# OLR-WA: Online Weighted Average Linear Regression in Multivariate Data Streams

arXiv: https://arxiv.org/abs/2512.14892 · HTML: https://mlsanity.com/paper/2512.14892/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 9 of 9)

- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Transferability in Machine Learning: from Phenomena to Black-Box Attacks using Adversarial Samples](https://mlsanity.com/paper/1605.07277/) (2016)
- [Online Stochastic Gradient Descent with Arbitrary Initialization Solves Non-smooth, Non-convex Phase Retrieval](https://mlsanity.com/paper/1910.12837/) (2019)
- [An Efficient Algorithm For Generalized Linear Bandit: Online Stochastic Gradient Descent and Thompson Sampling](https://mlsanity.com/paper/2006.04012/) (2020)
- [Choosing the Sample with Lowest Loss makes SGD Robust](https://mlsanity.com/paper/2001.03316/) (2020)
- [Reinforcement Learning for Learning Rate Control](https://mlsanity.com/paper/1705.11159/) (2017)
- [Can we globally optimize cross-validation loss? Quasiconvexity in ridge regression](https://mlsanity.com/paper/2107.09194/) (2021)
- [OLR-WA Online Regression with Weighted Average](https://mlsanity.com/paper/2307.02804/) (2023)

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

- [SCCM : Stream Cruise Control Method for Automated Drift Detection and Adaptation](https://mlsanity.com/paper/2609.09432/) (2026)

## Abstract (arXiv)

Online learning updates models incrementally with new data, avoiding large storage requirements and costly model recalculations. In this paper, we introduce "OLR-WA; OnLine Regression with Weighted Average", a novel and versatile multivariate online linear regression model. We also investigate scenarios involving drift, where the underlying patterns in the data evolve over time, conduct convergence analysis, and compare our approach with existing online regression models. The results of OLR-WA demonstrate its ability to achieve performance comparable to the batch regression, while also showcasing comparable or superior performance when compared with other state-of-the-art online models, thus establishing its effectiveness. Moreover, OLR-WA exhibits exceptional performance in terms of rapid convergence, surpassing other online models with consistently achieving high r2 values as a performance measure from the first iteration to the last iteration, even when initialized with minimal amount of data points, as little as 1% to 10% of the total data points. In addition to its ability to handle time-based (temporal drift) scenarios, remarkably, OLR-WA stands out as the only model capable of effectively managing confidence-based challenging scenarios. It achieves this by adopting a conservative approach in its updates, giving priority to older data points with higher confidence levels. In summary, OLR-WA's performance further solidifies its versatility and utility across different contexts, making it a valuable solution for online linear regression tasks.