变量分箱是评分卡建模流程中的关键环节,可以说是评分卡的核心环节。合理的分箱可以消除变量的量纲影响,而且能减少异常值等噪声数据的影响,有效避免模型过拟合。此外,分箱可以给模型实现业务上的可解释性,可以说是评分卡的核心了。
下面开始实现评分卡建立中的分箱操作。
首先,变量需要分为数值型变量和类别型变量。对于这两种类型的变量分箱过程中需要注意的点如下:
- 类别型变量
- 如果不超过5个,无需进行分箱;
- 超过5个,有两种方法。一,如果类别很多,可以对其进行bad_rate编码之后划入数值型变量;二,类别不是很多,对其进行降基处理,缩小至5个以内。
- 数值型变量
有无监督和有监督分箱两种方法。无监督分箱有等比分箱、等宽分箱、聚类分箱等。有监督分箱有卡方分箱、最优分箱等等。
num_features = ['int_rate_clean', 'emp_length_clean', 'annual_inc', 'dti', 'delinq_2yrs', 'earliest_cr_to_app',
'inq_last_6mths', \
'mths_since_last_record_clean', 'mths_since_last_delinq_clean', 'open_acc', 'pub_rec', 'total_acc',
'limit_income', 'earliest_cr_to_app']
cat_features = ['home_ownership', 'verification_status', 'desc_clean', 'purpose', 'zip_code', 'addr_state']
一共有14个数值型变量和6个类别型变量。‘zip_code’、'addr_state’两个变量的类别很多,进行bad_rate编码后划入数值型变量。另外4个变量单独进行分箱。
def binning_cate(df,col_list,target):
"""
df:数据集
col_list:变量list集合
target:目标变量的字段名
return:
bin_df :list形式,里面存储每个变量的分箱结果
iv_value:list形式,里面存储每个变量的IV值
"""
total = df[target].count()
bad = df[target].sum()
good = total-bad
all_odds = good*1.0/bad
bin_df =[]
iv_value=[]
for col in col_list:
d1 = df.groupby([col],as_index=True)
d2 = pd.DataFrame()
d2['min_bin'] = d1[col].min()
d2['max_bin'] = d1[col].max()
d2['total'] = d1[target].count()
d2['totalrate'] = d2['total']/total
d2['bad'] = d1[target].sum()
d2['badrate'] = d2['bad']/d2['total']
d2['good'] = d2['total'] - d2['bad']
d2['goodrate'] = d2['good']/d2['total']
d2['badattr'] = d2['bad']/bad
d2['goodattr'] = (d2['total']-d2['bad'])/good
d2['odds'] = d2['good']/d2['bad']
GB_list=[]
for i in d2.odds:
if i>=all_odds:
GB_index = str(round((i/all_odds)*100,0))+str('G')
else:
GB_index = str(round((all_odds/i)*100,0))+str('B')
GB_list.append(GB_index)
d2['GB_index'] = GB_list
d2['woe'] = np.log(d2['badattr']/d2['goodattr'])
d2['bin_iv'] = (d2['badattr']-d2['goodattr'])*d2['woe']
d2['IV'] = d2['bin_iv'].sum()
iv = d2['bin_iv'].sum().round(3)
print('变量名:{}'.format(col))
print('IV:{}'.format(iv))
print('\t')
bin_df.append(d2)
iv_value.append(iv)
return bin_df,iv_value
注意,如果类别型变量的某一箱只有好样本/坏样本,将造成变量的IV值为inf/-inf,此时就需要对变量进行降基处理或者重新分箱。
接着看一下每一箱的明细情况。
IV值一般大于0.01,就可以入模使用。IV值不宜过高,如果过高说明变量的预测能力过强,其实可以单独拿出来作为一条策略。评分卡的变量最好还是弱变量。此外,每一箱的WOE值也不宜大于1,因为大于1说明这一箱至少有65%以上的好坏样本,其实可以单独作为一条规则了。
下面利用条形图将分箱结果可视化展示。
# woe的可视化
def plot_woe(bin_df,hspace=0.4,wspace=0.4,plt_size=None,plt_num=None,x=None,y=None):
"""
bin_df:list形式,里面存储每个变量的分箱结果
hspace :子图之间的间隔(y轴方向)
wspace :子图之间的间隔(x轴方向)
plt_size :图纸的尺寸
plt_num :子图的数量
x :子图矩阵中一行子图的数量
y :子图矩阵中一列子图的数量
return :每个变量的woe变化趋势图
"""
plt.figure(figsize=plt_size)
plt.subplots_adjust(hspace=hspace,wspace=wspace)
for i,df in zip(range(1,plt_num+1,1),bin_df):
col_name = df.index.name
df = df.reset_index()
plt.subplot(x,y,i)
plt.title(col_name)
sns.barplot(data=df,x=col_name,y='woe')
plt.xlabel('')
plt.xticks(rotation=30)
return plt.show()
plot_woe(bin_df_cat,hspace=0.4,wspace=0.4,plt_size=(15,8),plt_num=4,x=2,y=2)
下面对zip_code、addr_state这两个变量进行bad_rate编码,就是将变量的每个类别映射成这个类别的坏样本率,这样就可以将类别型变量转化为数值型变量了。
def BadRateEncoding(df, col, target):
'''
:param df: dataframe containing feature and target
:param col: the feature that needs to be encoded with bad rate, usually categorical type
:param target: good/bad indicator
:return: the assigned bad rate to encode the categorical feature
'''
regroup = BinBadRate(df, col, target, grantRateIndicator=0)[1]
br_dict = regroup[[col,'bad_rate']].set_index([col]).to_dict(orient='index')
for k, v in br_dict.items():
br_dict[k] = v['bad_rate']
badRateEnconding = df[col].map(lambda x: br_dict[x])
return {'encoding':badRateEnconding, 'bad_rate':br_dict}
def BinBadRate(df, col, target, grantRateIndicator=0):
'''
:param df: 需要计算好坏比率的数据集
:param col: 需要计算好坏比率的特征
:param target: 好坏标签
:param grantRateIndicator: 1返回总体的坏样本率,0不返回
:return: 每箱的坏样本率,以及总体的坏样本率(当grantRateIndicator==1时)
'''
total = df.groupby([col])[target].count()
total = pd.DataFrame({'total': total})
bad = df.groupby([col])[target].sum()
bad = pd.DataFrame({'bad': bad})
regroup = total.merge(bad, left_index=True, right_index=True, how='left') # 每箱的坏样本数,总样本数
regroup.reset_index(level=0, inplace=True)
regroup['bad_rate'] = regroup.apply(lambda x: x.bad * 1.0 / x.total, axis=1) # 加上一列坏样本率
dicts = dict(zip(regroup[col],regroup['bad_rate'])) # 每箱对应的坏样本率组成的字典
if grantRateIndicator==0:
return (dicts, regroup)
N = sum(regroup['total'])
B = sum(regroup['bad'])
overallRate = B * 1.0 / N
return (dicts, regroup, overallRate)
# 对zip_code,addr_state进行bad_rate编码
br_encoding_dict = {}
more_value_features=['zip_code','addr_state']
for col in more_value_features:
br_encoding = BadRateEncoding(trainData, col, 'y')
trainData[col + '_br_encoding'] = br_encoding['encoding']
br_encoding_dict[col] = br_encoding['bad_rate']
num_features.append(col + '_br_encoding')
bad_rate编码之后产生两个新的列,将这两列划入数值型变量中一起进行卡方分箱。
# 数值型变量的分箱
# 先用卡方分箱输出变量的分割点
def split_data(df,col,split_num):
"""
df: 原始数据集
col:需要分箱的变量
split_num:分割点的数量
"""
df2 = df.copy()
count = df2.shape[0] # 总样本数
n = math.floor(count/split_num) # 按照分割点数目等分后每组的样本数
split_index = [i*n for i in range(1,split_num)] # 分割点的索引
values = sorted(list(df2[col])) # 对变量的值从小到大进行排序
split_value = [values[i] for i in split_index] # 分割点对应的value
split_value = sorted(list(set(split_value))) # 分割点的value去重排序
return split_value
def assign_group(x,split_bin):
"""
x:变量的value
split_bin:split_data得出的分割点list
"""
n = len(split_bin)
if x<=min(split_bin):
return min(split_bin) # 如果x小于分割点的最小值,则x映射为分割点的最小值
elif x>max(split_bin): # 如果x大于分割点的最大值,则x映射为分割点的最大值
return 10e10
else:
for i in range(n-1):
if split_bin[i]<x<=split_bin[i+1]:# 如果x在两个分割点之间,则x映射为分割点较大的值
return split_bin[i+1]
def bin_bad_rate(df,col,target,grantRateIndicator=0):
"""
df:原始数据集
col:原始变量/变量映射后的字段
target:目标变量的字段
grantRateIndicator:是否输出总体的违约率
"""
total = df.groupby([col])[target].count()
bad = df.groupby([col])[target].sum()
total_df = pd.DataFrame({'total':total})
bad_df = pd.DataFrame({'bad':bad})
regroup = pd.merge(total_df,bad_df,left_index=True,right_index=True,how='left')
regroup = regroup.reset_index()
regroup['bad_rate'] = regroup['bad']/regroup['total'] # 计算根据col分组后每组的违约率
dict_bad = dict(zip(regroup[col],regroup['bad_rate'])) # 转为字典形式
if grantRateIndicator==0:
return (dict_bad,regroup)
total_all= df.shape[0]
bad_all = df[target].sum()
all_bad_rate = bad_all/total_all # 计算总体的违约率
return (dict_bad,regroup,all_bad_rate)
def cal_chi2(df,all_bad_rate):
"""
df:bin_bad_rate得出的regroup
all_bad_rate:bin_bad_rate得出的总体违约率
"""
df2 = df.copy()
df2['expected'] = df2['total']*all_bad_rate # 计算每组的坏用户期望数量
combined = zip(df2['expected'],df2['bad']) # 遍历每组的坏用户期望数量和实际数量
chi = [(i[0]-i[1])**2/i[0] for i in combined] # 计算每组的卡方值
chi2 = sum(chi) # 计算总的卡方值
return chi2
def assign_bin(x,cutoffpoints):
"""
x:变量的value
cutoffpoints:分箱的切割点
"""
bin_num = len(cutoffpoints)+1 # 箱体个数
if x<=cutoffpoints[0]: # 如果x小于最小的cutoff点,则映射为Bin 0
return 'Bin 0'
elif x>cutoffpoints[-1]: # 如果x大于最大的cutoff点,则映射为Bin(bin_num-1)
return 'Bin {}'.format(bin_num-1)
else:
for i in range(0,bin_num-1):
if cutoffpoints[i]<x<=cutoffpoints[i+1]: # 如果x在两个cutoff点之间,则x映射为Bin(i+1)
return 'Bin {}'.format(i+1)
def ChiMerge(df,col,target,max_bin=5,min_binpct=0):
col_unique = sorted(list(set(df[col]))) # 变量的唯一值并排序
n = len(col_unique) # 变量唯一值得个数
df2 = df.copy()
if n>100: # 如果变量的唯一值数目超过100,则将通过split_data和assign_group将x映射为split对应的value
split_col = split_data(df2,col,100) # 通过这个目的将变量的唯一值数目人为设定为100
df2['col_map'] = df2[col].map(lambda x:assign_group(x,split_col))
else:
df2['col_map'] = df2[col] # 变量的唯一值数目没有超过100,则不用做映射
# 生成dict_bad,regroup,all_bad_rate的元组
(dict_bad,regroup,all_bad_rate) = bin_bad_rate(df2,'col_map',target,grantRateIndicator=1)
col_map_unique = sorted(list(set(df2['col_map']))) # 对变量映射后的value进行去重排序
group_interval = [[i] for i in col_map_unique] # 对col_map_unique中每个值创建list并存储在group_interval中
while (len(group_interval)>max_bin): # 当group_interval的长度大于max_bin时,执行while循环
chi_list=[]
for i in range(len(group_interval)-1):
temp_group = group_interval[i]+group_interval[i+1] # temp_group 为生成的区间,list形式,例如[1,3]
chi_df = regroup[regroup['col_map'].isin(temp_group)]
chi_value = cal_chi2(chi_df,all_bad_rate) # 计算每一对相邻区间的卡方值
chi_list.append(chi_value)
best_combined = chi_list.index(min(chi_list)) # 最小的卡方值的索引
# 将卡方值最小的一对区间进行合并
group_interval[best_combined] = group_interval[best_combined]+group_interval[best_combined+1]
# 删除合并前的右区间
group_interval.remove(group_interval[best_combined+1])
# 对合并后每个区间进行排序
group_interval = [sorted(i) for i in group_interval]
# cutoff点为每个区间的最大值
cutoffpoints = [max(i) for i in group_interval[:-1]]
# 检查是否有箱只有好样本或者只有坏样本
df2['col_map_bin'] = df2['col_map'].apply(lambda x:assign_bin(x,cutoffpoints)) # 将col_map映射为对应的区间Bin
# 计算每个区间的违约率
(dict_bad,regroup) = bin_bad_rate(df2,'col_map_bin',target)
# 计算最小和最大的违约率
[min_bad_rate,max_bad_rate] = [min(dict_bad.values()),max(dict_bad.values())]
# 当最小的违约率等于0,说明区间内只有好样本,当最大的违约率等于1,说明区间内只有坏样本
while min_bad_rate==0 or max_bad_rate==1:
bad01_index = regroup[regroup['bad_rate'].isin([0,1])].col_map_bin.tolist()# 违约率为1或0的区间
bad01_bin = bad01_index[0]
if bad01_bin==max(regroup.col_map_bin):
cutoffpoints = cutoffpoints[:-1] # 当bad01_bin是最大的区间时,删除最大的cutoff点
elif bad01_bin==min(regroup.col_map_bin):
cutoffpoints = cutoffpoints[1:] # 当bad01_bin是最小的区间时,删除最小的cutoff点
else:
bad01_bin_index = list(regroup.col_map_bin).index(bad01_bin) # 找出bad01_bin的索引
prev_bin = list(regroup.col_map_bin)[bad01_bin_index-1] # bad01_bin前一个区间
df3 = df2[df2.col_map_bin.isin([prev_bin,bad01_bin])]
(dict_bad,regroup1) = bin_bad_rate(df3,'col_map_bin',target)
chi1 = cal_chi2(regroup1,all_bad_rate) # 计算前一个区间和bad01_bin的卡方值
later_bin = list(regroup.col_map_bin)[bad01_bin_index+1] # bin01_bin的后一个区间
df4 = df2[df2.col_map_bin.isin([later_bin,bad01_bin])]
(dict_bad,regroup2) = bin_bad_rate(df4,'col_map_bin',target)
chi2 = cal_chi2(regroup2,all_bad_rate) # 计算后一个区间和bad01_bin的卡方值
if chi1<chi2: # 当chi1<chi2时,删除前一个区间对应的cutoff点
cutoffpoints.remove(cutoffpoints[bad01_bin_index-1])
else: # 当chi1>=chi2时,删除bin01对应的cutoff点
cutoffpoints.remove(cutoffpoints[bad01_bin_index])
df2['col_map_bin'] = df2['col_map'].apply(lambda x:assign_bin(x,cutoffpoints))
(dict_bad,regroup) = bin_bad_rate(df2,'col_map_bin',target)
# 重新将col_map映射至区间,并计算最小和最大的违约率,直达不再出现违约率为0或1的情况,循环停止
[min_bad_rate,max_bad_rate] = [min(dict_bad.values()),max(dict_bad.values())]
# 检查分箱后的最小占比
if min_binpct>0:
group_values = df2['col_map'].apply(lambda x:assign_bin(x,cutoffpoints))
df2['col_map_bin'] = group_values # 将col_map映射为对应的区间Bin
group_df = group_values.value_counts().to_frame()
group_df['bin_pct'] = group_df['col_map']/n # 计算每个区间的占比
min_pct = group_df.bin_pct.min() # 得出最小的区间占比
while min_pct<min_binpct and len(cutoffpoints)>2: # 当最小的区间占比小于min_pct且cutoff点的个数大于2,执行循环
# 下面的逻辑基本与“检验是否有箱体只有好/坏样本”的一致
min_pct_index = group_df[group_df.bin_pct==min_pct].index.tolist()
min_pct_bin = min_pct_index[0]
if min_pct_bin == max(group_df.index):
cutoffpoints=cutoffpoints[:-1]
elif min_pct_bin == min(group_df.index):
cutoffpoints=cutoffpoints[1:]
else:
minpct_bin_index = list(group_df.index).index(min_pct_bin)
prev_pct_bin = list(group_df.index)[minpct_bin_index-1]
df5 = df2[df2['col_map_bin'].isin([min_pct_bin,prev_pct_bin])]
(dict_bad,regroup3) = bin_bad_rate(df5,'col_map_bin',target)
chi3 = cal_chi2(regroup3,all_bad_rate)
later_pct_bin = list(group_df.index)[minpct_bin_index+1]
df6 = df2[df2['col_map_bin'].isin([min_pct_bin,later_pct_bin])]
(dict_bad,regroup4) = bin_bad_rate(df6,'col_map_bin',target)
chi4 = cal_chi2(regroup4,all_bad_rate)
if chi3<chi4:
cutoffpoints.remove(cutoffpoints[minpct_bin_index-1])
else:
cutoffpoints.remove(cutoffpoints[minpct_bin_index])
return cutoffpoints
# 数值型变量的分箱(卡方分箱)
def binning_num(df,target,col_list,max_bin=None,min_binpct=None):
"""
df:数据集
target:目标变量的字段名
col_list:变量list集合
max_bin:最大的分箱个数
min_binpct:区间内样本所占总体的最小比
return:
bin_df :list形式,里面存储每个变量的分箱结果
iv_value:list形式,里面存储每个变量的IV值
"""
total = df[target].count()
bad = df[target].sum()
good = total-bad
all_odds = good/bad
inf = float('inf')
ninf = float('-inf')
bin_df=[]
iv_value=[]
for col in col_list:
cut = ChiMerge(df,col,target,max_bin=max_bin,min_binpct=min_binpct)
cut.insert(0,ninf)
cut.append(inf)
bucket = pd.cut(df[col],cut)
d1 = df.groupby(bucket)
d2 = pd.DataFrame()
d2['min_bin'] = d1[col].min()
d2['max_bin'] = d1[col].max()
d2['total'] = d1[target].count()
d2['totalrate'] = d2['total']/total
d2['bad'] = d1[target].sum()
d2['badrate'] = d2['bad']/d2['total']
d2['good'] = d2['total'] - d2['bad']
d2['goodrate'] = d2['good']/d2['total']
d2['badattr'] = d2['bad']/bad
d2['goodattr'] = (d2['total']-d2['bad'])/good
d2['odds'] = d2['good']/d2['bad']
GB_list=[]
for i in d2.odds:
if i>=all_odds:
GB_index = str(round((i/all_odds)*100,0))+str('G')
else:
GB_index = str(round((all_odds/i)*100,0))+str('B')
GB_list.append(GB_index)
d2['GB_index'] = GB_list
d2['woe'] = np.log(d2['badattr']/d2['goodattr'])
d2['bin_iv'] = (d2['badattr']-d2['goodattr'])*d2['woe']
d2['IV'] = d2['bin_iv'].sum()
iv = d2['bin_iv'].sum().round(3)
print('变量名:{}'.format(col))
print('IV:{}'.format(iv))
print('\t')
bin_df.append(d2)
iv_value.append(iv)
return bin_df,iv_value
下面看一下woe可视化之后的图。
# woe的可视化
def plot_woe(bin_df,hspace=0.4,wspace=0.4,plt_size=None,plt_num=None,x=None,y=None):
"""
bin_df:list形式,里面存储每个变量的分箱结果
hspace :子图之间的间隔(y轴方向)
wspace :子图之间的间隔(x轴方向)
plt_size :图纸的尺寸
plt_num :子图的数量
x :子图矩阵中一行子图的数量
y :子图矩阵中一列子图的数量
return :每个变量的woe变化趋势图
"""
plt.figure(figsize=plt_size)
plt.subplots_adjust(hspace=hspace,wspace=wspace)
for i,df in zip(range(1,plt_num+1,1),bin_df):
col_name = df.index.name
df = df.reset_index()
plt.subplot(x,y,i)
plt.title(col_name)
sns.pointplot(data=df,x=col_name,y='woe')
plt.xlabel('')
plt.xticks(rotation=30)
return plt.show()
plot_woe(bin_df_num,hspace=0.6,wspace=0.4,plt_size=(15,15),plt_num=16,x=4,y=4)
评分卡要求模型的可解释性,所以最好每一箱的woe要单调。比如int_rate_clean这个变量分为4箱,woe值呈现单调上升,映射成评分之后也是单调上升的。这样评分卡的业务逻辑就比较容易解释。当然,如果一些变量的woe不单调,但是业务逻辑上能够解释,也允许出现U型的图,但是一波三折的图是不能接受的。
总结:变量分箱其实就是观察每一个特征值和坏样本率之间的对应关系。变量分箱的方法多种多样,需要结合业务逻辑选择合适的分箱方法。
【作者】:Labryant
【原创公众号】:风控猎人
【简介】:某创业公司策略分析师,积极上进,努力提升。乾坤未定,你我都是黑马。
【转载说明】:转载请说明出处,谢谢合作!~