Probabilistic Graphical ModelsIt is a theory that uses graphs to represent the probabilistic dependency of variables. It integrates the knowledge of probability theory and graph theory and uses graphs to represent the joint probability distribution of related variables.

The theory of probabilistic graphical models can be divided into the following three categories:

• Representation Theory of Probabilistic Graphical Models
• Probabilistic Graphical Model Inference Theory
• Probabilistic Graphical Model Learning Theory

Basic Problems with Probabilistic Graphical Models

• Representation problem: For a probabilistic model, how to describe the dependency relationship between variables through a graph structure?
• Inference problem: Given some known variables, calculate the posterior probability distribution of other variables;
• Learning problem: Graph model learning includes learning graph structure and learning parameters.

Classification of Probabilistic Graphical Models

Classification based on whether the edge has directionality:

• Directed graph model, also known as Bayesian Network (BN), uses a directed acyclic graph as its network structure;
• Undirected graph model, also known as Markov Network (MN), has an undirected graph structure.
• Locally directed models, that is, models with both directed and undirected edges, include Conditional Random Field (CRF) and ChainGraph.

According to the different levels of abstraction represented:

• Probabilistic graphical models based on random variables, such as Bayesian networks, Markov networks, conditional random fields, and chain graphs;
• Template-based probabilistic graphical models. This type of model can be divided into two types according to different application scenarios:
• Transient models, including dynamic Bayesian networks and state observation models, where the state observation model includes linear dynamic systems and hidden Markov models;
• Probabilistic graphical models in the object-relational domain, including disk models, probabilistic relational models, and relational Markov networks.

Sub-terms: Bayesian network, Markov random field