Tensor denoising and completion based on ordinal observations

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

Bibtex »Metadata »Paper »Supplemental »

Bibtek download is not availble in the pre-proceeding


Authors

Chanwoo Lee, Miaoyan Wang

Abstract

<p>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. </p>