# Forecasting time series with constraints

arXiv: https://arxiv.org/abs/2502.10485 · HTML: https://mlsanity.com/paper/2502.10485/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 54 references that are in the map.
- First posted on arXiv 14 Feb 2025.

## Builds on (most cited first, 18 of 18)

- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [A Second-order Bound with Excess Losses](https://mlsanity.com/paper/1402.2044/) (2014)
- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [On the Constrained Time-Series Generation Problem](https://mlsanity.com/paper/2307.01717/) (2023)
- [Fast calibrated additive quantile regression](https://mlsanity.com/paper/1707.03307/) (2017)
- [Adaptive Methods for Short-Term Electricity Load Forecasting During COVID-19 Lockdown in France](https://mlsanity.com/paper/2009.06527/) (2020)
- [Physics-informed machine learning as a kernel method](https://mlsanity.com/paper/2402.07514/) (2024)
- [Online Hierarchical Forecasting for Power Consumption Data](https://mlsanity.com/paper/2003.00585/) (2020)
- [Adaptive Probabilistic Forecasting of Electricity (Net-)Load](https://mlsanity.com/paper/2301.10090/) (2023)
- [Kernel regression, minimax rates and effective dimensionality: beyond the regular case](https://mlsanity.com/paper/1611.03979/) (2016)
- [Expert Aggregation for Financial Forecasting](https://mlsanity.com/paper/2111.15365/) (2021)
- [Forecasting Electric Vehicle Charging Station Occupancy: Smarter Mobility Data Challenge](https://mlsanity.com/paper/2306.06142/) (2023)
- [Coherent Hierarchical Probabilistic Forecasting of Electric Vehicle Charging Demand](https://mlsanity.com/paper/2411.00337/) (2024)
- [Hierarchical learning, forecasting coherent spatio-temporal individual and aggregated building loads](https://mlsanity.com/paper/2301.12967/) (2023)

## Built on by (most cited first, 2 of 2)

- [Fast kernel methods: Sobolev, physics-informed, and additive models](https://mlsanity.com/paper/2509.02649/) (2025)
- [Hierarchical Time Series Forecasting with Operator-Valued Kernels](https://mlsanity.com/paper/2610.18196/) (2026)

## Abstract (arXiv)

Time series forecasting presents unique challenges that limit the effectiveness of traditional machine learning algorithms. To address these limitations, various approaches have incorporated linear constraints into learning algorithms, such as generalized additive models and hierarchical forecasting. In this paper, we propose a unified framework for integrating and combining linear constraints in time series forecasting. Within this framework, we show that the exact minimizer of the constrained empirical risk can be computed efficiently using linear algebra alone. This approach allows for highly scalable implementations optimized for GPUs. We validate the proposed methodology through extensive benchmarking on real-world tasks, including electricity demand forecasting and tourism forecasting, achieving state-of-the-art performance.