# Online Forecasting Matrix Factorization

arXiv: https://arxiv.org/abs/1712.08734 · HTML: https://mlsanity.com/paper/1712.08734/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2017.

## Built on by (most cited first, 7 of 7)

- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [Act Now: A Novel Online Forecasting Framework for Large-Scale Streaming Data](https://mlsanity.com/paper/2412.00108/) (2024)
- [Forecasting Sparse Movement Speed of Urban Road Networks with Nonstationary Temporal Matrix Factorization](https://mlsanity.com/paper/2203.10651/) (2022)
- [Disentangling Long-Short Term State Under Unknown Interventions for Online Time Series Forecasting](https://mlsanity.com/paper/2502.12603/) (2025)
- [Online Time Series Forecasting with Theoretical Guarantees](https://mlsanity.com/paper/2510.18281/) (2025)
- [Compositional Spectral Prompts for LLM-based Online Time Series Forecasting](https://mlsanity.com/paper/2609.02093/) (2026)
- [Nonlinear Kalman Filtering with Reparametrization Gradients](https://mlsanity.com/paper/2303.04450/) (2023)

## Abstract (arXiv)

In this paper the problem of forecasting high dimensional time series is considered. Such time series can be modeled as matrices where each column denotes a measurement. In addition, when missing values are present, low rank matrix factorization approaches are suitable for predicting future values. This paper formally defines and analyzes the forecasting problem in the online setting, i.e. where the data arrives as a stream and only a single pass is allowed. We present and analyze novel matrix factorization techniques which can learn low-dimensional embeddings effectively in an online manner. Based on these embeddings a recursive minimum mean square error estimator is derived, which learns an autoregressive model on them. Experiments with two real datasets with tens of millions of measurements show the benefits of the proposed approach.