Tensor denoising and completion based on ordinal observations

Chanwoo Lee, Miaoyan Wang
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:5778-5788, 2020.

Abstract

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, and social network analysis. We consider the problem of low-rank tensor estimation from possibly incomplete, ordinal-valued observations. Two related problems are studied, one on tensor denoising and another on tensor completion. We propose a multi-linear cumulative link model, develop a rank-constrained M-estimator, and obtain theoretical accuracy guarantees. Our mean squared error bound enjoys a faster convergence rate than previous results, and we show that the proposed estimator is minimax optimal under the class of low-rank models. Furthermore, the procedure developed serves as an efficient completion method which guarantees consistent recovery of an order-K (d,...,d)-dimensional low-rank tensor using only O(Kd) noisy, quantized observations. We demonstrate the outperformance of our approach over previous methods on the tasks of clustering and collaborative filtering.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-lee20i, title = {Tensor denoising and completion based on ordinal observations}, author = {Lee, Chanwoo and Wang, Miaoyan}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {5778--5788}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/lee20i/lee20i.pdf}, url = { http://proceedings.mlr.press/v119/lee20i.html }, abstract = {Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, and social network analysis. We consider the problem of low-rank tensor estimation from possibly incomplete, ordinal-valued observations. Two related problems are studied, one on tensor denoising and another on tensor completion. We propose a multi-linear cumulative link model, develop a rank-constrained M-estimator, and obtain theoretical accuracy guarantees. Our mean squared error bound enjoys a faster convergence rate than previous results, and we show that the proposed estimator is minimax optimal under the class of low-rank models. Furthermore, the procedure developed serves as an efficient completion method which guarantees consistent recovery of an order-K (d,...,d)-dimensional low-rank tensor using only O(Kd) noisy, quantized observations. We demonstrate the outperformance of our approach over previous methods on the tasks of clustering and collaborative filtering.} }
Endnote
%0 Conference Paper %T Tensor denoising and completion based on ordinal observations %A Chanwoo Lee %A Miaoyan Wang %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-lee20i %I PMLR %P 5778--5788 %U http://proceedings.mlr.press/v119/lee20i.html %V 119 %X Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, and social network analysis. We consider the problem of low-rank tensor estimation from possibly incomplete, ordinal-valued observations. Two related problems are studied, one on tensor denoising and another on tensor completion. We propose a multi-linear cumulative link model, develop a rank-constrained M-estimator, and obtain theoretical accuracy guarantees. Our mean squared error bound enjoys a faster convergence rate than previous results, and we show that the proposed estimator is minimax optimal under the class of low-rank models. Furthermore, the procedure developed serves as an efficient completion method which guarantees consistent recovery of an order-K (d,...,d)-dimensional low-rank tensor using only O(Kd) noisy, quantized observations. We demonstrate the outperformance of our approach over previous methods on the tasks of clustering and collaborative filtering.
APA
Lee, C. & Wang, M.. (2020). Tensor denoising and completion based on ordinal observations. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:5778-5788 Available from http://proceedings.mlr.press/v119/lee20i.html .

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