task09：集成学习案例——蒸汽量预测

准备工作

背景介绍

使用的是经脱敏后的锅炉传感器采集的数据（采集频率是分钟级别）。根据锅炉的工况，预测产生的蒸汽量。

数据信息

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。我们需要利用训练数据训练出模型，预测测试数据的目标变量。

评价指标

最终的评价指标为均方误差MSE，即：

代码实战

导入包

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

数据读取

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)

数据预处理

探索数据分布，传感器是连续变量，所以使用 kdeplot(核密度估计图) 进行数据的初步分析，即EDA。
notes：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。

#输出v1-v37的核密度估计图
for column in data_all.columns[0:-2]:
    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()

特征"V5",“V9”,“V11”,“V17”,“V22”,"V28"中训练集数据分布和测试集数据分布不均，删除这些特征数据

for column in ["V5","V9","V11","V17","V22","V28"]:
    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()

data_all.drop(["V5","V9","V11","V17","V22","V28"],axis=1,inplace=True)

特征绘图，观察特征的变化分布情况。

data_train1=data_all[data_all["oringin"]=="train"].drop("oringin",axis=1)

fcols = 2
frows = len(data_train.columns)
plt.figure(figsize=(5*fcols,4*frows))

i=0
for col in data_train1.columns:
    i+=1
    ax=plt.subplot(frows,fcols,i)
    sns.regplot(x=col, y='target', data=data_train, ax=ax, 
                scatter_kws={
     'marker':'.','s':3,'alpha':0.3},
                line_kws={
     'color':'k'});
    plt.xlabel(col)
    plt.ylabel('target')
    
    i+=1
    ax=plt.subplot(frows,fcols,i)
    sns.distplot(data_train[col].dropna() , fit=stats.norm)
    plt.xlabel(col)

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

DataFrame.corr(method=‘pearson’, min_periods=1)
计算数值列的两两相关，不包括NA或者null值，注意，也不包括非数值特征列，例如分类特征。相关系数的变化范围是从-1到1，越接近1，表示有越强的正相关；系数越接近-1表示有越强的负相关；系数越接近0表示两属性之间没有线性相关性，注意，没有线性相关性不代表没有其他非线性相关性。函数返回的是一个相关性矩阵，正对角线的数值均为1，且为对称矩阵。
method : {‘pearson’, ‘kendall’, ‘spearman’}
pearson : standard correlation coefficient
kendall : Kendall Tau correlation coefficient
spearman : Spearman rank correlation

pandas.plotting.scatter_matrix(frame, alpha=0.5, figsize=None, ax=None, grid=False, diagonal=‘hist’, marker=’.’, density_kwds=None, hist_kwds=None, range_padding=0.05, **kwargs)
通过corr（）可以得到线性相关性的数值关系，不够形象，通常可以在使用corr之后再使用scatter_matrix绘制出图像，通过散点图更加直观的看见属性之间的联系

threshold = 0.1 #设置阈值
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，把数据映射到0～1范围之内处理，更加便捷快速。

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()

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。
quantitle-quantile(q-q)图https://blog.csdn.net/u012193416/article/details/83210790

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)

经过Box-Cox变换数据分布，更加正态化，所以进行Box-Cox变换很有必要。Box-Cox变换是Box和Cox在1964年提出的一种广义幂变换方法，是统计建模中常用的一种数据变换，用于连续的响应变量不满足正态分布的情况。

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（均方根误差）、mse（均方误差）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)

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')

# 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)