使用 pymc3 使用貝葉斯邏輯回歸進行預測

Question

我正在嘗試使用 pymc3 執行貝葉斯邏輯回歸，但我在使用模型執行預測時遇到了問題。

數據：

我的數據集是房貸違約數據，樣本數據如下：

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

問題：

我想對測試數據集進行預測，一種方法是使用共享變量方法：

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，使用上面的代碼（theano 共享變量）會導致以下問題：

錯誤信息：

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

可能的解決方案：

使用以下代碼確實解決了問題，但我不知道如何對測試數據使用相同的模型。

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')

完整代碼：

%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

如果您將# model training (error cause)和# AUC注釋之間的代碼替換為以下代碼，您應該能夠運行它並開始獲得一些結果：

# 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

我進行了以下更改：

• 我已將進入theano.shared變量更改為一個 numpy 數組。
• 這意味着X_train中的字符串列需要使用一種熱編碼或類似的方法進行轉換。 我還沒有這樣做，因此我只使用了前 3 列恰好是數字的
• 我還使用標准縮放器在運行 pymc3 之前重新縮放輸入。
• 最后，對於后驗預測，我使用.set_value更改了共享變量的值

采樣給出了很多分歧，但我認為以上為您提供了設置。