Learning Optimal Projection for Forecast Reconciliation of Hierarchical Time Series

Asterios Tsiourvas, Wei Sun, Georgia Perakis, Pin-Yu Chen, Yada Zhu
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:48713-48727, 2024.

Abstract

Hierarchical time series forecasting requires not only prediction accuracy but also coherency, i.e., forecasts add up appropriately across the hierarchy. Recent literature has shown that reconciliation via projection outperforms prior methods such as top-down or bottom-up approaches. Unlike existing work that pre-specifies a projection matrix (e.g., orthogonal), we study the problem of learning the optimal oblique projection from data for coherent forecasting of hierarchical time series. In addition to the unbiasedness-preserving property, oblique projection implicitly accounts for the hierarchy structure and assigns different weights to individual time series, providing significant adaptability over orthogonal projection which treats base forecast errors equally. We examine two broad classes of projections, namely Euclidean projection and general oblique projections. We propose to model the reconciliation step as a learnable, structured, projection layer in the neural forecaster architecture. The proposed approach allows for the efficient learning of the optimal projection in an end-to-end framework where both the neural forecaster and the projection layer are learned simultaneously. An empirical evaluation of real-world hierarchical time series datasets demonstrates the superior performance of the proposed method over existing state-of-the-art approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-tsiourvas24b, title = {Learning Optimal Projection for Forecast Reconciliation of Hierarchical Time Series}, author = {Tsiourvas, Asterios and Sun, Wei and Perakis, Georgia and Chen, Pin-Yu and Zhu, Yada}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {48713--48727}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/tsiourvas24b/tsiourvas24b.pdf}, url = {https://proceedings.mlr.press/v235/tsiourvas24b.html}, abstract = {Hierarchical time series forecasting requires not only prediction accuracy but also coherency, i.e., forecasts add up appropriately across the hierarchy. Recent literature has shown that reconciliation via projection outperforms prior methods such as top-down or bottom-up approaches. Unlike existing work that pre-specifies a projection matrix (e.g., orthogonal), we study the problem of learning the optimal oblique projection from data for coherent forecasting of hierarchical time series. In addition to the unbiasedness-preserving property, oblique projection implicitly accounts for the hierarchy structure and assigns different weights to individual time series, providing significant adaptability over orthogonal projection which treats base forecast errors equally. We examine two broad classes of projections, namely Euclidean projection and general oblique projections. We propose to model the reconciliation step as a learnable, structured, projection layer in the neural forecaster architecture. The proposed approach allows for the efficient learning of the optimal projection in an end-to-end framework where both the neural forecaster and the projection layer are learned simultaneously. An empirical evaluation of real-world hierarchical time series datasets demonstrates the superior performance of the proposed method over existing state-of-the-art approaches.} }
Endnote
%0 Conference Paper %T Learning Optimal Projection for Forecast Reconciliation of Hierarchical Time Series %A Asterios Tsiourvas %A Wei Sun %A Georgia Perakis %A Pin-Yu Chen %A Yada Zhu %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-tsiourvas24b %I PMLR %P 48713--48727 %U https://proceedings.mlr.press/v235/tsiourvas24b.html %V 235 %X Hierarchical time series forecasting requires not only prediction accuracy but also coherency, i.e., forecasts add up appropriately across the hierarchy. Recent literature has shown that reconciliation via projection outperforms prior methods such as top-down or bottom-up approaches. Unlike existing work that pre-specifies a projection matrix (e.g., orthogonal), we study the problem of learning the optimal oblique projection from data for coherent forecasting of hierarchical time series. In addition to the unbiasedness-preserving property, oblique projection implicitly accounts for the hierarchy structure and assigns different weights to individual time series, providing significant adaptability over orthogonal projection which treats base forecast errors equally. We examine two broad classes of projections, namely Euclidean projection and general oblique projections. We propose to model the reconciliation step as a learnable, structured, projection layer in the neural forecaster architecture. The proposed approach allows for the efficient learning of the optimal projection in an end-to-end framework where both the neural forecaster and the projection layer are learned simultaneously. An empirical evaluation of real-world hierarchical time series datasets demonstrates the superior performance of the proposed method over existing state-of-the-art approaches.
APA
Tsiourvas, A., Sun, W., Perakis, G., Chen, P. & Zhu, Y.. (2024). Learning Optimal Projection for Forecast Reconciliation of Hierarchical Time Series. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:48713-48727 Available from https://proceedings.mlr.press/v235/tsiourvas24b.html.

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