Structural Learning Of Chain Graphical Models

Although assocation and causation have been disscussed by statisticians for several centuries, causal inference becomes popular just in recent years.Graphical models are widely used to represent and analyze conditional independencies and causal relationships among random variables. Directed acyclic graphs includes directed edges,mainly used to describe the causal relationship between random variables. Undirected graphs includes undirected edges, generally used to describe the relationship between random variables. Chain graphs, which admit both directed and undirected edges, but no partially directed cycles, were introduced as a natural generalization of both undirected graphs and acyclic directed graphs.In the second part of this article,, I mainly talk about how to learn the local struc-ture of a Chain Graphs with its non-observed quantities were marginalized and how to recover the whole network graph from two local structures. Also, I explained how verify the marginalized sides are correct or not in terms of the conditions. Then, remove the wrong sides such that we can get the potential CG, according to the method of merging the local structures.In the third part of this article, I discussed another algorithm to study Chain Graphs which is called recursive algorithm. Firstly, observe all the data set and set up a com-plete undirected graphs. Then, remove some edges and get the undirected independence graphs. Next, decompose the new no phase diagram to smaller network graphs until it cannot been composed, according to the marginalization which has the algorithm like one to two, two to four. Finally, study the whole framework by the algorithm of merging framework. In addition, I deleted the redundant false sides and complicated the whole framework by the independence of conditions. In this way, we can get the potential model of Chain Graphs.