# Dynamic matrix recovery from incomplete observations under an exact low-rank constraint

arXiv: https://arxiv.org/abs/1610.09420 · HTML: https://mlsanity.com/paper/1610.09420/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2016.

## Built on by (most cited first, 3 of 3)

- [Deep inference of latent dynamics with spatio-temporal super-resolution using selective backpropagation through time](https://mlsanity.com/paper/2111.00070/) (2021)
- [Tailed Low-Rank Matrix Factorization for Similarity Matrix Completion](https://mlsanity.com/paper/2409.19550/) (2024)
- [Matrix Completion via Residual Spectral Matching](https://mlsanity.com/paper/2412.10005/) (2024)

## Abstract (arXiv)

Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by incorporating temporal information and allowing for the possibility of time-varying models, significant improvements are possible in practice. However, despite the reported superior empirical performance of these dynamic models over their static counterparts, there is limited theoretical justification for introducing these more complex models. In this paper we aim to address this gap by studying the problem of recovering a dynamically evolving low-rank matrix from incomplete observations. First, we propose the locally weighted matrix smoothing (LOWEMS) framework as one possible approach to dynamic matrix recovery. We then establish error bounds for LOWEMS in both the em matrix sensing and em matrix completion observation models. Our results quantify the potential benefits of exploiting dynamic constraints both in terms of recovery accuracy and sample complexity. To illustrate these benefits we provide both synthetic and real-world experimental results.