Study On Structural Learning And Algorithm Of Gaussian Structural Equation Model

Structural equation model is a common method to find relationships between variables,and it is widely used in various fields such as psychology,economics.In recent years,structural equation model has been used to deal with complex problem,and it has become a hot issue.Each structural equation model corresponds to a directed acyclic graph,which describes the causal relationship between variables.A Directed acyclic graph includes directed edges and has no directed cycles.If the data follow from linear a Gaussian structural equation model with equal error variances,we can recover the structural equation model from observed data.In this paper we discuss the recovery problem of Gaussian structural equation model.When dealing with high-dimensional data,the existing greedy search?GDS?algorithm is hard to compute,and its complexity is high.In order to reduce the complexity and reduce the runtime,instead we propose a greedy procedure,which we call GDS_YH algorithm.At first,we use l₁ penalty likelihood estimate to graph model's covariance inverse matrix of the non-zero,we use glasso algorithm to get the target DAG's moral graph,the moral graph limits the search scope of greedy search,and then within the scope we apply greedy search algorithm to remove the false edge,and get the final DAG.In this article,through the simulation study,we compare our greedy search algorithm with traditional algorithm such as GDS?PC and GES,and we find that our algorithm improves the existing greedy search's?GDS?computing speed,and reduce the runtime.