Deep Time-series Forecasting Needs Kernelized Moment Balancing

2026-01-31

AI Summary

This work addresses the limitation of existing deep time series forecasting methods, which rely on fixed balancing functions and fail to satisfy the first-moment matching condition required for distributional balance, leading to misalignment between predicted and true distributions. The authors reformulate forecasting as a distributional balancing problem and introduce, for the first time, a kernelized moment balancing mechanism that adaptively selects the most informative balancing functions in a reproducing kernel Hilbert space (RKHS). This approach achieves first-moment matching for arbitrary functions, rigorously fulfilling the Imbens distributional balancing criterion. The resulting differentiable and computable objective function enables end-to-end optimization and seamless integration with mainstream deep forecasting models. Extensive experiments demonstrate that the proposed method significantly improves prediction accuracy across multiple benchmark models and datasets, achieving state-of-the-art performance and confirming its effectiveness and generalizability.

Technology Category

• Machine Learning: Kernel Methods
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Deep time-series forecasting can be formulated as a distribution balancing problem aimed at aligning the distribution of the forecasts and ground truths. According to Imbens'criterion, true distribution balance requires matching the first moments with respect to any balancing function. We demonstrate that existing objectives fail to meet this criterion, as they enforce moment matching only for one or two predefined balancing functions, thus failing to achieve full distribution balance. To address this limitation, we propose direct forecasting with kernelized moment balancing (KMB-DF). Unlike existing objectives, KMB-DF adaptively selects the most informative balancing functions from a reproducing kernel hilbert space (RKHS) to enforce sufficient distribution balancing. We derive a tractable and differentiable objective that enables efficient estimation from empirical samples and seamless integration into gradient-based training pipelines. Extensive experiments across multiple models and datasets show that KMB-DF consistently improves forecasting accuracy and achieves state-of-the-art performance. Code is available at https://anonymous.4open.science/r/KMB-DF-403C.

Problem

• deep time-series forecasting
• distribution balancing
• moment matching
• balancing function
• Imbens' criterion

Innovation

• kernelized moment balancing
• distribution balancing
• reproducing kernel Hilbert space
• deep time-series forecasting
• moment matching