SG-PALM: a Fast Physically Interpretable Tensor Graphical Model

Yu Wang, Alfred Hero
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:10783-10793, 2021.

Abstract

We propose a new graphical model inference procedure, called SG-PALM, for learning conditional dependency structure of high-dimensional tensor-variate data. Unlike most other tensor graphical models the proposed model is interpretable and computationally scalable to high dimension. Physical interpretability follows from the Sylvester generative (SG) model on which SG-PALM is based: the model is exact for any observation process that is a solution of a partial differential equation of Poisson type. Scalability follows from the fast proximal alternating linearized minimization (PALM) procedure that SG-PALM uses during training. We establish that SG-PALM converges linearly (i.e., geometric convergence rate) to a global optimum of its objective function. We demonstrate scalability and accuracy of SG-PALM for an important but challenging climate prediction problem: spatio-temporal forecasting of solar flares from multimodal imaging data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-wang21k, title = {SG-PALM: a Fast Physically Interpretable Tensor Graphical Model}, author = {Wang, Yu and Hero, Alfred}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {10783--10793}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/wang21k/wang21k.pdf}, url = {https://proceedings.mlr.press/v139/wang21k.html}, abstract = {We propose a new graphical model inference procedure, called SG-PALM, for learning conditional dependency structure of high-dimensional tensor-variate data. Unlike most other tensor graphical models the proposed model is interpretable and computationally scalable to high dimension. Physical interpretability follows from the Sylvester generative (SG) model on which SG-PALM is based: the model is exact for any observation process that is a solution of a partial differential equation of Poisson type. Scalability follows from the fast proximal alternating linearized minimization (PALM) procedure that SG-PALM uses during training. We establish that SG-PALM converges linearly (i.e., geometric convergence rate) to a global optimum of its objective function. We demonstrate scalability and accuracy of SG-PALM for an important but challenging climate prediction problem: spatio-temporal forecasting of solar flares from multimodal imaging data.} }
Endnote
%0 Conference Paper %T SG-PALM: a Fast Physically Interpretable Tensor Graphical Model %A Yu Wang %A Alfred Hero %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-wang21k %I PMLR %P 10783--10793 %U https://proceedings.mlr.press/v139/wang21k.html %V 139 %X We propose a new graphical model inference procedure, called SG-PALM, for learning conditional dependency structure of high-dimensional tensor-variate data. Unlike most other tensor graphical models the proposed model is interpretable and computationally scalable to high dimension. Physical interpretability follows from the Sylvester generative (SG) model on which SG-PALM is based: the model is exact for any observation process that is a solution of a partial differential equation of Poisson type. Scalability follows from the fast proximal alternating linearized minimization (PALM) procedure that SG-PALM uses during training. We establish that SG-PALM converges linearly (i.e., geometric convergence rate) to a global optimum of its objective function. We demonstrate scalability and accuracy of SG-PALM for an important but challenging climate prediction problem: spatio-temporal forecasting of solar flares from multimodal imaging data.
APA
Wang, Y. & Hero, A.. (2021). SG-PALM: a Fast Physically Interpretable Tensor Graphical Model. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:10783-10793 Available from https://proceedings.mlr.press/v139/wang21k.html.

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