Studies On Causality For Linear Non-gaussian Acyclic Model

In recent years,the Linear Non-Gaussian Acyclic Model(LiNGAM)has received more and more attention from the complete identification of causal networks in the observation data without any prior knowledge,and is widely used in neuroscience,economics Genomics and other fields.Direct LiNGAM framework is one of the classical solution,but its existence when the dimension reaches 25 degrees or more,the problem of low recognition rate of exogenous variables,resulting in cascading effect,making the whole network estimation error increases with the number of layers,And the computational complexity reaches the third power of the dimension.In view of the above problems,this paper studies the identification of exogenous variables from three different perspectives:(1)From the point of local selection,the non-Gaussian of the variable is chosen as the criterion of the exogenous variable,and the k variables with the largest negative entropy are stored in the local target variable set Lv with the negative entropy.Lv to further look for exogenous variables,thereby improving the recognition rate of exogenous variables.(2)From the standpoint of independence,by introducing the independent independence judgment parameter,we can find the variables that are independent from the residuals of all the other variables,that is,the exogenous variables.The algorithm not only avoids the problem that the traditional algorithm is sensitive to the difference of independence value,but also avoids the defects that different data sets are sensitive to fixed independence parameters.(3)From the point of view of the estimation method,by introducing the metric of kurtosis,we find that when the disturbance variable obeys the independent distribution,the exogenous variable is the largest kurtosis value.Based on this feature,we propose a direct recognition of exogenous variables,The algorithm is not only a direct quantitative relationship,and the computational complexity is only the square of the dimension.The research results of this paper not only enrich the research of LiNGAM model,but also provide a new method to support exogenous variable recognition to a certain extent.