Multivariate Online Linear Regression for Hierarchical Forecasting

TL;DR

This paper introduces MultiVAW, a multivariate online linear regression method with logarithmic regret, applied to hierarchical forecasting, relaxing previous assumptions and extending existing algorithms.

Contribution

It extends the Vovk-Azoury-Warmuth algorithm to multivariate data and applies it to hierarchical forecasting, providing theoretical guarantees.

Findings

MultiVAW achieves logarithmic regret in multivariate online regression.

The method generalizes existing algorithms for hierarchical forecasting.

The approach relaxes previous assumptions in hierarchical forecasting analysis.

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.