使用 pymc3 使用贝叶斯逻辑回归进行预测

Question

我正在尝试使用 pymc3 执行贝叶斯逻辑回归，但我在使用模型执行预测时遇到了问题。

数据：

我的数据集是房贷违约数据，样本数据如下：

BAD LOAN MORTDUE VALUE  REASON  JOB     YOJ DEROG   DELINQ  CLAGE     NINQ  CLNO    DEBTINC
1   1700 0548    40320  HomeImp Other   9   0       0       101.466002  1   8      37.113614
1   1800 28502   43034  HomeImp Other   11  0       0       88.766030   0   8      36.884894
0   2300 102370  120953 HomeImp Office  2   0       0       90.992533   0   13     31.588503

问题：

我想对测试数据集进行预测，一种方法是使用共享变量方法：

X_shared = theano.shared(X_train)

with pm.Model() as logistic_model_pred:
    pm.glm.GLM(x=X_shared,
               y=y_train, 
               labels=labels,
               family=pm.glm.families.Binomial())


X_shared.set_value(X_test)
ppc = pm.sample_ppc(pred_trace,
                model=logistic_model_pred,
                samples=100)

但是，使用上面的代码（theano 共享变量）会导致以下问题：

错误信息：

AsTensorError: ('Variable type field must be a TensorType.', <Generic>, <theano.gof.type.Generic object at 0x00000216ABB16730>)

可能的解决方案：

使用以下代码确实解决了问题，但我不知道如何对测试数据使用相同的模型。

with pm.Model() as logistic_model_pred:
    pm.glm.GLM.from_formula('BAD ~ DELINQ + DEROG + DEBTINC + NINQ + CLNO + VALUE + MORTDUE + YOJ + LOAN + CLAGE + JOB',
                            data=pd.concat([y_train.reset_index(drop=True), X_train], axis=1),
                            family=pm.glm.families.Binomial())
    pred_trace = pm.sample(tune=1500,
                      draws=1000,
                         chains=4,
                         cores=1,
                      init='adapt_diag')

完整代码：

%matplotlib inline
from pathlib import Path
import pickle
from collections import OrderedDict
import pandas as pd
import numpy as np
from scipy import stats
import multiprocessing
import arviz as az

from sklearn import preprocessing
from sklearn.model_selection import train_test_split
from sklearn.metrics import (roc_curve, roc_auc_score, confusion_matrix, accuracy_score, f1_score, 
                             precision_recall_curve, balanced_accuracy_score) 
from mlxtend.plotting import plot_confusion_matrix

import theano
import pymc3 as pm
from pymc3.variational.callbacks import CheckParametersConvergence
import statsmodels.formula.api as smf

import arviz as az
import matplotlib.pyplot as plt
import matplotlib.cm as cm

import seaborn as sns
from IPython.display import HTML

import sys

if not sys.warnoptions:
    import warnings
    warnings.simplefilter("ignore")


# intialise data of lists. 
data = {'BAD':[1,1,0,1,0,0,0,1,1,0,0,1,0,0,1,0,1],
        'LOAN':[1700,1800,2300,2400,2400,2900,2900,2900,2900,
3000,3200,3300,3600,3600,3700,3800,3900],
        'MORTDUE':[30548,28502,102370,34863,98449,103949,104373,7750,61962,104570,
74864,130518,100693,52337,17857,51180,29896],
        'VALUE':[40320,43034,120953,47471,117195,112505,120702,67996,70915,121729,
87266,164317,114743,63989,21144,63459,45960],
        'REASON':['HomeImp','HomeImp','HomeImp','HomeImp','HomeImp',
'HomeImp','HomeImp','HomeImp',
                  'DebtCon','HomeImp','HomeImp','DebtCon','HomeImp','HomeImp',
'HomeImp','HomeImp','HomeImp'],
        'JOB':['Other','Other','Office','Mgr','Office','Office','Office',
'Other','Mgr','Office','ProfExe',
               'Other','Office','Office','Other','Office','Other'],
        'YOJ':[9,11,2,12,4,1,2,16,2,2,7,9,6,20,5,20,11],
        'DEROG':[0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0],
        'DELINQ':[0,0,0,0,0,0,0,0,0,0,0,6,0,0,0,0,0],
        'CLAGE':[101.4660019,88.76602988,90.99253347,70.49108003,
93.81177486,96.10232967,101.5402975,
                 122.2046628,282.8016592,85.8843719,250.6312692,
192.289149,88.47045214,204.2724988,
                 129.7173231,203.7515336,146.1232422],
        'NINQ':[1,0,0,1,0,0,0,2,3,0,0,0,0,0,1,0,0],
        'CLNO':[8,8,13,21,13,13,13,8,37,14,12,33,14,20,9,20,14],
        'DEBTINC':[37.11361356,36.88489409,31.58850318,38.26360073,
29.68182705,30.05113629,29.91585903,
                   36.211348,49.20639579,32.05978327,42.90999735,
35.73055919,29.39354338,20.47091551,
                   26.63434752,20.06704205,24.47888119]
       } 
  
# Create DataFrame 
data = pd.DataFrame(data) 

# datatype defining
data[['BAD', 'LOAN', 'MORTDUE', 'VALUE', 'YOJ', 'DEROG', 'DELINQ', 
'CLAGE', 'NINQ', 'CLNO', 'DEBTINC']] = data[['BAD', 'LOAN', 'MORTDUE', 
'VALUE', 'YOJ', 'DEROG', 'DELINQ', 'CLAGE', 'NINQ', 'CLNO', 'DEBTINC' ]].apply(pd.to_numeric) 
data[['REASON', 'JOB']] = data[['REASON', 'JOB']].apply(lambda x: x.astype('category'))
print(data.dtypes) 
data.dropna(axis=0, how='any',inplace=True)    

# test train split
X = data.drop('BAD', axis=1)
y = data.BAD
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=12345)
labels = X_train.columns


# model training (error cause)
X_shared = theano.shared(X_train)

with pm.Model() as logistic_model_pred:
    pm.glm.GLM(x=X_shared,
               y=y_train, 
               labels=labels,
               family=pm.glm.families.Binomial())


# Prediction on test data

X_shared = theano.shared(X_test)

ppc = pm.sample_ppc(pred_trace,
                    model=logistic_model_pred,
                    samples=100)


# AUC
np.mean(ppc['y'], axis=0).shape
y_score = np.mean(ppc['y'], axis=0)
roc_auc_score(y_score=np.mean(ppc['y'], axis=0), 
              y_true=y_test)

pred_scores = dict(y_true=y_test, y_score=y_score)
cols = ['False Positive Rate', 'True Positive Rate', 'threshold']
roc = pd.DataFrame(dict(zip(cols, roc_curve(**pred_scores))))

precision, recall, ts = precision_recall_curve(y_true=y_test, probas_pred=y_score)
pr_curve = pd.DataFrame({'Precision': precision, 'Recall': recall})

f1 = pd.Series({t: f1_score(y_true=y_test, y_pred=y_score>t) for t in ts})
best_threshold = f1.idxmax()




# Alternative solution

with pm.Model() as logistic_model_pred:
    pm.glm.GLM.from_formula('BAD ~ DELINQ + DEROG + DEBTINC + NINQ + 
CLNO + VALUE + MORTDUE + YOJ + LOAN + CLAGE + JOB',
                            data=pd.concat([y_train.reset_index(drop=True), X_train], axis=1),
                            family=pm.glm.families.Binomial())
    pred_trace = pm.sample(tune=1500,
                      draws=1000,
                         chains=4,
                         cores=1,
                      init='adapt_diag')

Answer 1

如果您将# model training (error cause)和# AUC注释之间的代码替换为以下代码，您应该能够运行它并开始获得一些结果：

# model training (error cause)
X_train2 = X_train[X_train.columns[0:3]].values
scaler = preprocessing.StandardScaler()
scaler.fit(X_train2)
X_train2 = scaler.transform(X_train2)

X_shared = theano.shared(X_train2) #theano.shared(X_train)

with pm.Model() as logistic_model_pred:
    pm.glm.GLM(x=X_shared,
               y=y_train.values, 
               labels=labels[0:3],
               family=pm.glm.families.Binomial())
    trace = pm.sample()


# Prediction on test data
X_test2 = scaler.transform(X_test[X_train.columns[0:3]].values)

#X_shared = theano.shared(X_test2)
X_shared.set_value(X_test2)

ppc = pm.sample_ppc(trace,
                    model=logistic_model_pred,
                    samples=100)
# AUC

我进行了以下更改：

• 我已将进入theano.shared变量更改为一个 numpy 数组。
• 这意味着X_train中的字符串列需要使用一种热编码或类似的方法进行转换。 我还没有这样做，因此我只使用了前 3 列恰好是数字的
• 我还使用标准缩放器在运行 pymc3 之前重新缩放输入。
• 最后，对于后验预测，我使用.set_value更改了共享变量的值

采样给出了很多分歧，但我认为以上为您提供了设置。