KS，AUC 和 PSI 是風控算法中最常計算的幾個指標，本文記錄了多種工具計算這些指標的方法。
生成本文的測試數據：
import pandas as pd
import numpy as np
import pyspark.sql.functions as F
from pyspark.sql.window import Window
from pyspark.sql.types import StringType, DoubleType
from pyspark.sql import SparkSession, functions
from sklearn.metrics import roc_auc_score,roc_curve
tmptable = pd.DataFrame({'y':[np.random.randint(2) for i in range(1000000)]})
tmptable['y'] = tmptable['score'].apply(lambda x:1 if np.random.rand()+x>0.8 else 0)
tmp_sparkdf = spark.createDataFrame(tmptable)
tmp_sparkdf.craeteOrReplaceTempView('tmpview')
一、KS
KS 指標來源於 Kolmogorov-Smirnov 檢驗，通常用於比較兩組樣本是否來源於同一分布。在建模中划分訓練集與測試集后，通常運用 KS 檢驗來檢驗訓練集與測試集的分布差異，如果分布差異過大，那可能就會因為訓練集、測試集划分不合理而降低模型的泛化性。（關於 KS 檢驗的更多細節）
在風控中，KS 指標通過來衡量模型對於好壞樣本的區分能力，其具體的算法為：
- 按模型分從小到大排序，並分為 n 組（等頻分組或每個不同的分值作為一組）
- 計算截至每一組的累積好樣本(y=0)占比與累積壞樣本(y=1)占比，記為 \(cumgoodratio_i\) 和 \(cumbadratio_i\)
如第 k 組：
累積好樣本占比=第 k 組前包括第 k 組 y=0 樣本數量 / 全部 y=0 樣本的數量
累積壞樣本占比=第 k 組前包括第 k 組 y=1 樣本數量 / 全部 y=1 樣本的數量 - 則 \(KS=max(abs(cumgoodratio_i-cumbadratio_i))\)
1. SQL 計算 KS
select max(abs(cumgood/totalgood-cumbad/totalbad)) as ks
from (
select score,
sum(totalbad)over(order by score) as cumbad,
sum(totalgood)over(order by score) as cumgood,
sum(totalbad) over() as totalbad,
sum(totalgood) over() as totalgood
from (
select
score,
sum(y) as totalbad,
sum(1-y) as totalgood
from tmpview
group by score
)
)
2. Python 計算 KS
def get_ks(y_true:pd.Series,y_pred:pd.Series):
'''
A staticmethod to caculate the KS of the model.
Args:
y_true: true value of the sample
y_pred: pred value of the sample
Returns:
max(tpr-fpr): KS of the model
'''
fpr,tpr,_ = roc_curve(y_true,y_pred)
return str(max(abs(tpr-fpr)))
ksdata = spark.sql('select * from tmpview').toPandas()
print(get_ks(ksdata['y'],ksdata['score']))
3. Pyspark 計算 KS
有兩種方法，1 是對用 pyspark 的語法把 SQL 的邏輯給寫出來，可以算出來 KS；2 就是包裝成 UDF 函數，這樣當需要 groupby 后計算 KS 時，可以直接調用 UDF 函數分組計算 KS
a. SQL 邏輯改寫
ksdata = spark.sql('select * from tmpview')
def calks(df,ycol='y',scorecol='score'):
return df.withColumn(ycol,F.col(ycol).cast('int')).withColumn(scorecol,F.col(scorecol).cast('float'))\
.withColumn('totalbad',F.sum(F.col(ycol)).over(Window.orderBy(F.lit(1))))\
.withColumn('totalgood',F.sum(1-F.col(ycol)).over(Window.orderBy(F.lit(1))))\
.withColumn('cumgood',F.sum(1-F.col(ycol)).over(Window.orderBy(F.col(scorecol).asc())))\
.withColumn('cumbad',F.sum(F.col(ycol)).over(Window.orderBy(F.col(scorecol).asc())))\
.select(F.max(F.abs(F.col('cumgood')/F.col('totalgood')-F.col('cumbad')/F.col('totalbad'))).alias('KS'))
calks(ksdata).show()
b. python 轉 UDF 函數
def get_ks(y_true:pd.Series,y_pred:pd.Series):
'''
A staticmethod to caculate the KS of the model.
Args:
y_true: true value of the sample
y_pred: pred value of the sample
Returns:
max(tpr-fpr): KS of the model
'''
fpr,tpr,_ = roc_curve(y_true,y_pred)
return str(max(abs(tpr-fpr)))
get_ks_udfs = F.udf(get_ks, returnType=StringType())
ksdata = spark.sql('select * from tmpview')
print(ksdata.withColumn('eval metrics',F.lit('KS'))\
.groupby('eval metrics')\
.agg(get_ks_udfs(F.collect_list(F.col('y')),F.collect_list(F.col('score'))).alias('KS'))\
.select('KS').toPandas())
二、AUC
AUC（Area Under Curve）被定義為 ROC 曲線下與坐標軸圍成的面積，通常用來衡量二分類模型全局的區分能力。在 python 和 pyspark 中可以直接調包計算，在 SQL 中可以根據公式計算獲得，其計算方法如下：
-
對 score 從小到大排序
-
根據公式計算：
\[AUC=\frac{\sum_{i\in{positiveClass}}rank_i-\frac{M(1+M)}{2}}{M\times N} \]其中，\(rank_i\) 代表第 i 個正樣本的排序序號，M 和 N 分別代表正樣本和負樣本的總個數。
關於該公式的詳細理解，可參考 AUC 的計算方法（及評論）
1. SQL 計算 AUC
select (sumpositivernk-totalbad*(1+totalbad)/2)/(totalbad*totalgood) as auc
from
(
select sum(if(y=1,rnk,0)) as sumpositivernk,
sum(y) as totalbad,
sum(1-y) as totalgood
from
(
select y,row_number() over (order by score) as rnk
from tmpview
)
)
2. Python 計算 AUC
ksdata = spark.sql('select * from tmpview').toPandas()
print(roc_auc_score(ksdata['y'],ksdata['score']))
3. Pyspark 計算 AUC
同 KS 的計算，除了提到的兩種方式，還可以調用 pyspark 的 ML 包下二分類評價，來計算 AUC
a. SQL 邏輯改寫
aucdata = spark.sql('select * from tmpview')
def calauc(df,ycol='y',scorecol='score'):
return df.withColumn(ycol,F.col(ycol).cast('int')).withColumn(scorecol,F.col(scorecol).cast('float'))\
.withColumn('totalbad',F.sum(F.col(ycol)).over(Window.orderBy(F.lit(1))))\
.withColumn('totalgood',F.sum(1-F.col(ycol)).over(Window.orderBy(F.lit(1))))\
.withColumn('rnk2',F.row_number().over(Window.orderBy(F.col(scorecol).asc())))\
.filter(F.col(ycol)==1)\
.select(((F.sum(F.col('rnk2'))-0.5*(F.max(F.col('totalbad')))*(1+F.max(F.col('totalbad'))))/(F.max(F.col('totalbad'))*F.max(F.col('totalgood')))).alias('AUC'))\
calauc(aucdata).show()
b. UDF 函數
def auc(ytrue,ypred):
return str(roc_auc_score(ytrue,ypred))
get_auc_udfs = F.udf(auc, returnType=StringType())
aucdata = spark.sql('select * from tmpview')
aucdata.withColumn('eval metrics',F.lit('AUC'))\
.groupby('eval metrics')\
.agg(get_auc_udfs(F.collect_list(F.col('y')),F.collect_list(F.col('score'))).alias('AUC'))\
.select('AUC').show()
c. 調包
from pyspark.ml.evaluation import BinaryClassificationEvaluator
evaluator = BinaryClassificationEvaluator(rawPredictionCol='score',labelCol='y')
aucdata = spark.sql('select * from tmpview')
evaluator.evaluate(aucdata)
三、PSI
PSI（Population Stability Index：群體穩定性指標），通常被用於衡量兩個樣本模型分分布的差異，在風控建模中通常有兩個作用：
- 用於建模時篩選掉不穩定的特征
- 用於建模后及上線后評估和監控模型分值的穩定程度
個人認為該指標無一個比較明確的標准，在樣本量較大的條件下，篩選特征時盡量控制特征 PSI<0.1，或更嚴格。
計算 PSI 首先需要一個分箱基准，假定本文隨機生成的模型分的分箱切分點為\([0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]\)
1. SQL 計算 PSI
select
sum(grouppsi) as psi
from (
select g
,log(count(1) / sum(count(1))over() / 0.1)*(count(1) / sum(count(1))over() - 0.1) as grouppsi
from (
select
case when score<cutpoint[1] then 1
when score<cutpoint[2] then 2
when score<cutpoint[3] then 3
when score<cutpoint[4] then 4
when score<cutpoint[5] then 5
when score<cutpoint[6] then 6
when score<cutpoint[7] then 7
when score<cutpoint[8] then 8
when score<cutpoint[9] then 9
when score<cutpoint[10] then 10 else 'error' end as g
from (
select *
,array(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1) as cutpoint
from tmpview
)
)
group by g
)
2. Python 計算 PSI
psidata = spark.sql('select * from tmpview').toPandas()
psidata['g'] = pd.cut(psidata['score'],cut_point)
psitable = psidata.groupby('g')['y'].count()
psitable /= psitable.sum()
standratio = 1/(len(cut_point)-1)
psi = sum((psitable-standratio)*np.log(psitable/standratio))
3. Pyspark 計算 PSI
參考 Pyspark 實現連續分桶映射並自定義標簽，調包分箱后按公式計算 PSI
from pyspark.ml.feature import Bucketizer
def psi(df, splits, inputCol, outputCol):
if len(splits) < 2:
raise RuntimeError("splits's length must grater then 2.")
standratio = 1 / (len(splits)-1)
bucketizer = Bucketizer(
splits=splits, inputCol=inputCol, outputCol='split')
with_split = bucketizer.transform(df)
with_split = with_split.groupby('split')\
.agg((F.count(F.col(inputCol))/F.sum(F.count(F.col(inputCol))).over(Window.orderBy(F.lit(1)))).alias('groupratio'))\
.select(F.sum((F.col('groupratio')-standratio)*F.log(F.col('groupratio')/standratio)).alias('PSI'))
return with_split
psi(aucdata,cut_point,'score','group').show()