?　變量分箱是評分卡建模流程中的關鍵環節，可以說是評分卡的核心環節。合理的分箱可以消除變量的量綱影響，而且能減少異常值等噪聲數據的影響，有效避免模型過擬合。此外，分箱可以給模型實現業務上的可解釋性，可以說是評分卡的核心了。

?　下面開始實現評分卡建立中的分箱操作。

?　首先，變量需要分為數值型變量和類別型變量。對于這兩種類型的變量分箱過程中需要注意的點如下：

類別型變量

• 如果不超過5個，無需進行分箱；
• 超過5個，有兩種方法。一，如果類別很多，可以對其進行bad_rate編碼之后劃入數值型變量；二，類別不是很多，對其進行降基處理，縮小至5個以內。

數值型變量
?　有無監督和有監督分箱兩種方法。無監督分箱有等比分箱、等寬分箱、聚類分箱等。有監督分箱有卡方分箱、最優分箱等等。

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個數值型變量和6個類別型變量。‘zip_code’、'addr_state’兩個變量的類別很多，進行bad_rate編碼后劃入數值型變量。另外4個變量單獨進行分箱。

def binning_cate(df,col_list,target):"""df:數據集col_list:變量list集合target:目標變量的字段名return: bin_df :list形式，里面存儲每個變量的分箱結果iv_value:list形式，里面存儲每個變量的IV值"""total = df[target].count()bad = df[target].sum()good = total-badall_odds = good*1.0/badbin_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']/totald2['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']/badd2['goodattr'] = (d2['total']-d2['bad'])/goodd2['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_listd2['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('變量名:{}'.format(col))print('IV:{}'.format(iv))print('\t')bin_df.append(d2)iv_value.append(iv)return bin_df,iv_value

?　注意，如果類別型變量的某一箱只有好樣本/壞樣本，將造成變量的IV值為inf/-inf，此時就需要對變量進行降基處理或者重新分箱。
接著看一下每一箱的明細情況。

?　IV值一般大于0.01，就可以入模使用。IV值不宜過高，如果過高說明變量的預測能力過強，其實可以單獨拿出來作為一條策略。評分卡的變量最好還是弱變量。此外，每一箱的WOE值也不宜大于1，因為大于1說明這一箱至少有65%以上的好壞樣本，其實可以單獨作為一條規則了。
?　下面利用條形圖將分箱結果可視化展示。

# woe的可視化 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，里面存儲每個變量的分箱結果hspace :子圖之間的間隔(y軸方向)wspace :子圖之間的間隔(x軸方向)plt_size :圖紙的尺寸plt_num :子圖的數量x :子圖矩陣中一行子圖的數量y :子圖矩陣中一列子圖的數量return :每個變量的woe變化趨勢圖"""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.namedf = 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)

?　下面對zip_code、addr_state這兩個變量進行bad_rate編碼，就是將變量的每個類別映射成這個類別的壞樣本率，這樣就可以將類別型變量轉化為數值型變量了。

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: 需要計算好壞比率的數據集:param col: 需要計算好壞比率的特征:param target: 好壞標簽:param grantRateIndicator: 1返回總體的壞樣本率，0不返回:return: 每箱的壞樣本率，以及總體的壞樣本率（當grantRateIndicator＝＝1時）'''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') # 每箱的壞樣本數，總樣本數regroup.reset_index(level=0, inplace=True)regroup['bad_rate'] = regroup.apply(lambda x: x.bad * 1.0 / x.total, axis=1) # 加上一列壞樣本率dicts = dict(zip(regroup[col],regroup['bad_rate'])) # 每箱對應的壞樣本率組成的字典if grantRateIndicator==0:return (dicts, regroup)N = sum(regroup['total'])B = sum(regroup['bad'])overallRate = B * 1.0 / Nreturn (dicts, regroup, overallRate) # 對zip_code,addr_state進行bad_rate編碼 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編碼之后產生兩個新的列，將這兩列劃入數值型變量中一起進行卡方分箱。

# 數值型變量的分箱 # 先用卡方分箱輸出變量的分割點 def split_data(df,col,split_num):"""df: 原始數據集col:需要分箱的變量split_num:分割點的數量"""df2 = df.copy()count = df2.shape[0] # 總樣本數n = math.floor(count/split_num) # 按照分割點數目等分后每組的樣本數split_index = [i*n for i in range(1,split_num)] # 分割點的索引values = sorted(list(df2[col])) # 對變量的值從小到大進行排序split_value = [values[i] for i in split_index] # 分割點對應的valuesplit_value = sorted(list(set(split_value))) # 分割點的value去重排序return split_valuedef assign_group(x,split_bin):"""x:變量的valuesplit_bin:split_data得出的分割點list"""n = len(split_bin)if x<=min(split_bin): return min(split_bin) # 如果x小于分割點的最小值，則x映射為分割點的最小值elif x>max(split_bin): # 如果x大于分割點的最大值，則x映射為分割點的最大值return 10e10else:for i in range(n-1):if split_bin[i]<x<=split_bin[i+1]:# 如果x在兩個分割點之間，則x映射為分割點較大的值return split_bin[i+1]def bin_bad_rate(df,col,target,grantRateIndicator=0):"""df:原始數據集col:原始變量/變量映射后的字段target:目標變量的字段grantRateIndicator:是否輸出總體的違約率"""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'] # 計算根據col分組后每組的違約率dict_bad = dict(zip(regroup[col],regroup['bad_rate'])) # 轉為字典形式if grantRateIndicator==0:return (dict_bad,regroup)total_all= df.shape[0]bad_all = df[target].sum()all_bad_rate = bad_all/total_all # 計算總體的違約率return (dict_bad,regroup,all_bad_rate)def cal_chi2(df,all_bad_rate):"""df:bin_bad_rate得出的regroupall_bad_rate:bin_bad_rate得出的總體違約率"""df2 = df.copy()df2['expected'] = df2['total']*all_bad_rate # 計算每組的壞用戶期望數量combined = zip(df2['expected'],df2['bad']) # 遍歷每組的壞用戶期望數量和實際數量chi = [(i[0]-i[1])**2/i[0] for i in combined] # 計算每組的卡方值chi2 = sum(chi) # 計算總的卡方值return chi2def assign_bin(x,cutoffpoints):"""x:變量的valuecutoffpoints:分箱的切割點"""bin_num = len(cutoffpoints)+1 # 箱體個數if x<=cutoffpoints[0]: # 如果x小于最小的cutoff點，則映射為Bin 0return 'Bin 0'elif x>cutoffpoints[-1]: # 如果x大于最大的cutoff點，則映射為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在兩個cutoff點之間，則x映射為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]))) # 變量的唯一值并排序n = len(col_unique) # 變量唯一值得個數df2 = df.copy()if n>100: # 如果變量的唯一值數目超過100，則將通過split_data和assign_group將x映射為split對應的valuesplit_col = split_data(df2,col,100) # 通過這個目的將變量的唯一值數目人為設定為100df2['col_map'] = df2[col].map(lambda x:assign_group(x,split_col))else:df2['col_map'] = df2[col] # 變量的唯一值數目沒有超過100，則不用做映射# 生成dict_bad,regroup,all_bad_rate的元組(dict_bad,regroup,all_bad_rate) = bin_bad_rate(df2,'col_map',target,grantRateIndicator=1)col_map_unique = sorted(list(set(df2['col_map']))) # 對變量映射后的value進行去重排序group_interval = [[i] for i in col_map_unique] # 對col_map_unique中每個值創建list并存儲在group_interval中while (len(group_interval)>max_bin): # 當group_interval的長度大于max_bin時，執行while循環chi_list=[]for i in range(len(group_interval)-1):temp_group = group_interval[i]+group_interval[i+1] # temp_group 為生成的區間,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) # 計算每一對相鄰區間的卡方值chi_list.append(chi_value)best_combined = chi_list.index(min(chi_list)) # 最小的卡方值的索引# 將卡方值最小的一對區間進行合并group_interval[best_combined] = group_interval[best_combined]+group_interval[best_combined+1]# 刪除合并前的右區間group_interval.remove(group_interval[best_combined+1])# 對合并后每個區間進行排序group_interval = [sorted(i) for i in group_interval]# cutoff點為每個區間的最大值cutoffpoints = [max(i) for i in group_interval[:-1]]# 檢查是否有箱只有好樣本或者只有壞樣本df2['col_map_bin'] = df2['col_map'].apply(lambda x:assign_bin(x,cutoffpoints)) # 將col_map映射為對應的區間Bin# 計算每個區間的違約率(dict_bad,regroup) = bin_bad_rate(df2,'col_map_bin',target)# 計算最小和最大的違約率[min_bad_rate,max_bad_rate] = [min(dict_bad.values()),max(dict_bad.values())]# 當最小的違約率等于0，說明區間內只有好樣本，當最大的違約率等于1，說明區間內只有壞樣本while min_bad_rate==0 or max_bad_rate==1:bad01_index = regroup[regroup['bad_rate'].isin([0,1])].col_map_bin.tolist()# 違約率為1或0的區間bad01_bin = bad01_index[0]if bad01_bin==max(regroup.col_map_bin):cutoffpoints = cutoffpoints[:-1] # 當bad01_bin是最大的區間時，刪除最大的cutoff點elif bad01_bin==min(regroup.col_map_bin):cutoffpoints = cutoffpoints[1:] # 當bad01_bin是最小的區間時，刪除最小的cutoff點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前一個區間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) # 計算前一個區間和bad01_bin的卡方值later_bin = list(regroup.col_map_bin)[bad01_bin_index+1] # bin01_bin的后一個區間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) # 計算后一個區間和bad01_bin的卡方值if chi1<chi2: # 當chi1<chi2時,刪除前一個區間對應的cutoff點cutoffpoints.remove(cutoffpoints[bad01_bin_index-1])else: # 當chi1>=chi2時,刪除bin01對應的cutoff點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)# 重新將col_map映射至區間，并計算最小和最大的違約率，直達不再出現違約率為0或1的情況，循環停止[min_bad_rate,max_bad_rate] = [min(dict_bad.values()),max(dict_bad.values())]# 檢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 # 將col_map映射為對應的區間Bingroup_df = group_values.value_counts().to_frame() group_df['bin_pct'] = group_df['col_map']/n # 計算每個區間的占比min_pct = group_df.bin_pct.min() # 得出最小的區間占比while min_pct<min_binpct and len(cutoffpoints)>2: # 當最小的區間占比小于min_pct且cutoff點的個數大于2，執行循環# 下面的邏輯基本與“檢驗是否有箱體只有好/壞樣本”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# 數值型變量的分箱（卡方分箱） def binning_num(df,target,col_list,max_bin=None,min_binpct=None):"""df:數據集target:目標變量的字段名col_list:變量list集合max_bin:最大的分箱個數min_binpct:區間內樣本所占總體的最小比return:bin_df :list形式，里面存儲每個變量的分箱結果iv_value:list形式，里面存儲每個變量的IV值"""total = df[target].count()bad = df[target].sum()good = total-badall_odds = good/badinf = 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']/totald2['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']/badd2['goodattr'] = (d2['total']-d2['bad'])/goodd2['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_listd2['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('變量名:{}'.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可視化之后的圖。

# woe的可視化 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，里面存儲每個變量的分箱結果hspace :子圖之間的間隔(y軸方向)wspace :子圖之間的間隔(x軸方向)plt_size :圖紙的尺寸plt_num :子圖的數量x :子圖矩陣中一行子圖的數量y :子圖矩陣中一列子圖的數量return :每個變量的woe變化趨勢圖"""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.namedf = 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)

?　評分卡要求模型的可解釋性，所以最好每一箱的woe要單調。比如int_rate_clean這個變量分為4箱，woe值呈現單調上升，映射成評分之后也是單調上升的。這樣評分卡的業務邏輯就比較容易解釋。當然，如果一些變量的woe不單調，但是業務邏輯上能夠解釋，也允許出現U型的圖，但是一波三折的圖是不能接受的。

總結：變量分箱其實就是觀察每一個特征值和壞樣本率之間的對應關系。變量分箱的方法多種多樣，需要結合業務邏輯選擇合適的分箱方法。

【作者】：Labryant
【原創公眾號】：風控獵人
【簡介】：某創業公司策略分析師，積極上進，努力提升。乾坤未定，你我都是黑馬。
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