问题链接:House Prices: Advanced Regression Techniques

问题描述: 通过79个变量(几乎)描述爱荷华州埃姆斯(Ames)住宅的每一个特征,在这个竞赛里,需要你预测每个住宅的最终价格,并最终提交。

参考文献:
第一次真正对这么复杂的数据进行操作,初学者都会有点不知所措。参考了其他参赛者的笔记:
1、Comprehensive data exploration with Python by Pedro Marcelino:非常适合初学者的数据探索分析[Exploratory Data Analysis]。

2、Stacked Regressions : Top 4% on LeaderBoard by Serigne :以成绩为导向的数据处理过程。

目录:
1、数据探索
2、数据处理
3、特征工程
4、模型选择
5、模型融合

数据探索(EDA)

我们拿到数据后,先对数据要有个大致的了解,我们有1460的训练数据和1459的测试数据,数据的特征列有79个,其中35个是数值类型的,44个类别类型。

导入数据:

#import some necessary librairies

import numpy as np # linear algebra
import pandas as pd # data processing, CSV file I/O (e.g. pd.read_csv)
%matplotlib inline
import matplotlib.pyplot as plt  # Matlab-style plotting
import seaborn as sns
color = sns.color_palette()
sns.set_style('darkgrid')
import warnings
def ignore_warn(*args, **kwargs):
    pass
warnings.warn = ignore_warn #ignore annoying warning (from sklearn and seaborn)


from scipy import stats
from scipy.stats import norm, skew #for some statistics


pd.set_option('display.float_format', lambda x: '{:.3f}'.format(x)) #Limiting floats output to 3 decimal points


from subprocess import check_output
print(check_output(["ls", "../input"]).decode("utf8")) #check the files available in the directory
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#Now let's import and put the train and test datasets in  pandas dataframe

train = pd.read_csv('../input/train.csv')
test = pd.read_csv('../input/test.csv')

##display the first five rows of the train dataset.
train.head(5)
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##display the first five rows of the test dataset.
test.head(5)
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ID特征对分类没有影响,但最后我们得到结果以后提交的时候需要,所以需要将ID单独提取出来:

#check the numbers of samples and features
print("The train data size before dropping Id feature is : {} ".format(train.shape))
print("The test data size before dropping Id feature is : {} ".format(test.shape))

#Save the 'Id' column
train_ID = train['Id']
test_ID = test['Id']

#Now drop the  'Id' colum since it's unnecessary for  the prediction process.
train.drop("Id", axis = 1, inplace = True)
test.drop("Id", axis = 1, inplace = True)

#check again the data size after dropping the 'Id' variable
print("\nThe train data size after dropping Id feature is : {} ".format(train.shape)) 
print("The test data size after dropping Id feature is : {} ".format(test.shape))
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数据处理

离群点处理:

当然数据探索部分并没有结束,在数据处理部分,我们会边探索边处理:

在数据中会有个别离群点,他们对分类结果噪音太大,我们选择将其删掉。但是如果不是太过分的离群点,就不能删掉,因为如果删掉所有噪声会影响模型的健壮性,对测试数据的泛化能力就会下降。

fig, ax = plt.subplots()
ax.scatter(x = train['GrLivArea'], y = train['SalePrice'])
plt.ylabel('SalePrice', fontsize=13)
plt.xlabel('GrLivArea', fontsize=13)
plt.show()
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右下方的两个数据,living area特别大,但是价格又低的离谱,应该是远离市区的无人地带。对最后的分类结果没有影响的离群点(Oultliers),我们可以放心将其删除。

删除后:

#Deleting outliers
train = train.drop(train[(train['GrLivArea']>4000) & (train['SalePrice']<300000)].index)

#Check the graphic again
fig, ax = plt.subplots()
ax.scatter(train['GrLivArea'], train['SalePrice'])
plt.ylabel('SalePrice', fontsize=13)
plt.xlabel('GrLivArea', fontsize=13)
plt.show()
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目标值处理:

线性的模型需要正态分布的目标值才能发挥最大的作用。我们需要检测房价时候偏离正态分布。使用probplot函数,即正太概率图

sns.distplot(train['SalePrice'] , fit=norm);

# Get the fitted parameters used by the function
(mu, sigma) = norm.fit(train['SalePrice'])
print( '\n mu = {:.2f} and sigma = {:.2f}\n'.format(mu, sigma))

#Now plot the distribution
plt.legend(['Normal dist. ($\mu=$ {:.2f} and $\sigma=$ {:.2f} )'.format(mu, sigma)],
            loc='best')
plt.ylabel('Frequency')
plt.title('SalePrice distribution')

#Get also the QQ-plot
fig = plt.figure()
res = stats.probplot(train['SalePrice'], plot=plt)
plt.show()
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按照参考文献的说法,此时正态分布明显属于右态分布,整体峰值向左偏离,并且skewness较大,需要对目标值做log转换,以恢复目标值的正态性。

#We use the numpy fuction log1p which  applies log(1+x) to all elements of the column
train["SalePrice"] = np.log1p(train["SalePrice"])

#Check the new distribution 
sns.distplot(train['SalePrice'] , fit=norm);

# Get the fitted parameters used by the function
(mu, sigma) = norm.fit(train['SalePrice'])
print( '\n mu = {:.2f} and sigma = {:.2f}\n'.format(mu, sigma))

#Now plot the distribution
plt.legend(['Normal dist. ($\mu=$ {:.2f} and $\sigma=$ {:.2f} )'.format(mu, sigma)],
            loc='best')
plt.ylabel('Frequency')
plt.title('SalePrice distribution')

#Get also the QQ-plot
fig = plt.figure()
res = stats.probplot(train['SalePrice'], plot=plt)
plt.show()
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特征工程

为了方便处理数据,我们将训练集和测试集先进行合并:

#We use the numpy fuction log1p which  applies log(1+x) to all elements of the column
train["SalePrice"] = np.log1p(train["SalePrice"])

#Check the new distribution 
sns.distplot(train['SalePrice'] , fit=norm);

# Get the fitted parameters used by the function
(mu, sigma) = norm.fit(train['SalePrice'])
print( '\n mu = {:.2f} and sigma = {:.2f}\n'.format(mu, sigma))

#Now plot the distribution
plt.legend(['Normal dist. ($\mu=$ {:.2f} and $\sigma=$ {:.2f} )'.format(mu, sigma)],
            loc='best')
plt.ylabel('Frequency')
plt.title('SalePrice distribution')

#Get also the QQ-plot
fig = plt.figure()
res = stats.probplot(train['SalePrice'], plot=plt)
plt.show()
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缺失数据可视化:

f, ax = plt.subplots(figsize=(15, 12))
plt.xticks(rotation='90')
sns.barplot(x=all_data_na.index, y=all_data_na)
plt.xlabel('Features', fontsize=15)
plt.ylabel('Percent of missing values', fontsize=15)
plt.title('Percent missing data by feature', fontsize=15)
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分析各个特征与房价的相关性,相关性的分析最好使用热力图:

#Correlation map to see how features are correlated with SalePrice
corrmat = train.corr()
plt.subplots(figsize=(12,9))
sns.heatmap(corrmat, vmax=0.9, square=True)
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可以看到对角线有一条白线,这代表相同的特征相关性为最高,但值得注意的是,有两个正方形小块:TotaLBsmtSF和1stFlrSF、GarageAreas和GarageCars处。这代表全部建筑面积TotaLBsmtSF与一层建筑面积1stFlrSF成强正相关,车库区域GarageAreas和车库车辆GarageCars成强正相关,那么在填补缺失值的时候就有了依据,我们可以直接删掉一个多余的特征或者使用一个填补另一个。

填补缺失值:
因为缺失值较多,就直接贴代码了:

We impute them by proceeding sequentially through features with missing values

PoolQC : data description says NA means "No Pool". That make sense, given the huge ratio of missing value (+99%) and majority of houses have no Pool at all in general.
In [14]:
all_data["PoolQC"] = all_data["PoolQC"].fillna("None")

MiscFeature : data description says NA means "no misc feature"
In [15]:
all_data["MiscFeature"] = all_data["MiscFeature"].fillna("None")

Alley : data description says NA means "no alley access"
In [16]:
all_data["Alley"] = all_data["Alley"].fillna("None")

Fence : data description says NA means "no fence"
In [17]:
all_data["Fence"] = all_data["Fence"].fillna("None")

FireplaceQu : data description says NA means "no fireplace"
In [18]:
all_data["FireplaceQu"] = all_data["FireplaceQu"].fillna("None")

LotFrontage : Since the area of each street connected to the house property most likely have a similar area to other houses in its neighborhood , we can fill in missing values by the median LotFrontage of the neighborhood.
In [19]:
#Group by neighborhood and fill in missing value by the median LotFrontage of all the neighborhood
all_data["LotFrontage"] = all_data.groupby("Neighborhood")["LotFrontage"].transform(
    lambda x: x.fillna(x.median()))

GarageType, GarageFinish, GarageQual and GarageCond : Replacing missing data with None
In [20]:
for col in ('GarageType', 'GarageFinish', 'GarageQual', 'GarageCond'):
GarageYrBlt, GarageArea and GarageCars : Replacing missing data with 0 (Since No garage = no cars in such garage.)
In [21]:
for col in ('GarageYrBlt', 'GarageArea', 'GarageCars'):
    all_data[col] = all_data[col].fillna(0)

BsmtFinSF1, BsmtFinSF2, BsmtUnfSF, TotalBsmtSF, BsmtFullBath and BsmtHalfBath : missing values are likely zero for having no basement
In [22]:
for col in ('BsmtFinSF1', 'BsmtFinSF2', 'BsmtUnfSF','TotalBsmtSF', 'BsmtFullBath', 'BsmtHalfBath'):
    all_data[col] = all_data[col].fillna(0)

BsmtQual, BsmtCond, BsmtExposure, BsmtFinType1 and BsmtFinType2 : For all these categorical basement-related features, NaN means that there is no basement.
In [23]:
for col in ('BsmtQual', 'BsmtCond', 'BsmtExposure', 'BsmtFinType1', 'BsmtFinType2'):

MasVnrArea and MasVnrType : NA most likely means no masonry veneer for these houses. We can fill 0 for the area and None for the type.
In [24]:
all_data["MasVnrType"] = all_data["MasVnrType"].fillna("None")
all_data["MasVnrArea"] = all_data["MasVnrArea"].fillna(0)

MSZoning (The general zoning classification) : 'RL' is by far the most common value. So we can fill in missing values with 'RL'
In [25]:
all_data['MSZoning'] = all_data['MSZoning'].fillna(all_data['MSZoning'].mode()[0])

Utilities : For this categorical feature all records are "AllPub", except for one "NoSeWa" and 2 NA . Since the house with 'NoSewa' is in the training set, this feature won't help in predictive modelling. We can then safely remove it.
In [26]:
all_data = all_data.drop(['Utilities'], axis=1)

Functional : data description says NA means typical
In [27]:
all_data["Functional"] = all_data["Functional"].fillna("Typ")

Electrical : It has one NA value. Since this feature has mostly 'SBrkr', we can set that for the missing value.
In [28]:
all_data['Electrical'] = all_data['Electrical'].fillna(all_data['Electrical'].mode()[0])

KitchenQual: Only one NA value, and same as Electrical, we set 'TA' (which is the most frequent) for the missing value in KitchenQual.
In [29]:
all_data['KitchenQual'] = all_data['KitchenQual'].fillna(all_data['KitchenQual'].mode()[0])

Exterior1st and Exterior2nd : Again Both Exterior 1 & 2 have only one missing value. We will just substitute in the most common string
In [30]:
all_data['Exterior1st'] = all_data['Exterior1st'].fillna(all_data['Exterior1st'].mode()[0])
all_data['Exterior2nd'] = all_data['Exterior2nd'].fillna(all_data['Exterior2nd'].mode()[0])

SaleType : Fill in again with most frequent which is "WD"
In [31]:
all_data['SaleType'] = all_data['SaleType'].fillna(all_data['SaleType'].mode()[0])

MSSubClass : Na most likely means No building class. We can replace missing values with None
In [32]:
all_data['MSSubClass'] = all_data['MSSubClass'].fillna("None")
Is there any remaining missing value ?

In [33]:
#Check remaining missing values if any 
all_data_na = (all_data.isnull().sum() / len(all_data)) * 100
all_data_na = all_data_na.drop(all_data_na[all_data_na == 0].index).sort_values(ascending=False)
missing_data = pd.DataFrame({'Missing Ratio' :all_data_na})
missing_data.head()

Out[33]:
Missing Ratio
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更多的数据工程:

1、有许多特征实际上是类别型的特征,但给出来的是数字。比如MSSubClass,是评价房子种类的一个特征,给出的是10-100的数字,但实际上是类别,所以我们需要将其转化为字符串类别。

#MSSubClass=The building class
all_data['MSSubClass'] = all_data['MSSubClass'].apply(str)


#Changing OverallCond into a categorical variable
all_data['OverallCond'] = all_data['OverallCond'].astype(str)


#Year and month sold are transformed into categorical features.
all_data['YrSold'] = all_data['YrSold'].astype(str)
all_data['MoSold'] = all_data['MoSold'].astype(str)
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2、接下来 LabelEncoder,对文本类别的特征进行编号。

from sklearn.preprocessing import LabelEncoder
cols = ('FireplaceQu', 'BsmtQual', 'BsmtCond', 'GarageQual', 'GarageCond', 
        'ExterQual', 'ExterCond','HeatingQC', 'PoolQC', 'KitchenQual', 'BsmtFinType1', 
        'BsmtFinType2', 'Functional', 'Fence', 'BsmtExposure', 'GarageFinish', 'LandSlope',
        'LotShape', 'PavedDrive', 'Street', 'Alley', 'CentralAir', 'MSSubClass', 'OverallCond', 
        'YrSold', 'MoSold')
# process columns, apply LabelEncoder to categorical features
for c in cols:
    lbl = LabelEncoder() 
    lbl.fit(list(all_data[c].values)) 
    all_data[c] = lbl.transform(list(all_data[c].values))

# shape        
print('Shape all_data: {}'.format(all_data.shape))
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3、接下来添加一个重要的特征,因为我们实际在购买房子的时候会考虑总面积的大小,但是此数据集中并没有包含此数据。总面积等于地下室面积+1层面积+2层面积。

# Adding total sqfootage feature 
all_data['TotalSF'] = all_data['TotalBsmtSF'] + all_data['1stFlrSF'] + all_data['2ndFlrSF']
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4、我们对房价进行分析,不符合正态分布我们将其log转换,使其符合正态分布。那么偏离正态分布太多的特征我们也对它进行转化:

numeric_feats = all_data.dtypes[all_data.dtypes != "object"].index

# Check the skew of all numerical features
skewed_feats = all_data[numeric_feats].apply(lambda x: skew(x.dropna())).sort_values(ascending=False)
print("\nSkew in numerical features: \n")
skewness = pd.DataFrame({'Skew' :skewed_feats})
skewness.head(10)
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skewness = skewness[abs(skewness) > 0.75]
print("There are {} skewed numerical features to Box Cox transform".format(skewness.shape[0]))

from scipy.special import boxcox1p
skewed_features = skewness.index
lam = 0.15
for feat in skewed_features:
    #all_data[feat] += 1
    all_data[feat] = boxcox1p(all_data[feat], lam)
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5、将类别特征进行哑变量转化:

all_data = pd.get_dummies(all_data)
print(all_data.shape)
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至此,我们的特征工程已经处理完毕。

模型选择

导入库:

from sklearn.linear_model import ElasticNet, Lasso,  BayesianRidge, LassoLarsIC
from sklearn.ensemble import RandomForestRegressor,  GradientBoostingRegressor
from sklearn.kernel_ridge import KernelRidge
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import RobustScaler
from sklearn.base import BaseEstimator, TransformerMixin, RegressorMixin, clone
from sklearn.model_selection import KFold, cross_val_score, train_test_split
from sklearn.metrics import mean_squared_error
import xgboost as xgb
import lightgbm as lgb
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我们使用Sklearn的cross_val_score函数。然而这个函数没有shuffle方法,我们添加了一行代码,为了在交叉验证之前shuffle数据集。

#Validation function
n_folds = 5

def rmsle_cv(model):
    kf = KFold(n_folds, shuffle=True, random_state=42).get_n_splits(train.values)
    rmse= np.sqrt(-cross_val_score(model, train.values, y_train, scoring="neg_mean_squared_error", cv = kf))
    return(rmse)
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Score的方法为MSE,求出几个模型的Baseline:

LASSO Regression :
This model may be very sensitive to outliers. So we need to made it more robust on them. For that we use the sklearn's Robustscaler() method on pipeline

In [43]:
lasso = make_pipeline(RobustScaler(), Lasso(alpha =0.0005, random_state=1))
Elastic Net Regression :
again made robust to outliers

In [44]:
ENet = make_pipeline(RobustScaler(), ElasticNet(alpha=0.0005, l1_ratio=.9, random_state=3))
Kernel Ridge Regression :
In [45]:
KRR = KernelRidge(alpha=0.6, kernel='polynomial', degree=2, coef0=2.5)
Gradient Boosting Regression :
With huber loss that makes it robust to outliers

In [46]:
GBoost = GradientBoostingRegressor(n_estimators=3000, learning_rate=0.05,
                                   max_depth=4, max_features='sqrt',
                                   min_samples_leaf=15, min_samples_split=10, 
                                   loss='huber', random_state =5)
XGBoost :
In [47]:
model_xgb = xgb.XGBRegressor(colsample_bytree=0.4603, gamma=0.0468, 
                             learning_rate=0.05, max_depth=3, 
                             min_child_weight=1.7817, n_estimators=2200,
                             reg_alpha=0.4640, reg_lambda=0.8571,
                             subsample=0.5213, silent=1,
                             random_state =7, nthread = -1)
LightGBM :
In [48]:
model_lgb = lgb.LGBMRegressor(objective='regression',num_leaves=5,
                              learning_rate=0.05, n_estimators=720,
                              max_bin = 55, bagging_fraction = 0.8,
                              bagging_freq = 5, feature_fraction = 0.2319,
                              feature_fraction_seed=9, bagging_seed=9,
                              min_data_in_leaf =6, min_sum_hessian_in_leaf = 11)
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我们来看一下各个模型的得分:

score = rmsle_cv(lasso)
print("\nLasso score: {:.4f} ({:.4f})\n".format(score.mean(), score.std()))
Lasso score: 0.1115 (0.0074)

In [50]:
score = rmsle_cv(ENet)
print("ElasticNet score: {:.4f} ({:.4f})\n".format(score.mean(), score.std()))
ElasticNet score: 0.1116 (0.0074)

In [51]:
score = rmsle_cv(KRR)
print("Kernel Ridge score: {:.4f} ({:.4f})\n".format(score.mean(), score.std()))
Kernel Ridge score: 0.1153 (0.0075)

In [52]:
score = rmsle_cv(GBoost)
print("Gradient Boosting score: {:.4f} ({:.4f})\n".format(score.mean(), score.std()))
Gradient Boosting score: 0.1177 (0.0080)

In [53]:
score = rmsle_cv(model_xgb)
print("Xgboost score: {:.4f} ({:.4f})\n".format(score.mean(), score.std()))
Xgboost score: 0.1161 (0.0079)

In [54]:
score = rmsle_cv(model_lgb)
print("LGBM score: {:.4f} ({:.4f})\n" .format(score.mean(), score.std()))
LGBM score: 0.1148 (0.0069)
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模型融合

Stacking模型融合:

Average-Stacking:

我们从最简单的平均基本模型的Stacking方法开始模型融合。建立一个新的类来扩展scikit模型融合方法:

class AveragingModels(BaseEstimator, RegressorMixin, TransformerMixin):
    def __init__(self, models):
        self.models = models

    # we define clones of the original models to fit the data in
    def fit(self, X, y):
        self.models_ = [clone(x) for x in self.models]

        # Train cloned base models
        for model in self.models_:
            model.fit(X, y)

        return self

    #Now we do the predictions for cloned models and average them
    def predict(self, X):
        predictions = np.column_stack([
            model.predict(X) for model in self.models_
        ])
        return np.mean(predictions, axis=1)  
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平均四个模型ENet,GBoost,KRR和lasso。利用上面重写的方法,我们可以轻松地添加更多的模型:

averaged_models = AveragingModels(models = (ENet, GBoost, KRR, lasso))

score = rmsle_cv(averaged_models)
print(" Averaged base models score: {:.4f} ({:.4f})\n".format(score.mean(), score.std()))

 Averaged base models score: 0.1091 (0.0075)
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可以看到,均方误差比单独使用几个模型有所下降,这还是最简单的模型融合,这鼓励我们向着更深的模型融合的方向继续努力。

Meta-model Stacking:

算法:

1、将整个训练集分解成两个不相交的集合(这里是train和.holdout)。
2、在第一部分(train)上训练几个基本模型。
3、在第二个部分(holdout)上测试这些基本模型。
4、使用(3)中的预测(称为 out-of-fold 预测)作为输入,并将正确的标签(目标变量)作为输出来训练更高层次的学习模型称为元模型。

前三个步骤是迭代完成的。例如,如果我们采取5倍的fold,我们首先将训练数据分成5次。然后我们会做5次迭代。在每次迭代中,我们训练每个基础模型4倍,并预测剩余的fold(holdout fold)。

这里写图片描述

class StackingAveragedModels(BaseEstimator, RegressorMixin, TransformerMixin):
    def __init__(self, base_models, meta_model, n_folds=5):
        self.base_models = base_models
        self.meta_model = meta_model
        self.n_folds = n_folds

    # We again fit the data on clones of the original models
    def fit(self, X, y):
        self.base_models_ = [list() for x in self.base_models]
        self.meta_model_ = clone(self.meta_model)
        kfold = KFold(n_splits=self.n_folds, shuffle=True, random_state=156)

        # Train cloned base models then create out-of-fold predictions
        # that are needed to train the cloned meta-model
        out_of_fold_predictions = np.zeros((X.shape[0], len(self.base_models)))
        for i, model in enumerate(self.base_models):
            for train_index, holdout_index in kfold.split(X, y):
                instance = clone(model)
                self.base_models_[i].append(instance)
                instance.fit(X[train_index], y[train_index])
                y_pred = instance.predict(X[holdout_index])
                out_of_fold_predictions[holdout_index, i] = y_pred

        # Now train the cloned  meta-model using the out-of-fold predictions as new feature
        self.meta_model_.fit(out_of_fold_predictions, y)
        return self

    #Do the predictions of all base models on the test data and use the averaged predictions as 
    #meta-features for the final prediction which is done by the meta-model
    def predict(self, X):
        meta_features = np.column_stack([
            np.column_stack([model.predict(X) for model in base_models]).mean(axis=1)
            for base_models in self.base_models_ ])
        return self.meta_model_.predict(meta_features)
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测试Meta-model Stacking结果:

tacked_averaged_models = StackingAveragedModels(base_models = (ENet, GBoost, KRR),
                                                 meta_model = lasso)

score = rmsle_cv(stacked_averaged_models)
print("Stacking Averaged models score: {:.4f} ({:.4f})".format(score.mean(), score.std()))

Stacking Averaged models score: 0.1085 (0.0074)
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我们得到了一个更好的结果!

然后为了得到最后提交的结果,我们将StackedRegressor、XGBoost和LightGBM进行融合,得到rmsle的结果。

def rmsle(y, y_pred):
    return np.sqrt(mean_squared_error(y, y_pred))
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最终的训练和预测:


StackedRegressor:

In [60]:
stacked_averaged_models.fit(train.values, y_train)
stacked_train_pred = stacked_averaged_models.predict(train.values)
stacked_pred = np.expm1(stacked_averaged_models.predict(test.values))
print(rmsle(y_train, stacked_train_pred))
0.0781571937916
XGBoost:

In [61]:
model_xgb.fit(train, y_train)
xgb_train_pred = model_xgb.predict(train)
xgb_pred = np.expm1(model_xgb.predict(test))
print(rmsle(y_train, xgb_train_pred))
0.0785165142425
LightGBM:

In [62]:
model_lgb.fit(train, y_train)
lgb_train_pred = model_lgb.predict(train)
lgb_pred = np.expm1(model_lgb.predict(test.values))
print(rmsle(y_train, lgb_train_pred))
0.0719406222196
In [63]:
'''RMSE on the entire Train data when averaging'''

print('RMSLE score on train data:')
print(rmsle(y_train,stacked_train_pred*0.70 +
               xgb_train_pred*0.15 + lgb_train_pred*0.15 ))
RMSLE score on train data:
0.0752452023077
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将三者进行融合,然后得到Ensemble prediction:

ensemble = stacked_pred*0.70 + xgb_pred*0.15 + lgb_pred*0.15
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得到待提交的CSV文件:

sub = pd.DataFrame()
sub['Id'] = test_ID
sub['SalePrice'] = ensemble
sub.to_csv('submission.csv',index=False)
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提交结果

共有2408提交结果,排名191,还需要继续探索数据,探索模型融合的方法。
这里写图片描述

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