138561 0.112095 0.124627 0.140166 0.14
min 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.00
25% 0.626676 0.679416 0.284327 0.532892 0.519928 0.299016 0.629414 0.399302 0.414436 0.51
50% 0.729488 0.752497 0.366469 0.591635 0.627809 0.391437 0.700258 0.456256 0.540294 0.61
75% 0.790195 0.799553 0.432965 0.641971 0.719958 0.489954 0.753279 0.501745 0.623125 0.70
max 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.00
8 rows × 25 columns
绘图显示 Box-Cox 变换对数据分布影响,Box-Cox 用于连续的响应变量不满足正态分布的情况。在进行 Box-Cox 变换之后,可以一定程度上减小不可观测的误差和预测变量的相关
性。
对于 quantitle-quantile(q-q)图,可参考: https://blog.csdn.net/u012193416/article/details/83210790
特征工程
cols_numeric=list(data_all.columns)
cols_numeric.remove("oringin")
def scale_minmax(col):
return (col-col.min())/(col.max()-col.min())
scale_cols = [col for col in cols_numeric if col!='target']
data_all[scale_cols] = data_all[scale_cols].apply(scale_minmax,axis=0)
data_all[scale_cols].describe()
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特征工程:绘图显示 Box-Cox 变换对数据分布影响,Box-Cox 用于连续的响应变量不满足正态分布的情况。在进行 Box-Cox 变换之后,可以一定程度上减小不可观测的误差和预测变量的相关性。
fcols = 6
frows = len(cols_numeric)-1
plt.figure(figsize=(4*fcols,4*frows))
i=0
for var in cols_numeric:
if var!='target':
dat = data_all[[var, 'target']].dropna()
i+=1
plt.subplot(frows,fcols,i)
sns.distplot(dat[var] , fit=stats.norm);
plt.title(var+' Original')
plt.xlabel('')
i+=1
plt.subplot(frows,fcols,i)
_=stats.probplot(dat[var], plot=plt)
plt.title('skew='+'{:.4f}'.format(stats.skew(dat[var])))
plt.xlabel('')
plt.ylabel('')
i+=1
plt.subplot(frows,fcols,i)
plt.plot(dat[var], dat['target'],'.',alpha=0.5)
plt.title('corr='+'{:.2f}'.format(np.corrcoef(dat[var], dat['target'])[0][1]))
i+=1
plt.subplot(frows,fcols,i)
trans_var, lambda_var = stats.boxcox(dat[var].dropna()+1)
trans_var = scale_minmax(trans_var)
sns.distplot(trans_var , fit=stats.norm);
plt.title(var+' Tramsformed')
plt.xlabel('')
i+=1
plt.subplot(frows,fcols,i)_=stats.probplot(trans_var, plot=plt)
plt.title('skew='+'{:.4f}'.format(stats.skew(trans_var)))
plt.xlabel('')
plt.ylabel('')
i+=1
plt.subplot(frows,fcols,i)
plt.plot(trans_var, dat['target'],'.',alpha=0.5)
plt.title('corr='+'{:.2f}'.format(np.corrcoef(trans_var,dat['target'])[0][1]))
# 进行 Box-Cox 变换
cols_transform=data_all.columns[0:-2]
for col in cols_transform:
# transform column
data_all.loc[:,col], _ = stats.boxcox(data_all.loc[:,col]+1)
print(data_all.target.describe())
plt.figure(figsize=(12,4))
plt.subplot(1,2,1)
sns.distplot(data_all.target.dropna() , fit=stats.norm);
plt.subplot(1,2,2)
_=stats.probplot(data_all.target.dropna(), plot=plt)
使用对数变换 target 目标值提升特征数据的正太性
sp = data_train.target
data_train.target1 =np.power(1.5,sp)
print(data_train.target1.describe())
plt.figure(figsize=(12,4))
plt.subplot(1,2,1)
sns.distplot(data_train.target1.dropna(),fit=stats.norm);
plt.subplot(1,2,2)
_=stats.probplot(data_train.target1.dropna(), plot=plt)
模型构建以及集成学习
# function to get training samples
def get_training_data():
# extract training samples
from sklearn.model_selection import train_test_split
df_train = data_all[data_all["oringin"]=="train"]
df_train["label"]=data_train.target1
# split SalePrice and features
y = df_train.target
X = df_train.drop(["oringin","target","label"],axis=1)X_train,X_valid,y_train,y_valid=train_test_split(X,y,test_size=0.3,random_state=100)
return X_train,X_valid,y_train,y_valid
# extract test data (without SalePrice)
def get_test_data():
df_test = data_all[data_all["oringin"]=="test"].reset_index(drop=True)
return df_test.drop(["oringin","target"],axis=1)
rmse、mse 的评价函数
from sklearn.metrics import make_scorer
# metric for evaluation
def rmse(y_true, y_pred):
diff = y_pred - y_true
sum_sq = sum(diff**2)
n = len(y_pred)
return np.sqrt(sum_sq/n)
def mse(y_ture,y_pred):
return mean_squared_error(y_ture,y_pred)
# scorer to be used in sklearn model fitting
rmse_scorer = make_scorer(rmse, greater_is_better=False)
#输入的 score_func 为记分函数时,该值为 True(默认值);输入函数为损失函数时,该值为 False
mse_scorer = make_scorer(mse, greater_is_better=False)
寻找离群值,并删除.
# function to detect outliers based on the predictions of a model
def find_outliers(model, X, y, sigma=3):
# predict y values using model
model.fit(X,y)
y_pred = pd.Series(model.predict(X), index=y.index)
# calculate residuals between the model prediction and true y values
resid = y - y_pred
mean_resid = resid.mean()
std_resid = resid.std()
# calculate z statistic, define outliers to be where |z|>sigma
z = (resid - mean_resid)/std_resid
outliers = z[abs(z)>sigma].index
# print and plot the results
print('R2=',model.score(X,y))
print('rmse=',rmse(y, y_pred))
print("mse=",mean_squared_error(y,y_pred))
print('---------------------------------------')
print('mean of residuals:',mean_resid)
print('std of residuals:',std_resid)
print('---------------------------------------')
print(len(outliers),'outliers:')
print(outliers.tolist())
plt.figure(figsize=(15,5))
ax_131 = plt.subplot(1,3,1)
plt.plot(y,y_pred,'.')
plt.plot(y.loc[outliers],y_pred.loc[outliers],'ro')
plt.legend(['Accepted','Outlier'])
plt.xlabel('y')
plt.ylabel('y_pred');
ax_132=plt.subplot(1,3,2)
plt.plot(y,y-y_pred,'.')
plt.plot(y.loc[outliers],y.loc[outliers]-y_pred.loc[outliers],'ro')
plt.legend(['Accepted','Outlier'])
plt.xlabel('y')
plt.ylabel('y - y_pred');
ax_133=plt.subplot(1,3,3)
z.plot.hist(bins=50,ax=ax_133)
z.loc[outliers].plot.hist(color='r',bins=50,ax=ax_133)
plt.legend(['Accepted','Outlier'])
plt.xlabel('z')
return outliers# get training data
X_train, X_valid,y_train,y_valid = get_training_data()
test=get_test_data()
# find and remove outliers using a Ridge model
outliers = find_outliers(Ridge(), X_train, y_train)
X_outliers=X_train.loc[outliers]
y_outliers=y_train.loc[outliers]
X_t=X_train.drop(outliers)
y_t=y_train.drop(outliers)
R2= 0.8766692300840108
rmse= 0.3490086770200251
mse= 0.12180705663526846
---------------------------------------
mean of residuals: 1.4843258844815303e-16
std of residuals: 0.34909505461744217
---------------------------------------
22 outliers:
[2655, 2159, 1164, 2863, 1145, 2697, 2528, 2645, 691, 1085, 1874, 2647, 884, 2696, 2668, 1310, 1901, 1458, 2769, 2002, 2669, 1972]
进行模型的训练
def get_trainning_data_omitoutliers():
#获取训练数据省略异常值
y=y_t.copy()
X=X_t.copy()
return X,y
def train_model(model, param_grid=[], X=[], y=[],
splits=5, repeats=5):
# 获取数据
if len(y)==0:
X,y = get_trainning_data_omitoutliers()
# 交叉验证
rkfold = RepeatedKFold(n_splits=splits, n_repeats=repeats)
# 网格搜索最佳参数
if len(param_grid)>0:
gsearch = GridSearchCV(model, param_grid, cv=rkfold,
scoring="neg_mean_squared_error",
verbose=1, return_train_score=True)
# 训练
gsearch.fit(X,y)
# 最好的模型
model = gsearch.best_estimator_
best_idx = gsearch.best_index_
# 获取交叉验证评价指标
grid_results = pd.DataFrame(gsearch.cv_results_)
cv_mean = abs(grid_results.loc[best_idx,'mean_test_score'])
cv_std = grid_results.loc[best_idx,'std_test_score']
# 没有网格搜索
else:
grid_results = []
cv_results = cross_val_score(model, X, y, scoring="neg_mean_squared_error", cv=rkfold)
cv_mean = abs(np.mean(cv_results))
cv_std = np.std(cv_results)# 合并数据
cv_score = pd.Series({'mean':cv_mean,'std':cv_std})
# 预测
y_pred = model.predict(X)
# 模型性能的统计数据
print('----------------------')
print(model)
print('----------------------')
print('score=',model.score(X,y))
print('rmse=',rmse(y, y_pred))
print('mse=',mse(y, y_pred))
print('cross_val: mean=',cv_mean,', std=',cv_std)
# 残差分析与可视化
y_pred = pd.Series(y_pred,index=y.index)
resid = y - y_pred
mean_resid = resid.mean()
std_resid = resid.std()
z = (resid - mean_resid)/std_resid
n_outliers = sum(abs(z)>3)
outliers = z[abs(z)>3].index
return model, cv_score, grid_results
# 定义训练变量存储数据
opt_models = dict()
score_models = pd.DataFrame(columns=['mean','std'])
splits=5
repeats=5
model = 'Ridge' #可替换,见案例分析一的各种模型
opt_models[model] = Ridge() #可替换,见案例分析一的各种模型
alph_range = np.arange(0.25,6,0.25)
param_grid = {'alpha': alph_range}
opt_models[model],cv_score,grid_results = train_model(opt_models[model], param_grid=param_grid,
splits=splits, repeats=repeats)
cv_score.name = model
score_models = score_models.append(cv_score)
plt.figure()
plt.errorbar(alph_range, abs(grid_results['mean_test_score']),
abs(grid_results['std_test_score'])/np.sqrt(splits*repeats))
plt.xlabel('alpha')
plt.ylabel('score')
Fitting 25 folds for each of 23 candidates, totalling 575 fits
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
----------------------
Ridge(alpha=0.25, copy_X=True, fit_intercept=True, max_iter=None,
normalize=False, random_state=None, solver='auto', tol=0.001)
----------------------
score= 0.8926884448727849
rmse= 0.32466407807582776
mse= 0.10540676359282722
cross_val: mean= 0.10890639745404394 , std= 0.007654061179739962
[Parallel(n_jobs=1)]: Done 575 out of 575 | elapsed: 2.7s finished
# 预测函数
def model_predict(test_data,test_y=[]):
i=0
y_predict_total=np.zeros((test_data.shape[0],))
for model in opt_models.keys():
if model!="LinearSVR" and model!="KNeighbors":
y_predict=opt_models[model].predict(test_data)
y_predict_total+=y_predict
i+=1
if len(test_y)>0:
print("{}_mse:".format(model),mean_squared_error(y_predict,test_y))
y_predict_mean=np.round(y_predict_total/i,6)
if len(test_y)>0:
print("mean_mse:",mean_squared_error(y_predict_mean,test_y))
else:
y_predict_mean=pd.Series(y_predict_mean)
return y_predict_mean
进行模型的预测以及结果的保存
y_ = model_predict(test)
y_.to_csv('predict.txt',header = None,index = False)
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