为部分可观测动态系统设计在线贝叶斯实验，实现高效信息采集。
Online Bayesian Experimental Design for Partially Observed Dynamical Systems
- 基于嵌套粒子滤波器，对潜在状态进行显式积分，解决信息增益计算难题。
- 在非线性状态空间模型中实现可扩展的随机优化，支持实时参数更新。
- 适用于流行病学和移动源定位等真实场景，兼顾观测不全与在线推理。
贝叶斯实验设计（BED）提供了一种优化数据采集的原理框架，通过选择对未知参数最具有信息量的实验来提升学习效率。然而，现有方法难以同时应对两个挑战：(a) 部分可观测动态系统，即仅能获得噪声且不完整的观测；(b) 完全在线推断，要求在计算高效的条件下顺序更新后验分布并选择实验设计。在部分可观测情形下，动态系统通常建模为状态空间模型（SSMs），其中隐状态介于参数与数据之间，导致似然函数——进而信息论目标如期望信息增益（EIG）——不可解析求解。本文通过推导新的EIG及其梯度估计器，显式对隐状态进行边缘化，从而在非线性SSM中实现可扩展的随机优化。所提方法利用嵌套粒子滤波器实现高效在线状态-参数推断，并具备收敛性保证。在流行病学模型（如SIR模型）及移动源定位任务中的应用表明，该框架成功处理了部分可观测性与在线推断双重挑战。
原文摘要 · Abstract (English)
Bayesian experimental design (BED) provides a principled framework for optimizing data collection by choosing experiments that are maximally informative about unknown parameters. However, existing methods cannot deal with the joint challenge of (a) partially observable dynamical systems, where only noisy and incomplete observations are available, and (b) fully online inference, which updates posterior distributions and selects designs sequentially in a computationally efficient manner. Under partial observability, dynamical systems are naturally modeled as state-space models (SSMs), where latent states mediate the link between parameters and data, making the likelihood -- and thus information-theoretic objectives like the expected information gain (EIG) -- intractable. We address these challenges by deriving new estimators of the EIG and its gradient that explicitly marginalize latent states, enabling scalable stochastic optimization in nonlinear SSMs. Our approach leverages nested particle filters for efficient online state-parameter inference with convergence guarantees. Applications to realistic models, such as the susceptible-infectious-recovered (SIR) and a moving source location task, show that our framework successfully handles both partial observability and online inference.
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