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KS,AUC 和 PSI 是风控算法中最常计算的几个指标,本文记录了多种工具计算这些指标的方法。
生成本文的测试数据:
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')
KS 指标来源于 Kolmogorov-smirnov 检验,通常用于比较两组样本是否来源于同一分布。在建模中划分训练集与测试集后,通常运用 KS 检验来检验训练集与测试集的分布差异,如果分布差异过大,那可能就会因为训练集、测试集划分不合理而降低模型的泛化性。(关于 KS 检验的更多细节)
在风控中,KS 指标通过来衡量模型对于好坏样本的区分能力,其具体的算法为:
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
)
)
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']))
有两种方法,1 是对用 pyspark 的语法把 SQL 的逻辑给写出来,可以算出来 KS;2 就是包装成 UDF 函数,这样当需要 groupby 后计算 KS 时,可以直接调用 UDF 函数分组计算 KS
a. SQL 逻辑改写
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 转 UDF 函数
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())
AUC(Area Under Curve)被定义为 ROC 曲线下与坐标轴围成的面积,通常用来衡量二分类模型全局的区分能力。在 python 和 pyspark 中可以直接调包计算,在 SQL 中可以根据公式计算获得,其计算方法如下:
对 score 从小到大排序
根据公式计算:
其中,(rank_i) 代表第 i 个正样本的排序序号,M 和 N 分别代表正样本和负样本的总个数。
关于该公式的详细理解,可参考 AUC 的计算方法(及评论)
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
)
)
ksdata = spark.sql('select * from tmpview').toPandas()
print(roc_auc_score(ksdata['y'],ksdata['score']))
同 KS 的计算,除了提到的两种方式,还可以调用 pyspark 的 ML 包下二分类评价,来计算 AUC
a. SQL 逻辑改写
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 函数
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. 调包
from pyspark.ml.evaluation import BinaryClassificationEvaluator
evaluator = BinaryClassificationEvaluator(rawPredictionCol='score',labelCol='y')
aucdata = spark.sql('select * from tmpview')
evaluator.evaluate(aucdata)
PSI(Population Stability Index:群体稳定性指标),通常被用于衡量两个样本模型分分布的差异,在风控建模中通常有两个作用:
个人认为该指标无一个比较明确的标准,在样本量较大的条件下,筛选特征时尽量控制特征 PSI<0.1,或更严格。
计算 PSI 首先需要一个分箱基准,假定本文随机生成的模型分的分箱切分点为([0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1])
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
)
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))
参考 Pyspark 实现连续分桶映射并自定义标签,调包分箱后按公式计算 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()
深入理解 AUC
SQL 计算多模型分的 PSI
Pyspark 实现连续分桶映射并自定义标签
使用 pyspark dataframe 的 groupby 计算 AUC
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