Decomposition of structural learning about directed acyclic graphs

Confounding of Three Binary-Variable Counterfactual Model with DAG

“…□ C [11] (pp. [7][8] gives an example, and illustrates two cases of irrelevant factor and confounder respectively. To illuminate conceptions of confounding and irrelevant factor and Lemma 1, we continue to discuss the relationship based on their original example and give two examples as follows.…”

“…in recent decades [1][2][3][4][5][6][7], and directed acyclic graph (DAG) is involved in describing the relationship between causal connections [4]. Confounding and confounder are two basic concepts for epidemiology causal inference [1,3].…”

A project of applied statistical methods in China: review and outlook

“…To construct DAGs from observed data, the IC algorithm searches for a separator S from all possible variable subsets such that two variables u and v are independent conditional on S, and the PC algorithm limits possible separators to vertices that are adjacent to u and v [56,76]. [87] presented a decomposition approach for recovering structures of DAGs. The decomposition approach starts with an undirected independence graph which may not be a moral graph and may have extra edges added to the moral graph.…”

“…This prior knowledge of conditional independence can be used for decomposition in the approach. [86] gives a divide-and-conquer strategy in which structural learning for a large DAG is split recursively into those for subgraphs. The recursive algorithm can be depicted as a binary tree whose top node is the full set of all variables and whose other nodes are proper subsets of variables at its parent node.…”

“…For an undirected independence graphical model, given a vertex, its neighbor set can be found based on the mutual information between the vertex and a potential neighbor set [13]. For a very large graphical model, [87] and [90] presented decomposition approaches in which a problem of structural learning for a large graphical model is decomposed into problems for small models. [82] combined clustering with structural learning.…”