Forecasting time series with constraints

2025-02-14

AI Summary

Time-series forecasting under linear constraints—such as additive structure or hierarchical consistency—lacks unified, exact solution methods. Method: This paper introduces the first unified framework enabling closed-form, analytically exact optimization for such constrained forecasting tasks. It encodes arbitrary linear equality and inequality constraints directly into the empirical risk minimization objective, yielding an efficient, algebraically tractable solution via linear algebra operations. The approach integrates generalized additive models, hierarchical forecasting, and constrained optimization, with end-to-end GPU acceleration. Contribution/Results: The framework supports arbitrary combinations of linear constraints and scales seamlessly on GPUs. Evaluated on real-world datasets—including electricity demand and tourism flow—it consistently outperforms both constrained and unconstrained baselines, achieving state-of-the-art (SOTA) accuracy while preserving structural validity.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Time-Series/Data Streams
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Enhancing time series forecasting accuracy
• Integrating linear constraints in models
• Optimizing for GPU scalability

Innovation

• Unified framework for constraints
• Linear algebra for risk minimization
• GPU-optimized scalable implementations