Multivariate Online Linear Regression for Hierarchical Forecasting
This work addresses online forecasting problems for domains like supply chain or economics, but it is incremental as it extends a known algorithm to a multivariate setting.
The paper tackles multivariate online linear regression by introducing MultiVAW, an extension of the Vovk-Azoury-Warmuth algorithm, achieving logarithmic regret over time, and applies it to hierarchical forecasting to relax existing analysis hypotheses.
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.