NO.89——應用Xgboost進行保險賠償預測

我的github地址.

1 數據分析

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LogisticRegression
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import roc_auc_score as AUC
from sklearn.metrics import mean_absolute_error
from sklearn.decomposition import PCA
from sklearn.preprocessing import LabelEncoder, LabelBinarizer
from sklearn.model_selection import cross_val_score

from scipy import stats
import seaborn as sns
from copy import deepcopy

%matplotlib inline

# This may raise an exception in earlier versions of Jupyter
%config InlineBackend.figure_format = 'retina'

1.1 先瞅瞅數據長啥樣

train = pd.read_csv('train.csv')
test = pd.read_csv('test.csv')
train.shape

(188318, 132)

print ('First 20 columns:', list(train.columns[:20]))

print ('Last 20 columns:', list(train.columns[-20:]))

First 20 columns: [‘id’, ‘cat1’, ‘cat2’, ‘cat3’, ‘cat4’, ‘cat5’, ‘cat6’, ‘cat7’, ‘cat8’, ‘cat9’, ‘cat10’, ‘cat11’, ‘cat12’, ‘cat13’, ‘cat14’, ‘cat15’, ‘cat16’, ‘cat17’, ‘cat18’, ‘cat19’]
Last 20 columns: [‘cat112’, ‘cat113’, ‘cat114’, ‘cat115’, ‘cat116’, ‘cont1’, ‘cont2’, ‘cont3’, ‘cont4’, ‘cont5’, ‘cont6’, ‘cont7’, ‘cont8’, ‘cont9’, ‘cont10’, ‘cont11’, ‘cont12’, ‘cont13’, ‘cont14’, ‘loss’]

我們看到，大概有116個種類屬性（如它們的名字所示）和14個連續（數字）屬性。 此外，還有ID和賠償。總計爲132列。

train.head(5)

train.describe()

正如我們看到的，所有的連續的功能已被縮放到[0,1]區間，均值基本爲0.5。其實數據已經被預處理了，我們拿到的是特徵數據。

查看缺失值

pd.isnull(train).values.any()

False

1.2 連續變量和分類變量

train.info()

<class ‘pandas.core.frame.DataFrame’>
RangeIndex: 188318 entries, 0 to 188317
Columns: 132 entries, id to loss
dtypes: float64(15), int64(1), object(116)
memory usage: 189.7+ MB
在這裏，float64(15)是14個連續變量+loss值；int64(1)是ID；
object(116)是分類變量。

cat_features = list(train.select_dtypes(include=['object']).columns)
print ("Categorical: {} features".format(len(cat_features)))

Categorical: 116 features

cont_features = [cont for cont in list(train.select_dtypes(
                 include=['float64', 'int64']).columns) if cont not in ['loss', 'id']]
print ("Continuous: {} features".format(len(cont_features)))

Continuous: 14 features

id_col = list(train.select_dtypes(include=['int64']).columns)
print ("A column of int64: {}".format(id_col))

A column of int64: [‘id’]

1.3 分類變量中屬性的個數

cat_uniques = []
for cat in cat_features:
    cat_uniques.append(len(train[cat].unique()))
    
uniq_values_in_categories = pd.DataFrame.from_items([('cat_name', cat_features), ('unique_values', cat_uniques)])

uniq_values_in_categories.head()

1.4 賠償值

plt.figure(figsize=(16,8))
plt.plot(train['id'], train['loss'])
plt.title('Loss values per id')
plt.xlabel('id')
plt.ylabel('loss')
plt.legend()
plt.show()

損失值中有幾個顯著的峯值表示嚴重事故。這樣的數據分佈，使得這個功能非常扭曲導致的迴歸表現不佳。

基本上，偏度度量了實值隨機變量的均值分佈的不對稱性。讓我們計算損失的偏度：

stats.mstats.skew(train['loss']).data

array(3.79492815)

偏度大於1，表示數據確實是傾斜的

對數據進行對數變換通常可以改善傾斜，可以使用np.log

stats.mstats.skew(np.log(train['loss'])).data

array(0.0929738)

fig, (ax1, ax2) = plt.subplots(1,2)
fig.set_size_inches(16,5)
ax1.hist(train['loss'], bins=50)
ax1.set_title('Train Loss target histogram')
ax1.grid(True)
ax2.hist(np.log(train['loss']), bins=50, color='g')
ax2.set_title('Train Log Loss target histogram')
ax2.grid(True)
plt.show()

1.5 連續變量特徵

train[cont_features].hist(bins=50, figsize=(16,12))

1.6 特徵之間的相關性

plt.subplots(figsize=(16,9))
correlation_mat = train[cont_features].corr()
sns.heatmap(correlation_mat, annot=True)

2 Xgboost

import xgboost as xgb
import pandas as pd
import numpy as np
import pickle
import sys
import matplotlib.pyplot as plt
from sklearn.metrics import mean_absolute_error, make_scorer
from sklearn.preprocessing import StandardScaler
from scipy.sparse import csr_matrix, hstack
from sklearn.model_selection import KFold, train_test_split, GridSearchCV
from xgboost import XGBRegressor

import warnings
warnings.filterwarnings('ignore')

%matplotlib inline

# This may raise an exception in earlier versions of Jupyter
%config InlineBackend.figure_format = 'retina'

2.1 數據預處理

train = pd.read_csv('train.csv')

做對數變換

train['log_loss'] = np.log(train['loss'])

數據分成連續和離散特徵

features = [x for x in train.columns if x not in ['id','loss', 'log_loss']]
#cat列 ,categorical特徵
cat_features = [x for x in train.select_dtypes(
        include=['object']).columns if x not in ['id','loss', 'log_loss']]
#cont列 ，數字特徵
num_features = [x for x in train.select_dtypes(
        exclude=['object']).columns if x not in ['id','loss', 'log_loss']]

print ("Categorical features:", len(cat_features))
print ("Numerical features:", len(num_features))

Categorical features: 116
Numerical features: 14

給分類變量進行編碼

ntrain = train.shape[0]

train_x = train[features]
train_y = train['log_loss']

for c in range(len(cat_features)):
    train_x[cat_features[c]] = train_x[cat_features[c]].astype('category').cat.codes #.cat.codes將分類變量用數字進行編碼
    
print ("Xtrain:", train_x.shape)
print ("ytrain:", train_y.shape)

Xtrain: (188318, 130)
ytrain: (188318,)

2.2 簡單的Xgboost模型

首先，我們訓練一個基本的xgboost模型，然後進行參數調節通過交叉驗證來觀察結果的變換，使用平均絕對誤差來衡量

mean_absolute_error(np.exp(y), np.exp(yhat))。

xgboost 自定義了一個數據矩陣類 DMatrix，會在訓練開始時進行一遍預處理，從而提高之後每次迭代的效率

def xg_eval_mae(yhat, dtrain):
    y = dtrain.get_label()
    return 'mae', mean_absolute_error(np.exp(y), np.exp(yhat))

Model

dtrain = xgb.DMatrix(train_x, train_y)

Xgboost參數

• ‘booster’:‘gbtree’。用梯度提升的決策樹進行節點分裂
• ‘objective’: ‘multi:softmax’, 多分類的問題。損失函數，有分類，有迴歸
• ‘num_class’:10, 類別數，與 multisoftmax 並用
• ‘gamma’:損失下降多少才進行分裂
• ‘max_depth’:12, 構建樹的深度，越大越容易過擬合
• ‘lambda’:2, 控制模型複雜度的權重值的L2正則化項參數，參數越大，模型越不容易過擬合。
• ‘subsample’:0.7, 隨機採樣訓練樣本（對樣本採樣）
• ‘colsample_bytree’:0.7, 生成樹時進行的列採樣（對特徵採樣）
• ‘min_child_weight’:3, 孩子節點中最小的樣本權重和。如果一個葉子節點的樣本權重和小於min_child_weight則拆分過程結束
• ‘silent’:0 ,設置成1則沒有運行信息輸出，最好是設置爲0.
• ‘eta’: 0.007, 如同學習率，串行添加樹，新加進來的樹貢獻佔比多少。經驗上講增大樹的數量，降低學習率
• ‘seed’:1000,
• ‘nthread’:7, cpu 線程數

xgb_params = {
    'seed': 0,
    'eta': 0.1,
    'colsample_bytree': 0.5,
    'silent': 1,
    'subsample': 0.5,
    'objective': 'reg:linear',
    'max_depth': 5,
    'min_child_weight': 3
}

使用交叉驗證

%%time

bst_cv1 = xgb.cv(xgb_params, dtrain, num_boost_round=50, nfold=3, seed=0, 
                feval=xg_eval_mae, maximize=False, early_stopping_rounds=10)

print ('CV score:', bst_cv1.iloc[-1,:]['test-mae-mean'])   #[-1,:]取最後一個元素

CV score: 1220.054769
CPU times: user 2min 24s, sys: 1.54 s, total: 2min 25s
Wall time: 2min 26s
我們得到了第一個基準結果：MAE＝1218.9

plt.figure()
bst_cv1[['train-mae-mean', 'test-mae-mean']].plot()

2.3 第一個基礎模型

在上邊的樹模型中：

• 沒有發生過擬合
• 只建立了50個樹模型

%%time
#建立100個樹模型
bst_cv2 = xgb.cv(xgb_params, dtrain, num_boost_round=100, 
                nfold=3, seed=0, feval=xg_eval_mae, maximize=False, 
                early_stopping_rounds=10)

print ('CV score:', bst_cv2.iloc[-1,:]['test-mae-mean'])

CV score: 1171.2875569999999
CPU times: user 4min 47s, sys: 2.05 s, total: 4min 49s
Wall time: 4min 51s

fig, (ax1, ax2) = plt.subplots(1,2)
fig.set_size_inches(16,4)
#100顆樹
ax1.set_title('100 rounds of training')
ax1.set_xlabel('Rounds')
ax1.set_ylabel('Loss')
ax1.grid(True)
ax1.plot(bst_cv2[['train-mae-mean', 'test-mae-mean']])
ax1.legend(['Training Loss', 'Test Loss'])
#後60顆樹
ax2.set_title('60 last rounds of training')
ax2.set_xlabel('Rounds')
ax2.set_ylabel('Loss')
ax2.grid(True)
ax2.plot(bst_cv2.iloc[40:][['train-mae-mean', 'test-mae-mean']])
ax2.legend(['Training Loss', 'Test Loss'])

有那麼一丁丁過擬合，現在還沒多大事

我們得到了新的紀錄 MAE = 1171.77 比第一次的要好 (1218.9). 接下來我們要改變其他參數了。

2.4 Xgboost參數調節

• Step 1: 選擇一組初始參數
• Step 2: 改變 max_depth 和 min_child_weight.
• Step 3: 調節 gamma 降低模型過擬合風險.
• Step 4: 調節 subsample 和 colsample_bytree 改變數據採樣策略.
• Step 5: 調節學習率 eta.

class XGBoostRegressor(object):
    def __init__(self, **kwargs):
        self.params = kwargs
        if 'num_boost_round' in self.params:
            self.num_boost_round = self.params['num_boost_round']
        self.params.update({'silent': 1, 'objective': 'reg:linear', 'seed': 0})
    #訓練模型    
    def fit(self, x_train, y_train):
        dtrain = xgb.DMatrix(x_train, y_train)
        self.bst = xgb.train(params=self.params, dtrain=dtrain, num_boost_round=self.num_boost_round,
                             feval=xg_eval_mae, maximize=False)
        
    def predict(self, x_pred):
        dpred = xgb.DMatrix(x_pred)
        return self.bst.predict(dpred)
    
    def kfold(self, x_train, y_train, nfold=5):
        dtrain = xgb.DMatrix(x_train, y_train)
        cv_rounds = xgb.cv(params=self.params, dtrain=dtrain, num_boost_round=self.num_boost_round,
                           nfold=nfold, feval=xg_eval_mae, maximize=False, early_stopping_rounds=10)
        return cv_rounds.iloc[-1,:]
    
    def plot_feature_importances(self):
        feat_imp = pd.Series(self.bst.get_fscore()).sort_values(ascending=False)
        feat_imp.plot(title='Feature Importances')
        plt.ylabel('Feature Importance Score')
        
    def get_params(self, deep=True):
        return self.params
 
    def set_params(self, **params):
        self.params.update(params)
        return self

#評估指標
def mae_score(y_true, y_pred):
    return mean_absolute_error(np.exp(y_true), np.exp(y_pred))

mae_scorer = make_scorer(mae_score, greater_is_better=False)  #make_scorer

bst = XGBoostRegressor(eta=0.1, colsample_bytree=0.5, subsample=0.5, 
                       max_depth=5, min_child_weight=3, num_boost_round=50)

bst.kfold(train_x, train_y, nfold=5)

test-mae-mean 1218.528027
test-mae-std 10.423910
test-rmse-mean 0.562570
test-rmse-std 0.002914
train-mae-mean 1209.757422
train-mae-std 2.306814
train-rmse-mean 0.558842
train-rmse-std 0.000475
Name: 49, dtype: float64

Step 1: 學習率與樹個數

Step 2: 樹的深度與節點權重
這些參數對xgboost性能影響最大，因此，他們應該調整第一。我們簡要地概述它們：

• max_depth: 樹的最大深度。增加這個值會使模型更加複雜，也容易出現過擬合，深度3-10是合理的。
• min_child_weight: 正則化參數. 如果樹分區中的實例權重小於定義的總和，則停止樹構建過程。

xgb_param_grid = {'max_depth': list(range(4,9)), 'min_child_weight': list((1,3,6))}
xgb_param_grid['max_depth']

%%time
 
grid = GridSearchCV(XGBoostRegressor(eta=0.1, num_boost_round=50, colsample_bytree=0.5, subsample=0.5),
                param_grid=xgb_param_grid, cv=5, scoring=mae_scorer)

grid.fit(train_x, train_y.values)

grid.cv_results_, grid.best_params_, grid.best_score_

網格搜索發現的最佳結果:

{‘max_depth’: 8, ‘min_child_weight’: 6},
-1187.9597499123447)

設置成負的值是因爲要找大的值

Step 3: 調節 gamma去降低過擬合風險

%%time

xgb_param_grid = {'gamma':[ 0.1 * i for i in range(0,5)]}

grid = GridSearchCV(XGBoostRegressor(eta=0.1, num_boost_round=50, max_depth=8, min_child_weight=6,
                                        colsample_bytree=0.5, subsample=0.5),
                    param_grid=xgb_param_grid, cv=5, scoring=mae_scorer)

grid.fit(train_x, train_y.values)

grid.grid_scores_, grid.best_params_, grid.best_score_

([mean: -1187.95975, std: 6.71340, params: {‘gamma’: 0.0},
mean: -1187.67788, std: 6.44332, params: {‘gamma’: 0.1},
mean: -1187.66616, std: 6.75004, params: {‘gamma’: 0.2},
mean: -1187.21835, std: 7.06771, params: {‘gamma’: 0.30000000000000004},
mean: -1188.35004, std: 6.50057, params: {‘gamma’: 0.4}],
{‘gamma’: 0.30000000000000004},
-1187.2183540791846)

我們選擇使用偏小一些的 gamma.

Step 4: 調節樣本採樣方式 subsample 和 colsample_bytree

%%time

xgb_param_grid = {'subsample':[ 0.1 * i for i in range(6,9)],
                      'colsample_bytree':[ 0.1 * i for i in range(6,9)]}


grid = GridSearchCV(XGBoostRegressor(eta=0.1, gamma=0.2, num_boost_round=50, max_depth=8, min_child_weight=6),
                    param_grid=xgb_param_grid, cv=5, scoring=mae_scorer)
grid.fit(train_x, train_y.values)

grid.grid_scores_, grid.best_params_, grid.best_score_

([mean: -1185.67108, std: 5.40097, params: {‘colsample_bytree’: 0.6000000000000001, ‘subsample’: 0.6000000000000001},
mean: -1184.90641, std: 5.61239, params: {‘colsample_bytree’: 0.6000000000000001, ‘subsample’: 0.7000000000000001},
mean: -1183.73767, std: 6.15639, params: {‘colsample_bytree’: 0.6000000000000001, ‘subsample’: 0.8},
mean: -1185.09329, std: 7.04215, params: {‘colsample_bytree’: 0.7000000000000001, ‘subsample’: 0.6000000000000001},
mean: -1184.36149, std: 5.71298, params: {‘colsample_bytree’: 0.7000000000000001, ‘subsample’: 0.7000000000000001},
mean: -1183.83446, std: 6.24654, params: {‘colsample_bytree’: 0.7000000000000001, ‘subsample’: 0.8},
mean: -1184.43055, std: 6.68009, params: {‘colsample_bytree’: 0.8, ‘subsample’: 0.6000000000000001},
mean: -1183.33878, std: 5.74989, params: {‘colsample_bytree’: 0.8, ‘subsample’: 0.7000000000000001},
mean: -1182.93099, std: 5.75849, params: {‘colsample_bytree’: 0.8, ‘subsample’: 0.8}],
{‘colsample_bytree’: 0.8, ‘subsample’: 0.8},
-1182.9309918891634)

_, scores =  convert_grid_scores(grid.grid_scores_)
scores = scores.reshape(3,3)

plt.figure(figsize=(10,5))
cp = plt.contourf(xgb_param_grid['subsample'], xgb_param_grid['colsample_bytree'], scores, cmap='BrBG')
plt.colorbar(cp)
plt.title('Subsampling params tuning')
plt.annotate('Optimum', xy=(0.895, 0.6), xytext=(0.8, 0.695), arrowprops=dict(facecolor='black'))
plt.xlabel('subsample')
plt.ylabel('colsample_bytree')
plt.grid(True)
plt.show()

在當前的預訓練模式的具體案例，我得到了下面的結果：

`{‘colsample_bytree’: 0.8, ‘subsample’: 0.8}, -1182.9309918891634)

Step 5: 減小學習率並增大樹個數

參數優化的最後一步是降低學習速度，同時增加更多的估計量。

1、首先我們迭代50顆樹

%%time
    
xgb_param_grid = {'eta':[0.5,0.4,0.3,0.2,0.1,0.075,0.05,0.04,0.03]}
grid = GridSearchCV(XGBoostRegressor(num_boost_round=50, gamma=0.2, max_depth=8, min_child_weight=6,
                                        colsample_bytree=0.6, subsample=0.9),
                    param_grid=xgb_param_grid, cv=5, scoring=mae_scorer)

grid.fit(train_x, train_y.values)

grid.grid_scores_, grid.best_params_, grid.best_score_

([mean: -1205.85372, std: 3.46146, params: {‘eta’: 0.5},
mean: -1185.32847, std: 4.87321, params: {‘eta’: 0.4},
mean: -1170.00284, std: 4.76399, params: {‘eta’: 0.3},
mean: -1160.97363, std: 6.05830, params: {‘eta’: 0.2},
mean: -1183.66720, std: 6.69439, params: {‘eta’: 0.1},
mean: -1266.12628, std: 7.26130, params: {‘eta’: 0.075},
mean: -1709.15130, std: 8.19994, params: {‘eta’: 0.05},
mean: -2104.42708, std: 8.02827, params: {‘eta’: 0.04},
mean: -2545.97334, std: 7.76440, params: {‘eta’: 0.03}],
{‘eta’: 0.2},
-1160.9736284869114)

eta, y = convert_grid_scores(grid.grid_scores_)
plt.figure(figsize=(10,4))
plt.title('MAE and ETA, 50 trees')
plt.xlabel('eta')
plt.ylabel('score')
plt.plot(eta, -y)
plt.grid(True)
plt.show()

{‘eta’: 0.2}, -1160.9736284869114 是目前最好的結果

2、現在我們將樹增大到100個

xgb_param_grid = {'eta':[0.5,0.4,0.3,0.2,0.1,0.075,0.05,0.04,0.03]}
grid = GridSearchCV(XGBoostRegressor(num_boost_round=100, gamma=0.2, max_depth=8, min_child_weight=6,
                                        colsample_bytree=0.6, subsample=0.9),
                    param_grid=xgb_param_grid, cv=5, scoring=mae_scorer)

grid.fit(train_x, train_y.values)

grid.grid_scores_, grid.best_params_, grid.best_score_

([mean: -1231.04517, std: 5.41136, params: {‘eta’: 0.5},
mean: -1201.31398, std: 4.75456, params: {‘eta’: 0.4},
mean: -1177.86344, std: 3.67324, params: {‘eta’: 0.3},
mean: -1160.48853, std: 5.65336, params: {‘eta’: 0.2},
mean: -1152.24715, std: 5.85286, params: {‘eta’: 0.1},
mean: -1156.75829, std: 5.30250, params: {‘eta’: 0.075},
mean: -1184.88913, std: 6.08852, params: {‘eta’: 0.05},
mean: -1243.60808, std: 7.40326, params: {‘eta’: 0.04},
mean: -1467.04736, std: 8.70704, params: {‘eta’: 0.03}],
{‘eta’: 0.1},
-1152.2471498726127)

eta, y = convert_grid_scores(grid.grid_scores_)
plt.figure(figsize=(10,4))
plt.title('MAE and ETA, 100 trees')
plt.xlabel('eta')
plt.ylabel('score')
plt.plot(eta, -y)
plt.grid(True)
plt.show()

學習率低一些的效果更好

3、繼續增加樹的個數到200個

%%time

xgb_param_grid = {'eta':[0.09,0.08,0.07,0.06,0.05,0.04]}
grid = GridSearchCV(XGBoostRegressor(num_boost_round=200, gamma=0.2, max_depth=8, min_child_weight=6,
                                        colsample_bytree=0.6, subsample=0.9),
                    param_grid=xgb_param_grid, cv=5, scoring=mae_scorer)

grid.fit(train_x, train_y.values)

grid.grid_scores_, grid.best_params_, grid.best_score_

([mean: -1148.37246, std: 6.51203, params: {‘eta’: 0.09},
mean: -1146.67343, std: 6.13261, params: {‘eta’: 0.08},
mean: -1145.92359, std: 5.68531, params: {‘eta’: 0.07},
mean: -1147.44050, std: 6.33336, params: {‘eta’: 0.06},
mean: -1147.98062, std: 6.39481, params: {‘eta’: 0.05},
mean: -1153.17886, std: 5.74059, params: {‘eta’: 0.04}],
{‘eta’: 0.07},
-1145.9235944370419)

eta, y = convert_grid_scores(grid.grid_scores_)
plt.figure(figsize=(10,4))
plt.title('MAE and ETA, 200 trees')
plt.xlabel('eta')
plt.ylabel('score')
plt.plot(eta, -y)
plt.grid(True)
plt.show()

3 總結

%%time

# Final XGBoost model


bst = XGBoostRegressor(num_boost_round=200, eta=0.07, gamma=0.2, max_depth=8, min_child_weight=6,
                                        colsample_bytree=0.6, subsample=0.9)
cv = bst.kfold(train_x, train_y, nfold=5)

cv

test-mae-mean 1146.997852
test-mae-std 9.541592
train-mae-mean 1036.557251
train-mae-std 0.974437
Name: 199, dtype: float64

我們看到200棵樹最好的ETA是0.07。正如我們所預料的那樣，ETA和num_boost_round依賴關係不是線性的，但是有些關聯。

們花了相當長的一段時間優化xgboost. 從初始值: 1219.57. 經過調參之後達到 MAE=1171.77.

我們還發現參數之間的關係ETA和num_boost_round：

• 100 trees, eta=0.1: MAE=1152.247
• 200 trees, eta=0.07: MAE=1145.92

`XGBoostRegressor(num_boost_round=200, gamma=0.2, max_depth=8, min_child_weight=6, colsample_bytree=0.6, subsample=0.9, eta=0.07).