# Multivariate Online Linear Regression for Hierarchical Forecasting

arXiv: https://arxiv.org/abs/2402.14578 · HTML: https://mlsanity.com/paper/2402.14578/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 22 Feb 2024.

## Builds on (most cited first, 7 of 7)

- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Relative Loss Bounds for On-line Density Estimation with the Exponential Family of Distributions](https://mlsanity.com/paper/1301.6677/) (2013)
- [Optimal learning with Bernstein Online Aggregation](https://mlsanity.com/paper/1404.1356/) (2014)
- [A machine learning approach for forecasting hierarchical time series](https://mlsanity.com/paper/2006.00630/) (2020)
- [Uniform regret bounds over Rd for the sequential linear regression problem with the square loss](https://mlsanity.com/paper/1805.11386/) (2018)
- [Online Hierarchical Forecasting for Power Consumption Data](https://mlsanity.com/paper/2003.00585/) (2020)
- [Stochastic Online Linear Regression: the Forward Algorithm to Replace Ridge](https://mlsanity.com/paper/2111.01602/) (2021)

## Built on by (most cited first, 1 of 1)

- [Probabilistic Forecasting of Electric Vehicle Charging in a Time-varying Hierarchical Infrastructure](https://mlsanity.com/paper/2610.13588/) (2026)

## Abstract (arXiv)

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.