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

TMLR Paper5905 Authors

Abstract: In modern time series problems, one aims at forecasting multiple times 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.

Submission Length: Long submission (more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=RH7ibCiQ0i

Changes Since Last Submission: In view of the last report, we have reorganized the manuscript to improve readability, specifically by unifying notations and moving definitions to the Introduction. We have sharpened the discussion of our contributions to emphasize the novelty of the Sliding Mask Method (SMM) framework and its specific theoretical guarantees for deterministic block-missing patterns, which differ from general matrix completion results. Furthermore, we have expanded the experimental section to include a detailed analysis of why SMM outperforms state-of-the-art Deep Learning models in specific regimes and provided clear guidelines for selecting between mAMF and mNMF. We believe these revisions, alongside the inclusion of the suggested citations, have significantly strengthened the paper’s quality and focus.

Assigned Action Editor: ~Kejun_Huang1

Submission Number: 5905