分箱、WOE、IV的計算

%matplotlib inline

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt 
import seaborn as sns
import warnings
from scipy import stats
warnings.filterwarnings('ignore')

plt.style.use("seaborn")
plt.rc('font', family='SimHei', size=13)  # 顯示中文
plt.rcParams['axes.unicode_minus'] = False  # 用來正常顯示負

# 載入數據
data = pd.read_csv(r"./cs_training.csv",encoding='gbk')
# 查看數據集
# data.head(10)

# 將特徵名字改爲中文
column={'SeriousDlqin2yrs':'好壞客戶',
        'RevolvingUtilizationOfUnsecuredLines':'可用額度比值',
        'age':'年齡',
        'NumberOfTime30-59DaysPastDueNotWorse':'逾期30-59天筆數',
        'DebtRatio':'負債率',
        'MonthlyIncome':'月收入',
        'NumberOfOpenCreditLinesAndLoans':'信貸數量',
        'NumberOfTimes90DaysLate':'逾期90天筆數',
        'NumberRealEstateLoansOrLines':'固定資產貸款量',
        'NumberOfTime60-89DaysPastDueNotWorse':'逾期60-89天筆數',
        'NumberOfDependents':'家屬數量'}
data.rename(columns=column,inplace=True)
data.head()

	好壞客戶	可用額度比值	年齡	逾期30-59天筆數	負債率	月收入	信貸數量	逾期90天筆數	固定資產貸款量	逾期60-89天筆數	家屬數量
0	1	0.766127	45	2	0.802982	9120.0	13	0	6	0	2.0
1	0	0.957151	40	0	0.121876	2600.0	4	0	0	0	1.0
2	0	0.658180	38	1	0.085113	3042.0	2	1	0	0	0.0
3	0	0.233810	30	0	0.036050	3300.0	5	0	0	0	0.0
4	0	0.907239	49	1	0.024926	63588.0	7	0	1	0	0.0

from sklearn.ensemble import RandomForestRegressor

# 用隨機森林對缺失值預測填充函數
def set_missing(df):
    # 把已有的數值型特徵取出來
    process_df = df.iloc[:,[5,0,1,2,3,4,6,7,8,9]]
    # 分成已知該特徵和未知該特徵兩部分
    # dataframe.values獲取的是dataframe中的數據爲數組array
    known = process_df[process_df['月收入'].notnull()].values
    unknown = process_df[process_df['月收入'].isnull()].values
    # X爲已知月收入的特徵屬性值
    X = known[:, 1:]
    # y爲結果標籤值月收入
    y = known[:, 0]
    # X與y用於訓練隨機森林模型，fit到RandomForestRegressor之中
    rfr = RandomForestRegressor(random_state=0, n_estimators=200,max_depth=3,n_jobs=-1)
    rfr.fit(X,y)
    # 用得到的模型進行未知特徵值預測
    predicted = rfr.predict(unknown[:, 1:]).round(0)
    # 用得到的預測結果填補原缺失數據
    df.loc[df['月收入'].isnull(), '月收入'] = predicted
    return df

# 用隨機森林填補比較多的缺失值
data=set_missing(data)   

# 刪除比較少的缺失值
data=data.dropna()   

# 刪除重複項
data = data.drop_duplicates()    

data.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 145563 entries, 0 to 149999
Data columns (total 11 columns):
好壞客戶          145563 non-null int64
可用額度比值        145563 non-null float64
年齡            145563 non-null int64
逾期30-59天筆數    145563 non-null int64
負債率           145563 non-null float64
月收入           145563 non-null float64
信貸數量          145563 non-null int64
逾期90天筆數       145563 non-null int64
固定資產貸款量       145563 non-null int64
逾期60-89天筆數    145563 non-null int64
家屬數量          145563 non-null float64
dtypes: float64(4), int64(7)
memory usage: 13.3 MB

# 刪除逾期30-59天筆數、逾期90天筆數、逾期60-89天筆數大於80的數據
data = data[data['逾期30-59天筆數'] < 80]
data = data[data['逾期90天筆數'] < 80]
data = data[data['逾期60-89天筆數'] < 80]

data = data[data['年齡'] > 0]

col_list = data.columns.values
col_list

array(['好壞客戶', '可用額度比值', '年齡', '逾期30-59天筆數', '負債率', '月收入', '信貸數量',
       '逾期90天筆數', '固定資產貸款量', '逾期60-89天筆數', '家屬數量'], dtype=object)

new_col_list = []
for i in range(len(col_list)):
    if i != 0 and i != 3 and i != 7 and i != 9:
        new_col_list.append(col_list[i])

# 去除單側99%上部分異常值
for item in new_col_list:
    data = data[data[item] < data[item].quantile(0.99)]
    

import woe.feature_process as fp
import woe.eval as eval

data.columns

Index(['好壞客戶', '可用額度比值', '年齡', '逾期30-59天筆數', '負債率', '月收入', '信貸數量', '逾期90天筆數',
       '固定資產貸款量', '逾期60-89天筆數', '家屬數量'],
      dtype='object')

data.rename(columns={'好壞客戶': 'target'}, inplace=True)

# woe分箱, iv and transform
data_woe = data # 用於存儲所有數據的woe值
civ_list = []
n_positive = sum(data['target'])
n_negtive = len(data) - n_positive
for column in list(data.columns[1:]):
    if data[column].dtypes == 'object':
        civ = fp.proc_woe_discrete(data, column, n_positive, n_negtive, 0.05 * len(data), alpha=0.05)
    else:            
        civ = fp.proc_woe_continuous(data, column, n_positive, n_negtive, 0.05 * len(data), alpha=0.05)
    civ_list.append(civ)
    data_woe[column] = fp.woe_trans(data[column], civ)
    
civ_df = eval.eval_feature_detail(civ_list,'output_feature_detail_0315.csv')
# 刪除iv值過小的變量
iv_thre = 0.001
iv = civ_df[['var_name','iv']].drop_duplicates()
x_columns = iv.var_name[iv.iv > iv_thre]

-------------process continuous variable:可用額度比值-------------
---------------process continuous variable:年齡---------------
-----------process continuous variable:逾期30-59天筆數-----------
--------------process continuous variable:負債率---------------
--------------process continuous variable:月收入---------------
--------------process continuous variable:信貸數量--------------
------------process continuous variable:逾期90天筆數-------------
------------process continuous variable:固定資產貸款量-------------
-----------process continuous variable:逾期60-89天筆數-----------
--------------process continuous variable:家屬數量--------------
可用額度比值
年齡
逾期30-59天筆數
負債率
月收入
信貸數量
逾期90天筆數
固定資產貸款量
逾期60-89天筆數
家屬數量

civ_df

	var_name	split_list	sub_total_sample_num	positive_sample_num	negative_sample_num	sub_total_num_percentage	positive_rate_in_sub_total	woe_list	iv_list	iv
0	可用額度比值	(-INF,0.0]	9352	281	9071	0.071213	0.030047	-0.757463	0.029626	1.097527
1	可用額度比值	(0.0,0.04215617400000002]	29188	365	28823	0.222259	0.012505	-1.652011	0.312454	1.097527
2	可用額度比值	(0.04215617400000002,0.0596119858]	6962	111	6851	0.053014	0.015944	-1.405599	0.059004	1.097527
3	可用額度比值	(0.0596119858,0.13857709429999995]	17901	375	17526	0.136312	0.020949	-1.127495	0.108464	1.097527
4	可用額度比值	(0.13857709429999995,0.21535932080000003]	10113	295	9818	0.077008	0.029170	-0.787977	0.034242	1.097527
5	可用額度比值	(0.21535932080000003,0.30067412204]	8274	296	7978	0.063004	0.035775	-0.577063	0.016386	1.097527
6	可用額度比值	(0.30067412204,0.3974544458]	7510	371	7139	0.057187	0.049401	-0.240106	0.002970	1.097527
7	可用額度比值	(0.3974544458,0.5331554074]	8506	586	7920	0.064771	0.068893	0.113193	0.000872	1.097527
8	可用額度比值	(0.5331554074,0.74050784496]	9985	996	8989	0.076033	0.099750	0.517010	0.025541	1.097527
9	可用額度比值	(0.74050784496,0.90349439404]	7295	1103	6192	0.055550	0.151199	0.991796	0.084555	1.097527
10	可用額度比值	(0.90349439404,+INF)	16238	3360	12878	0.123648	0.206922	1.373441	0.423411	1.097527
0	年齡	(-INF,32.0]	13531	1392	12139	0.103035	0.102875	0.551338	0.039964	0.046040
1	年齡	(32.0,+INF)	117793	6747	111046	0.896965	0.057278	-0.083827	0.006076	0.046040
0	逾期30-59天筆數	(-INF,0.0]	111119	4279	106840	0.846144	0.038508	-0.500593	0.170989	0.606073
1	逾期30-59天筆數	(0.0,+INF)	20205	3860	16345	0.153856	0.191042	1.273765	0.435084	0.606073
0	負債率	(-INF,0.018495376]	10665	466	10199	0.081211	0.043694	-0.368839	0.009420	0.088009
1	負債率	(0.018495376,0.087064379]	8843	577	8266	0.067337	0.065249	0.054956	0.000208	0.088009
2	負債率	(0.087064379,0.138218834]	7533	449	7084	0.057362	0.059604	-0.041551	0.000097	0.088009
3	負債率	(0.138218834,0.191269577]	9148	493	8655	0.069660	0.053892	-0.148363	0.001437	0.088009
4	負債率	(0.191269577,0.229044637]	6898	383	6515	0.052527	0.055523	-0.116807	0.000681	0.088009
5	負債率	(0.229044637,0.26480176767999997]	6780	313	6467	0.051628	0.046165	-0.311244	0.004370	0.088009
6	負債率	(0.26480176767999997,0.33095571454]	12054	618	11436	0.091788	0.051269	-0.201013	0.003398	0.088009
7	負債率	(0.33095571454,0.37664756308]	7551	440	7111	0.057499	0.058270	-0.065603	0.000240	0.088009
8	負債率	(0.37664756308,0.4237495164599999]	6696	406	6290	0.050988	0.060633	-0.023343	0.000028	0.088009
9	負債率	(0.4237495164599999,0.54743575044]	12664	918	11746	0.096433	0.072489	0.167949	0.002929	0.088009
10	負債率	(0.54743575044,0.7263413320000001]	9112	825	8287	0.069386	0.090540	0.409960	0.013976	0.088009
11	負債率	(0.7263413320000001,2.6823588614000204]	9111	1026	8085	0.069378	0.112611	0.652677	0.039439	0.088009
12	負債率	(2.6823588614000204,1009.0]	10925	639	10286	0.083191	0.058490	-0.061614	0.000307	0.088009
13	負債率	(1009.0,+INF)	13344	586	12758	0.101611	0.043915	-0.363574	0.011478	0.088009
0	月收入	(-INF,1159.0]	13281	877	12404	0.101132	0.066034	0.067753	0.000478	0.114078
...	...	...	...	...	...	...	...	...	...	...
7	月收入	(4831.0,5332.68]	7201	470	6731	0.054834	0.065269	0.055274	0.000172	0.114078
8	月收入	(5332.68,5917.0]	7381	432	6949	0.056205	0.058529	-0.060907	0.000203	0.114078
9	月收入	(5917.0,6667.0]	8647	533	8114	0.065845	0.061640	-0.005805	0.000002	0.114078
10	月收入	(6667.0,7916.0]	10306	519	9787	0.078478	0.050359	-0.219886	0.003448	0.114078
11	月收入	(7916.0,8333.0]	7967	327	7640	0.060667	0.041044	-0.434172	0.009484	0.114078
12	月收入	(8333.0,10300.0]	10340	489	9851	0.078737	0.047292	-0.285946	0.005687	0.114078
13	月收入	(10300.0,+INF)	13361	474	12887	0.101741	0.035476	-0.585747	0.027165	0.114078
0	信貸數量	(-INF,3.0]	18632	1864	16768	0.141878	0.100043	0.520272	0.048333	0.067247
1	信貸數量	(3.0,4.0]	10396	620	9776	0.079163	0.059638	-0.040946	0.000130	0.067247
2	信貸數量	(4.0,5.0]	11689	671	11018	0.089009	0.057404	-0.081496	0.000570	0.067247
3	信貸數量	(5.0,6.0]	12373	651	11722	0.094217	0.052615	-0.173693	0.002635	0.067247
4	信貸數量	(6.0,7.0]	12102	629	11473	0.092154	0.051975	-0.186600	0.002958	0.067247
5	信貸數量	(7.0,8.0]	11422	518	10904	0.086976	0.045351	-0.329890	0.008205	0.067247
6	信貸數量	(8.0,9.0]	10219	568	9651	0.077815	0.055583	-0.115675	0.000990	0.067247
7	信貸數量	(9.0,10.0]	8745	488	8257	0.066591	0.055803	-0.111481	0.000788	0.067247
8	信貸數量	(10.0,11.0]	7431	405	7026	0.056585	0.054501	-0.136466	0.000993	0.067247
9	信貸數量	(11.0,13.0]	11199	615	10584	0.085278	0.054916	-0.128456	0.001330	0.067247
10	信貸數量	(13.0,+INF)	17116	1110	16006	0.130334	0.064852	0.048416	0.000312	0.067247
0	逾期90天筆數	(-INF,0.0]	124488	5426	119062	0.947946	0.043587	-0.371422	0.111376	0.800610
1	逾期90天筆數	(0.0,+INF)	6836	2713	4123	0.052054	0.396870	2.298494	0.689234	0.800610
0	固定資產貸款量	(-INF,0.0]	49471	3805	45666	0.376710	0.076914	0.231982	0.022454	0.043142
1	固定資產貸款量	(0.0,1.0]	48153	2429	45724	0.366673	0.050443	-0.218124	0.015867	0.043142
2	固定資產貸款量	(1.0,2.0]	28413	1538	26875	0.216358	0.054130	-0.143694	0.004196	0.043142
3	固定資產貸款量	(2.0,+INF)	5287	367	4920	0.040259	0.069416	0.121318	0.000625	0.043142
0	逾期60-89天筆數	(-INF,0.0]	125162	6053	119109	0.953078	0.048361	-0.262465	0.058584	0.515526
1	逾期60-89天筆數	(0.0,+INF)	6162	2086	4076	0.046922	0.338526	2.047152	0.456942	0.515526
0	家屬數量	(-INF,0.0]	79954	4351	75603	0.608830	0.054419	-0.138070	0.010928	0.028199
1	家屬數量	(0.0,1.0]	24473	1683	22790	0.186356	0.068770	0.111276	0.002423	0.028199
2	家屬數量	(1.0,2.0]	18117	1377	16740	0.137957	0.076006	0.219126	0.007295	0.028199
3	家屬數量	(2.0,3.0]	8780	728	8052	0.066858	0.082916	0.313645	0.007553	0.028199

66 rows × 10 columns

x_columns

0        可用額度比值
0            年齡
0    逾期30-59天筆數
0           負債率
0           月收入
0          信貸數量
0       逾期90天筆數
0       固定資產貸款量
0    逾期60-89天筆數
0          家屬數量
Name: var_name, dtype: object

iv

	var_name	iv
0	可用額度比值	1.097527
0	年齡	0.046040
0	逾期30-59天筆數	0.606073
0	負債率	0.088009
0	月收入	0.114078
0	信貸數量	0.067247
0	逾期90天筆數	0.800610
0	固定資產貸款量	0.043142
0	逾期60-89天筆數	0.515526
0	家屬數量	0.028199

data_woe.head()

	target	可用額度比值	年齡	逾期30-59天筆數	負債率	月收入	信貸數量	逾期90天筆數	固定資產貸款量	逾期60-89天筆數	家屬數量
1	0	1.373441	-0.083827	-0.500593	-0.041551	0.461028	-0.040946	-0.371422	0.231982	-0.262465	0.111276
2	0	0.517010	-0.083827	1.273765	0.054956	0.461028	0.520272	2.298494	0.231982	-0.262465	-0.138070
3	0	-0.577063	0.551338	-0.500593	0.054956	0.461028	-0.081496	-0.371422	0.231982	-0.262465	-0.138070
5	0	-0.787977	-0.083827	-0.500593	-0.065603	0.243014	0.520272	-0.371422	-0.218124	-0.262465	0.111276
7	0	0.991796	-0.083827	-0.500593	-0.116807	0.243014	-0.329890	-0.371422	0.231982	-0.262465	-0.138070

模型建立

信用評分卡模型在國外是一種成熟的預測方法，尤其在信用風險評估以及金融風險控制領域更是得到了比較廣泛的使用，其原理是將模型變量WOE編碼方式離散化之後運用logistic迴歸模型進行的一種二分類變量的廣義線性模型，下面將模型目標標量爲1記爲違約用戶，對於目標變量爲0記爲正常用戶，採用sklearn中LogisticRegression進行建模

from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
# 模型評估
from sklearn.metrics import accuracy_score
from sklearn import metrics
from sklearn.metrics import auc

# 數據提取與數據分割
col_names = data_woe.columns.values
X = data_woe[col_names[1:]]  # 特徵列
y = data_woe[col_names[0]]  # 標籤列
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3,random_state=0)

lr = LogisticRegression(C=1000.0, random_state=0)
result = lr.fit(X_train, y_train)

result

LogisticRegression(C=1000.0, class_weight=None, dual=False, fit_intercept=True,
                   intercept_scaling=1, l1_ratio=None, max_iter=100,
                   multi_class='warn', n_jobs=None, penalty='l2',
                   random_state=0, solver='warn', tol=0.0001, verbose=0,
                   warm_start=False)

# 模型預測
y_pred = lr.predict(X_test)
y_pred

array([0, 0, 0, ..., 0, 0, 0], dtype=int64)

# 預測爲壞的客戶的概率
prob_pred = [round(u[1], 5) for u in lr.predict_proba(X_test)]

# 預測的準確率
accuracy_score(y_test, y_pred)

0.9387532362048835

# 樣本類別不平衡，用PR不好評價，採用ROC曲線
FPR, TPR, thresholds = metrics.roc_curve(y_test, prob_pred, pos_label=1)
metrics.auc(FPR, TPR)

0.8499778184241903

# 畫圖對預測值和實際值進行比較
plt.plot(FPR, TPR, 'b', label='AUC = %0.2f' % metrics.auc(FPR, TPR)) # 生成ROC曲線
plt.legend(loc='lower right')
plt.plot([0, 1], [0, 1], 'r--')
plt.xlim([0, 1])
plt.ylim([0, 1])
plt.ylabel('真正率')
plt.xlabel('假正率')
plt.show()

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從上圖可知，AUC值爲0.85，說明該模型的預測效果還是不錯的，正確率較高

評分卡計算方法

odds爲good用戶概率（p）與bad用戶概率（1-p）的比值

$\operatorname{odds}=\frac{p}{1-p}$

評分卡設定的分值刻度可以通過將分值表示爲比率對數的現行表達式來定義。公式如下：

$score_{總}=A+B{*}\ln(odds)$

常數 A 和 B 通常被稱爲補償和刻度，它們的值可以通過將兩個已知或者假設的分值帶入$score_{總}=A+B{*}\ln(odds)$ 中得到。通常，需要兩個假設：

• 在某個特定的比率設定特定的預期分值$P_{0}$
• 指定比率翻番的分數（PDO，Point-to-Double Odds）

首先，設定比率爲odds的特定點的分值爲$P_{0}$。然後，比率爲 2odds的點分值爲$P_{0}-PDO$，帶入可以得到
$B=\frac{PDO}{\log (2)}$

$A=P_{0}+B \log \left(odds\right)$

import math

# PDO爲比率翻番的分數，P0爲特定比例的預期分值，B爲刻度
PDO = 20
P0 = 600
B = PDO / math.log(2)
B

28.85390081777927

# A爲補償
A = P0 + B * math.log(1 / 60)
A

481.8621880878296

基於Logistic的評分卡構建

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最終，評分卡的分值可以寫成下列形式：

Score$=A-B\left(\beta_{0}+\beta_{1} x_{1}+\cdots+\beta_{p} x_{p}\right)$

變量$x_{1}$,⋯, $x_{p}$爲自變量對應WOE, $\beta_{0}$,⋯,$\beta_{p}$爲邏輯斯蒂迴歸方程的係數

# 邏輯斯蒂迴歸的係數列表
coef_list = list(result.coef_[0])
coef_list.insert(0, result.intercept_[0])

# 計算信用評分
def credit_socre(data, coef): 
    score_list = []
    for i in range(data.shape[0]):
        tmp_score = coef[0]
        for j in range(data.shape[1]):
            tmp_score += data.iat[i, j] * coef[j + 1]
        score = A - B * tmp_score
        score_list.append(score)
    return score_list

score_list = credit_socre(data_woe.iloc[:, 1:], coef_list)

data_woe.insert(11, 'credit_score', score_list)

data_woe.head().append(data_woe.tail())

# 在原始數據中插入信用評分
data.insert(11, 'credit_socre', score_list)

data.head().append(data.tail())