Bayesian Networks (also known as Bayesian belief networks or belief networks)

Naive Bayesian classification has a restrictive condition, that is, feature attributes must be conditional independent or basic independent (in fact, in practical applications almost impossible to complete independence)
A Bayesian network definition consists of a direction-free graph (DAG) and a set of conditional probability tables . Each node in the DAG represents a random variable, which can be directly observed or hidden, while a directed edge represents a conditional dependency between random variables ; Each element in a conditional probability table corresponds to the only node in the DAG that stores the node for all of its immediate predecessor nodes. Joint conditional probability .
In general, multivariate independent joint conditional probability distributions have the following formula:

In Bayesian networks, because of the foregoing properties, the joint conditional probability distributions of arbitrary random variable combinations are reduced to

Where parents represents the union of the direct precursor node of XI, the probability value can be found in the corresponding conditional probability table.

The construction and training of Bayesian networks is divided into the following two steps:

1, determine the topological relationship between the random variables and form dag.       This step usually requires domain experts to complete, and in order to build a good topology, often need to continue to iterate and improve. 2, training Bayesian network . This step is to complete the construction of the conditional probability table , if the value of each random variable can be directly observed, like our example above, then this step of training is intuitive, the method is similar to naive Bayesian classification. However, there are usually hidden variable nodes in Bayesian networks, so the training method is more complex, for example, using gradient descent method. Because these content is too obscure and involves deeper mathematics knowledge, here no longer repeat, interested friends can consult the relevant literature.