# Tensor denoising and completion based on ordinal observations

arXiv: https://arxiv.org/abs/2002.06524 · HTML: https://mlsanity.com/paper/2002.06524/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2020.

## Built on by (most cited first, 8 of 8)

- [Multiplex Graph Networks for Multimodal Brain Network Analysis](https://mlsanity.com/paper/2108.00158/) (2021)
- [Quantized Radio Map Estimation Using Tensor and Deep Generative Models](https://mlsanity.com/paper/2303.01770/) (2023)
- [Beyond the Signs: Nonparametric Tensor Completion via Sign Series](https://mlsanity.com/paper/2102.00384/) (2021)
- [Under-Counted Tensor Completion with Neural Incorporation of Attributes](https://mlsanity.com/paper/2306.03273/) (2023)
- [Nonparametric Trace Regression in High Dimensions via Sign Series Representation](https://mlsanity.com/paper/2105.01783/) (2021)
- [Tensor Denoising via Amplification and Stable Rank Methods](https://mlsanity.com/paper/2301.03761/) (2023)
- [Downlink MIMO Channel Estimation from Bits: Recoverability and Algorithm](https://mlsanity.com/paper/2411.16043/) (2024)
- [Near-Efficient and Non-Asymptotic Multiway Inference](https://mlsanity.com/paper/2511.05368/) (2025)

## Abstract (arXiv)

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. 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 the other 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,ldots,d)-dimensional low-rank tensor using only tildeO(Kd) noisy, quantized observations. We demonstrate the outperformance of our approach over previous methods on the tasks of clustering and collaborative filtering.