Bayes' theorem (English: Bayes' theorem) is a theorem in probability theory, which is related to the conditional probability of machine variables and the marginal probability distribution. In some explanations of probability, Bayes' theorem (Bayes' formula) can tell us how to use new evidence to modify existing views. The name comes from Thomas Bayes.
The popular explanation is if you know the probability of event A and event B respectively, and the probability of event B occurring when event A occurs. According to the formula, we can know the probability of event A when event B occurs.
A classic example is that you walk on the street, see a black man, and then predict that he is from that continent. In theory, the largest is African. Although there are also some blacks in America and Asia, in terms of probability, Africa is possible. Sex is greater. The principle of this idea is the basic idea of Naive Bayes.
At the same time, according to the different ways of seeking conditional probability, it is divided into Gaussian Naive Bayes and Polynomial Naive Bayes. According to the formula in the theorem, the conditional probability sometimes presents a continuous distribution, and it is impossible to directly obtain the conditional probability. In this case, it is often necessary to refer to the Gaussian distribution to obtain it. The polynomial naive Bayes reference Gaussian distribution.
Bayesian network
A Bayesian network definition includes a directed acyclic graph (DAG) and a set of conditional probability tables. Each node in the DAG represents a random variable, which can be a directly observable variable or a hidden variable, and a directed edge represents the conditional dependence between random variables; each element in the conditional probability table corresponds to a unique node in the DAG, and this node is stored The joint conditional probability of all its immediate predecessor nodes.
The Bayesian network has an important property. The probability of each node occurring is only affected by its input node, and the node that is not directly related to it does not affect the probability of the current node. As shown below.
The probability of occurrence of node D is only directly affected by the C event and indirectly affected by the A event.
As an uncertain causality reasoning model, Bayesian network is good at probabilistic reasoning and decision-making, that is, when you don’t know whether the preconditions occur, but only know the probability of occurrence, you can use Bayesian network to reason about subsequent events. Probability of occurrence. It has a wide range of applications in medical diagnosis, prediction, and identification of dangerous events.