逻辑回归评分卡

一、基础知识点

(1)逻辑回归表达式

in:

import numpy as np
import matplotlib.pyplot as plt
import tqdm
import os


file = 'testSet.txt'
if os.path.exists(file):
    data = np.loadtxt(file)
features = data[:, :2]
labels = data[:, -1]

print(features.shape, labels.shape)

out:

in:

print('特征的维度: {0}'.format(features.shape[1]))
print('总共有{0}个类别'.format(len(np.unique(labels))))

out:
特征的维度: 2
总共有2个类别

figure = plt.figure()
plt.scatter([x[0] for x in features], [x[1] for x in features])
plt.show()

(2)sigmoid函数的导数

损失函数(Cross-entropy, 交叉熵损失函数)

def loss(Y_t, Y_p):
    '''
        算交叉熵损失函数
        Y_t: 独热编码之后的真实值向量
        Y_p: 预测的值向量        
    '''
    trans = np.zeros(shape=Y_t.shape)
    for sample_idx in range(len(trans)):
        # print(trans[sample_idx], [Y_p[sample_idx], 1.0 - Y_p[sample_idx]])
        # 避免出现0
        trans[sample_idx] = [Y_p[0][sample_idx] , 1.0 - Y_p[0][sample_idx] + 1e-5]
    log_y_p = np.log(trans)
    return -np.sum(np.multiply(Y_t, log_y_p))

Y_t = np.array([[0, 1], [1, 0]])
Y_p = np.array([[0.8, 1]])

loss(Y_t=Y_t, Y_p=Y_p)

交叉熵求导

def delta_cross_entropy(Y_t, Y_p):
    trans = np.zeros(shape=Y_t.shape)
    for sample_idx in range(len(trans)):
        trans[sample_idx] = [Y_p[0][sample_idx] + 1e-8, 1.0 - Y_p[0][sample_idx] + 1e-8]
    
    Y_t[Y_t == 0] += 1e-8
    error = Y_t * (1 / trans)
    error[:, 0] = -error[:, 0]
    return np.sum(error, axis=1, keepdims=True)

Y_t = np.array([[0, 1], [1, 0]], dtype=np.float)
Y_p = np.array([[0.8, 1]])
delta_cross_entropy(Y_t=Y_t, Y_p=Y_p)

准确率计算

def accuracy(Y_p, Y_t):
    Y_p[Y_p >= 0.5] = 1
    Y_p[Y_p < 0.5] = 0
    predict = np.sum(Y_p == Y_t)
    return predict /  len(Y_t)

评估指标

def recall(Y_p, Y_t):
    return np.sum(np.argmax(Y_p) == np.argmax(Y_t)) / np.sum(Y_p == 1)

二、导入库和数据集

导入库

import pandas as pd
from sklearn.metrics import roc_auc_score,roc_curve,auc
from sklearn.model_selection import train_test_split
from sklearn import metrics
from sklearn.linear_model import LogisticRegression
import numpy as np
import random
import math

读取数据

data = pd.read_csv('Acard.txt')
data.head()

三、分析与训练

#这是我们全部的变量，info结尾的是自己做的无监督系统输出的个人表现，score结尾的是收费的外部征信数据
feature_lst = ['person_info','finance_info','credit_info','act_info','td_score','jxl_score','mj_score','rh_score']

x = train[feature_lst]
y = train['bad_ind']

val_x =  val[feature_lst]
val_y = val['bad_ind']

lr_model = LogisticRegression(C=0.1)
lr_model.fit(x,y)

四、模型评价

ROC曲线

描绘的是不同的截断点时，并以FPR和TPR为横纵坐标轴，描述随着截断点的变小，TPR随着FPR的变化。
纵轴：TPR=正例分对的概率 = TP/(TP+FN)，其实就是查全率
横轴：FPR=负例分错的概率 = FP/(FP+TN)

作图步骤：

根据学习器的预测结果（注意，是正例的概率值，非0/1变量）对样本进行排序（从大到小）-----这就是截断点依次选取的顺序 按顺序选取截断点，并计算TPR和FPR—也可以只选取n个截断点，分别在1/n，2/n，3/n等位置 连接所有的点（TPR，FPR）即为ROC图

在这里插入代码片

KS值

作图步骤：

根据学习器的预测结果（注意，是正例的概率值，非0/1变量）对样本进行排序（从大到小）-----这就是截断点依次选取的顺序
按顺序选取截断点，并计算TPR和FPR —也可以只选取n个截断点，分别在1/n，2/n，3/n等位置
横轴为样本的占比百分比（最大100%），纵轴分别为TPR和FPR，可以得到KS曲线
TPR和FPR曲线分隔最开的位置就是最好的”截断点“，最大间隔距离就是KS值，通常>0.2即可认为模型有比较好偶的预测准确性。

y_pred = lr_model.predict_proba(x)[:,1]
fpr_lr_train,tpr_lr_train,_ = roc_curve(y,y_pred)
train_ks = abs(fpr_lr_train - tpr_lr_train).max()
print('train_ks : ',train_ks)

y_pred = lr_model.predict_proba(val_x)[:,1]
fpr_lr,tpr_lr,_ = roc_curve(val_y,y_pred)
val_ks = abs(fpr_lr - tpr_lr).max()
print('val_ks : ',val_ks)

from matplotlib import pyplot as plt
plt.plot(fpr_lr_train,tpr_lr_train,label = 'train LR')
plt.plot(fpr_lr,tpr_lr,label = 'evl LR')
plt.plot([0,1],[0,1],'k--')
plt.xlabel('False positive rate')
plt.ylabel('True positive rate')
plt.title('ROC Curve')
plt.legend(loc = 'best')
plt.show()

train_ks : 0.4151676259891534
val_ks : 0.3856283523530577

再做特征筛选

#再做特征筛选
from statsmodels.stats.outliers_influence import variance_inflation_factor
X = np.array(x)
for i in range(X.shape[1]):
    print(variance_inflation_factor(X,i))

import lightgbm as lgb
from sklearn.model_selection import train_test_split
train_x,test_x,train_y,test_y = train_test_split(x,y,random_state=0,test_size=0.2)
def  lgb_test(train_x,train_y,test_x,test_y):
    clf =lgb.LGBMClassifier(boosting_type = 'gbdt',
                           objective = 'binary',
                           metric = 'auc',
                           learning_rate = 0.1,
                           n_estimators = 24,
                           max_depth = 5,
                           num_leaves = 20,
                           max_bin = 45,
                           min_data_in_leaf = 6,
                           bagging_fraction = 0.6,
                           bagging_freq = 0,
                           feature_fraction = 0.8,
                           )
    clf.fit(train_x,train_y,eval_set = [(train_x,train_y),(test_x,test_y)],eval_metric = 'auc')
    return clf,clf.best_score_['valid_1']['auc'],
lgb_model , lgb_auc  = lgb_test(train_x,train_y,test_x,test_y)
feature_importance = pd.DataFrame({'name':lgb_model.booster_.feature_name(),
                                   'importance':lgb_model.feature_importances_}).sort_values(by=['importance'],ascending=False)
feature_importance

feature_lst = ['person_info','finance_info','credit_info','act_info']
x = train[feature_lst]
y = train['bad_ind']

val_x =  val[feature_lst]
val_y = val['bad_ind']

lr_model = LogisticRegression(C=0.1,class_weight='balanced')
lr_model.fit(x,y)
y_pred = lr_model.predict_proba(x)[:,1]
fpr_lr_train,tpr_lr_train,_ = roc_curve(y,y_pred)
train_ks = abs(fpr_lr_train - tpr_lr_train).max()
print('train_ks : ',train_ks)

y_pred = lr_model.predict_proba(val_x)[:,1]
fpr_lr,tpr_lr,_ = roc_curve(val_y,y_pred)
val_ks = abs(fpr_lr - tpr_lr).max()
print('val_ks : ',val_ks)
from matplotlib import pyplot as plt
plt.plot(fpr_lr_train,tpr_lr_train,label = 'train LR')
plt.plot(fpr_lr,tpr_lr,label = 'evl LR')
plt.plot([0,1],[0,1],'k--')
plt.xlabel('False positive rate')
plt.ylabel('True positive rate')
plt.title('ROC Curve')
plt.legend(loc = 'best')
plt.show()

# 系数
print('变量名单：',feature_lst)
print('系数：',lr_model.coef_)
print('截距：',lr_model.intercept_)

生成报告

#生成报告
model = lr_model
row_num, col_num = 0, 0
bins = 20
Y_predict = [s[1] for s in model.predict_proba(val_x)]
Y = val_y
nrows = Y.shape[0]
lis = [(Y_predict[i], Y[i]) for i in range(nrows)]
ks_lis = sorted(lis, key=lambda x: x[0], reverse=True)
bin_num = int(nrows/bins+1)
bad = sum([1 for (p, y) in ks_lis if y > 0.5])
good = sum([1 for (p, y) in ks_lis if y <= 0.5])
bad_cnt, good_cnt = 0, 0
KS = []
BAD = []
GOOD = []
BAD_CNT = []
GOOD_CNT = []
BAD_PCTG = []
BADRATE = []
dct_report = {}
for j in range(bins):
    ds = ks_lis[j*bin_num: min((j+1)*bin_num, nrows)]
    bad1 = sum([1 for (p, y) in ds if y > 0.5])
    good1 = sum([1 for (p, y) in ds if y <= 0.5])
    bad_cnt += bad1
    good_cnt += good1
    bad_pctg = round(bad_cnt/sum(val_y),3)
    badrate = round(bad1/(bad1+good1),3)
    ks = round(math.fabs((bad_cnt / bad) - (good_cnt / good)),3)
    KS.append(ks)
    BAD.append(bad1)
    GOOD.append(good1)
    BAD_CNT.append(bad_cnt)
    GOOD_CNT.append(good_cnt)
    BAD_PCTG.append(bad_pctg)
    BADRATE.append(badrate)
    dct_report['KS'] = KS
    dct_report['BAD'] = BAD
    dct_report['GOOD'] = GOOD
    dct_report['BAD_CNT'] = BAD_CNT
    dct_report['GOOD_CNT'] = GOOD_CNT
    dct_report['BAD_PCTG'] = BAD_PCTG
    dct_report['BADRATE'] = BADRATE
val_repot = pd.DataFrame(dct_report)
val_repot

五、行为评分卡模型表现

from pyecharts.charts import *
from pyecharts import options as opts
from pylab import *
mpl.rcParams['font.sans-serif'] = ['SimHei']
np.set_printoptions(suppress=True)
pd.set_option('display.unicode.ambiguous_as_wide', True)
pd.set_option('display.unicode.east_asian_width', True)
line = (

    Line()
    .add_xaxis(list(val_repot.index))
    .add_yaxis(
        "分组坏人占比",
        list(val_repot.BADRATE),
        yaxis_index=0,
        color="red",
    )
    .set_global_opts(
        title_opts=opts.TitleOpts(title="行为评分卡模型表现"),
    )
    .extend_axis(
        yaxis=opts.AxisOpts(
            name="累计坏人占比",
            type_="value",
            min_=0,
            max_=0.5,
            position="right",
            axisline_opts=opts.AxisLineOpts(
                linestyle_opts=opts.LineStyleOpts(color="red")
            ),
            axislabel_opts=opts.LabelOpts(formatter="{value}"),
        )

    )
    .add_xaxis(list(val_repot.index))
    .add_yaxis(
        "KS",
        list(val_repot['KS']),
        yaxis_index=1,
        color="blue",
        label_opts=opts.LabelOpts(is_show=False),
    )
)
line.render_notebook()

from pyecharts.charts import *
from pyecharts import options as opts
from pylab import *
mpl.rcParams['font.sans-serif'] = ['SimHei']
np.set_printoptions(suppress=True)
pd.set_option('display.unicode.ambiguous_as_wide', True)
pd.set_option('display.unicode.east_asian_width', True)
line = (

    Line()
    .add_xaxis(list(val_repot.index))
    .add_yaxis(
        "分组坏人占比",
        list(val_repot.BADRATE),
        yaxis_index=0,
        color="red",
    )
    .set_global_opts(
        title_opts=opts.TitleOpts(title="行为评分卡模型表现"),
    )
    .extend_axis(
        yaxis=opts.AxisOpts(
            name="累计坏人占比",
            type_="value",
            min_=0,
            max_=0.5,
            position="right",
            axisline_opts=opts.AxisLineOpts(
                linestyle_opts=opts.LineStyleOpts(color="red")
            ),
            axislabel_opts=opts.LabelOpts(formatter="{value}"),
        )

    )
    .add_xaxis(list(val_repot.index))
    .add_yaxis(
        "KS",
        list(val_repot['KS']),
        yaxis_index=1,
        color="blue",
        label_opts=opts.LabelOpts(is_show=False),
    )
)
line.render_notebook()

import seaborn as sns
sns.distplot(val.score,kde=True)

val = val.sort_values('score',ascending=True).reset_index(drop=True)
df2=val.bad_ind.groupby(val['level']).sum()
df3=val.bad_ind.groupby(val['level']).count()
print(df2/df3) 

总结