ICA Based Inference Of Causality Between Variables

Causal inference is an important and complex problem that has been widely concerned in statistics,artificial intelligence and economics in recent years.Independent component analysis(ICA),as a statistical analysis method,plays an important role in the study of causal inference.This thesis studies causal models with time invariant coefficients and timevarying coefficients,and puts forward a new two-step estimation method based on ICA in view of the time-varying causal model,as well as focuses on the causal models' application in environmental analysis and stock analysis respectively.The specific works of thesis are generalized as below:Firstly,the basic theory and the most commonly used algorithms of ICA are briefly summarized.The basic model of ICA,the constraint conditions of independent components,the basic data pretreatment process and the uncertainties in the estimated part are introduced.At the same time,the fundamental principle of the common estimation algorithm of ICA problem named Fast ICA algorithm is introduced and the algorithm description is given specifically.Secondly,the time-invariant causal model and its application in environmental analysis are studied.First the composition of the structure vector autoregressive model(SVAR)is reviewed,this model combines the vector auto regression model(VAR)and structural equation model(SEM),which joins the structural information in a VAR and then a new algorithm named VAR-Li NGAM algorithm based on ICA and linear non-Gaussian acyclic model(Li NGAM)to solve the foregoing causal model SVAR is introduced,and finally through the R software,this thesis does actual data experiment of the SVAR model in the application of environmental analysis,and obtains that six common air pollution indexes have a causal order in contemporary and with time delay as well as influence coefficients among them.Finally,the time-varying causal model and its application are studied.The time-invariant causal model is generalized to a causal model with time-varying coefficients.In most practical cases,particularly in economics,the causal relationship between variables changes over time,and most of the noise items are limited to have non-Gaussian distributions.Thus a time varying linear causal(TVLC)model with non-Gaussian noise is proposed in this thesis,and in view of the new proposed model,the deformation of model is divided into two parts,one part is of the convolution model,the other part is an ICA model with mixed matrix coefficient changing with time,and therefore an ICA based two steps estimation method is put forward,then the granger causality test is applied to verify the causal sequence between the variables,finally through the artificial data simulation results,the effectiveness of the proposed method is verified,and the time-varying causal model as well as the new proposed approach is applied to the real stock data to determine the causal relationships among three common stock with higher international influence,the result is in accord with the fact.