Bayesian Continuous-Time Tucker Decomposition

Shikai Fang, Akil Narayan, Robert Kirby, Shandian Zhe
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:6235-6245, 2022.

Abstract

Tensor decomposition is a dominant framework for multiway data analysis and prediction. Although practical data often contains timestamps for the observed entries, existing tensor decomposition approaches overlook or under-use this valuable time information. They either drop the timestamps or bin them into crude steps and hence ignore the temporal dynamics within each step or use simple parametric time coefficients. To overcome these limitations, we propose Bayesian Continuous-Time Tucker Decomposition. We model the tensor-core of the classical Tucker decomposition as a time-varying function, and place a Gaussian process prior to flexibly estimate all kinds of temporal dynamics. In this way, our model maintains the interpretability while is flexible enough to capture various complex temporal relationships between the tensor nodes. For efficient and high-quality posterior inference, we use the stochastic differential equation (SDE) representation of temporal GPs to build an equivalent state-space prior, which avoids huge kernel matrix computation and sparse/low-rank approximations. We then use Kalman filtering, RTS smoothing, and conditional moment matching to develop a scalable message passing inference algorithm. We show the advantage of our method in simulation and several real-world applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-fang22b, title = {{B}ayesian Continuous-Time Tucker Decomposition}, author = {Fang, Shikai and Narayan, Akil and Kirby, Robert and Zhe, Shandian}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {6235--6245}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/fang22b/fang22b.pdf}, url = {https://proceedings.mlr.press/v162/fang22b.html}, abstract = {Tensor decomposition is a dominant framework for multiway data analysis and prediction. Although practical data often contains timestamps for the observed entries, existing tensor decomposition approaches overlook or under-use this valuable time information. They either drop the timestamps or bin them into crude steps and hence ignore the temporal dynamics within each step or use simple parametric time coefficients. To overcome these limitations, we propose Bayesian Continuous-Time Tucker Decomposition. We model the tensor-core of the classical Tucker decomposition as a time-varying function, and place a Gaussian process prior to flexibly estimate all kinds of temporal dynamics. In this way, our model maintains the interpretability while is flexible enough to capture various complex temporal relationships between the tensor nodes. For efficient and high-quality posterior inference, we use the stochastic differential equation (SDE) representation of temporal GPs to build an equivalent state-space prior, which avoids huge kernel matrix computation and sparse/low-rank approximations. We then use Kalman filtering, RTS smoothing, and conditional moment matching to develop a scalable message passing inference algorithm. We show the advantage of our method in simulation and several real-world applications.} }
Endnote
%0 Conference Paper %T Bayesian Continuous-Time Tucker Decomposition %A Shikai Fang %A Akil Narayan %A Robert Kirby %A Shandian Zhe %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-fang22b %I PMLR %P 6235--6245 %U https://proceedings.mlr.press/v162/fang22b.html %V 162 %X Tensor decomposition is a dominant framework for multiway data analysis and prediction. Although practical data often contains timestamps for the observed entries, existing tensor decomposition approaches overlook or under-use this valuable time information. They either drop the timestamps or bin them into crude steps and hence ignore the temporal dynamics within each step or use simple parametric time coefficients. To overcome these limitations, we propose Bayesian Continuous-Time Tucker Decomposition. We model the tensor-core of the classical Tucker decomposition as a time-varying function, and place a Gaussian process prior to flexibly estimate all kinds of temporal dynamics. In this way, our model maintains the interpretability while is flexible enough to capture various complex temporal relationships between the tensor nodes. For efficient and high-quality posterior inference, we use the stochastic differential equation (SDE) representation of temporal GPs to build an equivalent state-space prior, which avoids huge kernel matrix computation and sparse/low-rank approximations. We then use Kalman filtering, RTS smoothing, and conditional moment matching to develop a scalable message passing inference algorithm. We show the advantage of our method in simulation and several real-world applications.
APA
Fang, S., Narayan, A., Kirby, R. & Zhe, S.. (2022). Bayesian Continuous-Time Tucker Decomposition. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:6235-6245 Available from https://proceedings.mlr.press/v162/fang22b.html.

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