Multivariate Online Linear Regression for Hierarchical Forecasting

Massil Hihat; Guillaume Garrigos; Adeline Fermanian; Simon Bussy

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arXiv · 2402.14578

Multivariate Online Linear Regression for Hierarchical Forecasting

Massil Hihat·Guillaume Garrigos·Adeline Fermanian·Simon Bussy

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Abstract

In this paper, we consider a deterministic online linear regression model where we allow the responses to be multivariate. To address this problem, we introduce MultiVAW, a method that extends the well-known Vovk-Azoury-Warmuth algorithm to the multivariate setting, and show that it also enjoys logarithmic regret in time. We apply our results to the online hierarchical forecasting problem and recover an algorithm from this literature as a special case, allowing us to relax the hypotheses usually made for its analysis.

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Massil Hihat, Guillaume Garrigos, Adeline Fermanian, Simon Bussy. 2024-02-22. Multivariate Online Linear Regression for Hierarchical Forecasting. https://arxiv.org/abs/2402.14578

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