Time series recovery from partial observations via Nonnegative 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: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=to1OL4qBku

Changes Since Last Submission:

Dear Editors,

The paper has been substantially rewritten to ease readability and more detailed implementation instructions have been added. Its introduction has been remelt to address the previous concerns. We are grateful for the previous reviews and the time you will spend on this new version.

Sincerely,

Assigned Action Editor: ~Kejun_Huang1

Submission Number: 5905