A Multi-Task Learning Approach to Linear Multivariate Forecasting

Liran Nochumsohn, Hedi Zisling, Omri Azencot
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:2638-2646, 2025.

Abstract

Accurate forecasting of multivariate time series data is important in many engineering and scientific applications. Recent state-of-the-art works ignore the inter-relations between variates, using their model on each variate independently. This raises several research questions related to proper modeling of multivariate data. In this work, we propose to view multivariate forecasting as a multi-task learning problem, facilitating the analysis of forecasting by considering the angle between task gradients and their balance. To do so, we analyze linear models to characterize the behavior of tasks. Our analysis suggests that tasks can be defined by grouping similar variates together, which we achieve via a simple clustering that depends on correlation-based similarities. Moreover, to balance tasks, we scale gradients with respect to their prediction error. Then, each task is solved with a linear model within our MTLinear framework. We evaluate our approach on challenging benchmarks in comparison to strong baselines, and we show it obtains on-par or better results on multivariate forecasting problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-nochumsohn25a, title = {A Multi-Task Learning Approach to Linear Multivariate Forecasting}, author = {Nochumsohn, Liran and Zisling, Hedi and Azencot, Omri}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {2638--2646}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/nochumsohn25a/nochumsohn25a.pdf}, url = {https://proceedings.mlr.press/v258/nochumsohn25a.html}, abstract = {Accurate forecasting of multivariate time series data is important in many engineering and scientific applications. Recent state-of-the-art works ignore the inter-relations between variates, using their model on each variate independently. This raises several research questions related to proper modeling of multivariate data. In this work, we propose to view multivariate forecasting as a multi-task learning problem, facilitating the analysis of forecasting by considering the angle between task gradients and their balance. To do so, we analyze linear models to characterize the behavior of tasks. Our analysis suggests that tasks can be defined by grouping similar variates together, which we achieve via a simple clustering that depends on correlation-based similarities. Moreover, to balance tasks, we scale gradients with respect to their prediction error. Then, each task is solved with a linear model within our MTLinear framework. We evaluate our approach on challenging benchmarks in comparison to strong baselines, and we show it obtains on-par or better results on multivariate forecasting problems.} }
Endnote
%0 Conference Paper %T A Multi-Task Learning Approach to Linear Multivariate Forecasting %A Liran Nochumsohn %A Hedi Zisling %A Omri Azencot %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-nochumsohn25a %I PMLR %P 2638--2646 %U https://proceedings.mlr.press/v258/nochumsohn25a.html %V 258 %X Accurate forecasting of multivariate time series data is important in many engineering and scientific applications. Recent state-of-the-art works ignore the inter-relations between variates, using their model on each variate independently. This raises several research questions related to proper modeling of multivariate data. In this work, we propose to view multivariate forecasting as a multi-task learning problem, facilitating the analysis of forecasting by considering the angle between task gradients and their balance. To do so, we analyze linear models to characterize the behavior of tasks. Our analysis suggests that tasks can be defined by grouping similar variates together, which we achieve via a simple clustering that depends on correlation-based similarities. Moreover, to balance tasks, we scale gradients with respect to their prediction error. Then, each task is solved with a linear model within our MTLinear framework. We evaluate our approach on challenging benchmarks in comparison to strong baselines, and we show it obtains on-par or better results on multivariate forecasting problems.
APA
Nochumsohn, L., Zisling, H. & Azencot, O.. (2025). A Multi-Task Learning Approach to Linear Multivariate Forecasting. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:2638-2646 Available from https://proceedings.mlr.press/v258/nochumsohn25a.html.

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