The Functional LiNGAM

Tianle Yang, Joe Suzuki
Proceedings of The 11th International Conference on Probabilistic Graphical Models, PMLR 186:25-36, 2022.

Abstract

We consider a causal order such as the cause and effect among variables. In the Linear Non-Gaussian Acyclic Model (LiNGAM), we can only identify the order if at least one of the variables is non-Gaussian. This paper extends the notion of variables to functions (Functional Linear Non-Gaussian Acyclic Model, Func-LiNGAM). We first prove that we can identify the order among random functions if and only if one of them is a non-Gaussian process. In the actual procedure, we approximate the functions by random vectors. To improve the correctness and efficiency, we propose to optimize the coordinates of the vectors in such a way as functional principal component analysis. The experiments contain an order identification simulation among multiple functions for given samples. In particular, we apply the Func-LiNGAM to recognize the brain connectivity pattern with fMRI data. We can see the improvements in accuracy and execution speed compared to existing methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v186-yang22a, title = {The Functional {LiNGAM}}, author = {Yang, Tianle and Suzuki, Joe}, booktitle = {Proceedings of The 11th International Conference on Probabilistic Graphical Models}, pages = {25--36}, year = {2022}, editor = {Salmerón, Antonio and Rumı́, Rafael}, volume = {186}, series = {Proceedings of Machine Learning Research}, month = {05--07 Oct}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v186/yang22a/yang22a.pdf}, url = {https://proceedings.mlr.press/v186/yang22a.html}, abstract = {We consider a causal order such as the cause and effect among variables. In the Linear Non-Gaussian Acyclic Model (LiNGAM), we can only identify the order if at least one of the variables is non-Gaussian. This paper extends the notion of variables to functions (Functional Linear Non-Gaussian Acyclic Model, Func-LiNGAM). We first prove that we can identify the order among random functions if and only if one of them is a non-Gaussian process. In the actual procedure, we approximate the functions by random vectors. To improve the correctness and efficiency, we propose to optimize the coordinates of the vectors in such a way as functional principal component analysis. The experiments contain an order identification simulation among multiple functions for given samples. In particular, we apply the Func-LiNGAM to recognize the brain connectivity pattern with fMRI data. We can see the improvements in accuracy and execution speed compared to existing methods.} }
Endnote
%0 Conference Paper %T The Functional LiNGAM %A Tianle Yang %A Joe Suzuki %B Proceedings of The 11th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2022 %E Antonio Salmerón %E Rafael Rumı́ %F pmlr-v186-yang22a %I PMLR %P 25--36 %U https://proceedings.mlr.press/v186/yang22a.html %V 186 %X We consider a causal order such as the cause and effect among variables. In the Linear Non-Gaussian Acyclic Model (LiNGAM), we can only identify the order if at least one of the variables is non-Gaussian. This paper extends the notion of variables to functions (Functional Linear Non-Gaussian Acyclic Model, Func-LiNGAM). We first prove that we can identify the order among random functions if and only if one of them is a non-Gaussian process. In the actual procedure, we approximate the functions by random vectors. To improve the correctness and efficiency, we propose to optimize the coordinates of the vectors in such a way as functional principal component analysis. The experiments contain an order identification simulation among multiple functions for given samples. In particular, we apply the Func-LiNGAM to recognize the brain connectivity pattern with fMRI data. We can see the improvements in accuracy and execution speed compared to existing methods.
APA
Yang, T. & Suzuki, J.. (2022). The Functional LiNGAM. Proceedings of The 11th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 186:25-36 Available from https://proceedings.mlr.press/v186/yang22a.html.

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