如何利用pgmpy在贝叶斯网络中求出新事件的概率？

Question

我用pgmpy库训练了一个贝叶斯网络。我希望找到一个新事件的联合概率(作为每个变量的概率的乘积，如果它有父母的话)。

目前我正在做

infer = VariableElimination(model)
evidence = dict(x_test.iloc[0])
result = infer.query(variables=[], evidence=evidence, joint=True)
print(result)

这里x_test是测试数据。

result是非常大的输出，所有组合的列车数据和他们的概率。

+----------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------+------------------------------------------+-----------------+---------------------------+-----------------------------------------+------------------------------+------------------------+---------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------+
| data_devicetype                                                                                                                              | data_username                      | data_applicationtype                     | event_type      | servicename               | data_applicationname                    | tenantname                   | data_origin            | geoip_country_name        |   phi(data_devicetype,data_username,data_applicationtype,event_type,servicename,data_applicationname,tenantname,data_origin,geoip_country_name) |
+==============================================================================================================================================+====================================+==========================================+=================+===========================+=========================================+==============================+========================+===========================+=================================================================================================================================================+
| data_devicetype(Mozilla_5_0_Windows_NT_10_0_Win64_x64_AppleWebKit_537_36_KHTML_like_Gecko_Chrome_94_0_4606_81_Safari_537_36)                 | data_username(christofer) | data_applicationtype(Custom_Application) | event_type(sso) | servicename(saml_runtime) | data_applicationname(GD)            | tenantname(amx-sni-ksll0) | data_origin(1_0_64_66) | geoip_country_name(Japan) |                                                                                                                                          0.0326 |
+----------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------+------------------------------------------+-----------------+---------------------------+-----------------------------------------+------------------------------+------------------------+---------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------+
| data_devicetype(Mozilla_5_0_Windows_NT_10_0_Win64_x64_AppleWebKit_537_36_KHTML_like_Gecko_Chrome_94_0_4606_81_Safari_537_36)                 | data_username(marty) | data_applicationtype(Custom_Application) | event_type(sso) | servicename(saml_runtime) | data_applicationname(VAULT)      | tenantname(login_pqr_com) | data_origin(1_0_64_66) | geoip_country_name(Japan) |                                                                                                                                          0.0156 |
+----------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------+------------------------------------------+-----------------+---------------------------+-----------------------------------------+------------------------------+------------------------+---------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------+
| data_devicetype(Mozilla_5_0_Windows_NT_10_0_Win64_x64_AppleWebKit_537_36_KHTML_like_Gecko_Chrome_94_0_4606_81_Safari_537_36)                 | data_username(lincon) | data_applicationtype(Custom_Application) | event_type(sso) | servicename(saml_runtime) | data_applicationname(apps_think4ch_com) | tenantname(login_abc_com) | data_origin(1_0_64_66) | geoip_country_name(Japan) |                                                                                                                                          0.0113 |
......contd

请帮助我了解如何才能找到新事件的概率(即测试数据中的一行)。概率表达式为P(data_devicetype, data_username, data_applicationtype, event_type, servicename, data_applicationname, tenantname, data_origin, geoip_country_name)

Answer 1

如果我正确地理解了你，你就会试图计算一个新的数据点的概率。不幸的是，在pgmpy中还没有直接的方法来实现它。虽然可以从推理结果中得到概率值。就像这样：

infer = VariableElimination(model)
result = infer.query(variables=list(model.nodes()), joint=True)
evidence = dict(x_test.iloc[0])
p_evidence = result.get_value(**evidence)

本质上，我们在这里计算所有变量的联合分布，然后取evidence数据点的概率值。正如您所预期的那样，在大型网络的情况下，这在计算上是非常低的。在这种情况下，计算概率的一种近似方法是使用模拟。

nsamples = int(1e6)
samples = model.simulate(nsamples)
evidence = dict(x_test.iloc[0])
matching_samples = samples[np.logical_and.reduce([samples[k]==v for k, v in evidence.items()])]
p_evidence = matching_samples.shape[0] / nsamples

用模拟的方法，我们从模型中生成一些模拟数据，并检验这些样本中有多少与我们的数据点相匹配，这就是概率。