先校正后预测：用于时间序列预测的观测器状态空间模型

中文摘要 AI 辅助

时间序列预测需要对观测过程在最后一个可用测量点之后的动态进行外推。然而，循环预测模型通常将观测值视为直接控制其潜在动态的输入。当这些观测值在预测时变得不可用时，这会导致机制转变。遵循状态估计的视角，我们引入了观测器状态空间模型（OSSMs），这是一类将观测输入时间序列解释为底层自主动力系统测量的循环模型。OSSMs明确地将潜在状态传播与测量同化分开：一个单一的转换控制上下文区间和预测区间内的动态，而可用的观测值通过观测器校正估计的状态。这种表述自然地暴露了经典控制理论性质，包括可观测性和状态估计误差的收敛性。我们进一步表明，传统和近期的SSMs可以作为我们OSSM框架的特例恢复，从而为其循环动态提供统一的解释并揭示建模不一致性。我们在多个基准上进行了实验，表明OSSM在保持与相应SSM基线相同的参数数量和训练设置的同时，实现了显著的改进。这些结果支持循环预测的一个简单原则：观测值应校正估计的潜在状态，而不是控制用于传播它的动态。

英文摘要

Time series forecasting requires extrapolating the dynamics of an observed process beyond the last available measurement. Yet recurrent forecasting models typically treat observations as inputs that directly control their latent dynamics. It leads to a regime change when these observations become unavailable at prediction time. Following a state-estimation perspective, we introduce Observer State-Space Models (OSSMs), a class of recurrent models that interprets the observed input time series as measurements of an underlying autonomous dynamical system. OSSMs explicitly separate latent-state propagation from measurement assimilation: a single transition governs the dynamics across both context and forecasting intervals, while available observations correct the estimated state through an observer. This formulation naturally exposes classical control-theoretic properties, including observability and convergence of the state estimation error. We further show that conventional and recent SSMs can be recovered as particular instances of our OSSM framework, thereby providing a unified interpretation of their recurrent dynamics and revealing modeling inconsistencies. We perform experiments across several benchmarks showing that OSSM achieves substantial improvements while maintaining the same parameter count and training setup as the corresponding SSM baseline. These results support a simple principle for recurrent forecasting: observations should correct the estimated latent state, rather than control the dynamics used to propagate it.

发表机构

• MICS, CentraleSupélec, Université Paris-Saclay（巴黎萨克雷大学中央理工-高等电力学院MICS实验室）
• CentraleSupélec, IETR UMR CNRS 6164（法国国家科学研究中心IETR联合研究单位6164，中央理工-高等电力学院）
• Università di Torino（都灵大学）

机构由 AI 辅助整理，请以论文原文为准。