| Bayesian networks are also called directed acyclic graphs.The Bayesian network is based on graph theory and probability theory.It can use conditional independence to represent joint probability distributions of multiple variable nodes in a graph,and the probability Inference,machine learning,and causal inference have universal applications.In a directed acyclic graph model,if there are hidden variables,then the set of edge distributions that may exist for the observed variables is usually very complex and cannot be represented by any kind of directed acyclic graph.To overcome this,we introduce a larger hybrid graph model and use this edge model to overcome this problem.However,these hybrid graph models do not represent all the model diagrams produced by the edges.This is because ordinary hybrid maps are basically insufficient to capture the diversity of various marginal models.In this paper,the study of marginalization has a directed acyclic graph.Through the use of hidden variables projection from directed acyclic graph containing hidden variables get marginalized directed acyclic graph,study of marginalized directed acyclic graph structure,and presents a marginalized directed acyclic graph edge distribution algorithm.Based on the study of marginalized directed acyclic graphs,a class of graph-oriented directed acyclic mixed graphs are studied.The independence of graphs is studied by using d-separability criterion and m-separability criterion.The hidden variable map model has unidentifiable parameters and non-regular asymptotic behavior.On the contrary,the nested Markov model can be identified.In a directed acyclic graph with hidden variables,a parametric nested Markov model is given to study its marginal distribution and factorization,this is a hidden variable hyper-graph close to the directed acyclic graph.Hidden variable hyper-graph.This model is widely used in causal inference and machine learning,and studies the structural properties of such graph models. |
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