Tensor Regression Meets Gaussian Processes

Rose Yu, Guangyu Li, Yan Liu
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:482-490, 2018.

Abstract

Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, especially for multi-way data analysis. We show that low-rank tensor regression is essentially learning a multi-linear kernel in Gaussian processes, and the low-rank assumption translates to the constrained Bayesian inference problem. We prove the oracle inequality and derive the average case learning curve for the equivalent GP model. Our finding implies that low-rank tensor regression, though empirically successful, is highly dependent on the eigenvalues of covariance functions as well as variable correlations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-yu18a, title = {Tensor Regression Meets Gaussian Processes}, author = {Yu, Rose and Li, Guangyu and Liu, Yan}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {482--490}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/yu18a/yu18a.pdf}, url = {https://proceedings.mlr.press/v84/yu18a.html}, abstract = {Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, especially for multi-way data analysis. We show that low-rank tensor regression is essentially learning a multi-linear kernel in Gaussian processes, and the low-rank assumption translates to the constrained Bayesian inference problem. We prove the oracle inequality and derive the average case learning curve for the equivalent GP model. Our finding implies that low-rank tensor regression, though empirically successful, is highly dependent on the eigenvalues of covariance functions as well as variable correlations. } }
Endnote
%0 Conference Paper %T Tensor Regression Meets Gaussian Processes %A Rose Yu %A Guangyu Li %A Yan Liu %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-yu18a %I PMLR %P 482--490 %U https://proceedings.mlr.press/v84/yu18a.html %V 84 %X Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, especially for multi-way data analysis. We show that low-rank tensor regression is essentially learning a multi-linear kernel in Gaussian processes, and the low-rank assumption translates to the constrained Bayesian inference problem. We prove the oracle inequality and derive the average case learning curve for the equivalent GP model. Our finding implies that low-rank tensor regression, though empirically successful, is highly dependent on the eigenvalues of covariance functions as well as variable correlations.
APA
Yu, R., Li, G. & Liu, Y.. (2018). Tensor Regression Meets Gaussian Processes. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:482-490 Available from https://proceedings.mlr.press/v84/yu18a.html.

Related Material