# HOPS: High-order Polynomials with Self-supervised Dimension Reduction for Load Forecasting

arXiv: https://arxiv.org/abs/2501.10637 · HTML: https://mlsanity.com/paper/2501.10637/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 18 Jan 2025.

## Builds on (most cited first, 2 of 2)

- [Review of Smart Meter Data Analytics: Applications, Methodologies, and Challenges](https://mlsanity.com/paper/1802.04117/) (2018)
- [Lasso estimation for GEFCom2014 probabilistic electric load forecasting](https://mlsanity.com/paper/1603.01376/) (2016)

## Abstract (arXiv)

Load forecasting is a fundamental task in smart grid. Many techniques have been applied to developing load forecasting models. Due to the challenges such as the Curse of Dimensionality, overfitting, and limited computing resources, multivariate higher-order polynomial models have received limited attention in load forecasting, despite their desirable mathematical foundations and optimization properties. In this paper, we propose low rank approximation and self-supervised dimension reduction to address the aforementioned issues. To further improve computational efficiency, we also utilize a fast Conjugate Gradient based algorithm for the proposed polynomial models. Based on the load datasets from the ISO New England, the proposed method high-order polynomials with self-supervised dimension reduction (HOPS) demonstrates higher forecasting accuracy over several competitive models. Additionally, experimental results indicate that our approach alleviates redundant variable construction, achieving better forecasts with fewer input variables.