# Time series forecasting from partial observations via Non-negative Matrix Factorization

arXiv: https://arxiv.org/abs/2102.05314 · HTML: https://mlsanity.com/paper/2102.05314/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 10 Feb 2021.

## Builds on (most cited first, 7 of 7)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [The Why and How of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1401.5226/) (2014)
- [Non-negative Matrix Factorization via Archetypal Analysis](https://mlsanity.com/paper/1705.02994/) (2017)
- [Recovering Joint Probability of Discrete Random Variables from Pairwise Marginals](https://mlsanity.com/paper/2006.16912/) (2020)
- [Exact and Heuristic Algorithms for Semi-Nonnegative Matrix Factorization](https://mlsanity.com/paper/1410.7220/) (2014)
- [Nonnegative matrix factorization with side information for time series recovery and prediction](https://mlsanity.com/paper/1709.06320/) (2017)

## Abstract (arXiv)

In modern time series problems, one aims at forecasting multiple time series with possible missing and noisy values. In this paper, we introduce the Sliding Mask Method (SMM) for forecasting multiple nonnegative time series by means of nonnegative matrix completion: observed noisy values and forecast/missing values are collected into matrix form, and learning is achieved by representing its rows as a convex combination of a small number of nonnegative vectors, referred to as the archetypes. We introduce two estimates, the mask Archetypal Matrix factorization (mAMF) and the mask normalized Nonnegative Matrix Factorization (mNMF) which can be combined with the SMM method. We prove that these estimates recover the true archetypes with an error proportional to the noise. We use a proximal alternating linearized method (PALM) to compute the archetypes and the convex combination weights. We compared our estimators with state-of-the-art methods (Transformers, LSTM, SARIMAX...) in multiple time series forecasting on real data and obtain that our method outperforms them in most of the experiments.