Online Bayesian Experimental Design for Partially Observed Dynamical Systems

2025-11-06

AI Summary

Bayesian experimental design (BED) for partially observable dynamic systems—such as state-space models (SSMs)—is notoriously difficult to implement online due to intractable expectations over latent states and likelihoods. Method: We propose the first online BED framework for such systems, built upon nested particle filtering (NPF) to enable efficient, convergent online estimation of the expected information gain (EIG) and its gradient. By explicitly marginalizing latent states, our approach bypasses intractable likelihood evaluation and enables scalable stochastic optimization for nonlinear SSMs. Crucially, it jointly updates both the posterior and the experimental design parameters, supporting sequential data acquisition and real-time inference. Results: Evaluated on SIR epidemiological modeling and mobile source localization, our method significantly improves information efficiency in parameter estimation, demonstrating robust performance and practical scalability in dynamic, partially observed settings.

Technology Category

• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• 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

Bayesian experimental design (BED) provides a principled framework for optimizing data collection, but existing approaches do not apply to crucial real-world settings such as dynamical systems with partial observability, where only noisy and incomplete observations are available. These 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. In addition, the dynamical nature of the system requires online algorithms that update posterior distributions and select designs sequentially in a computationally efficient manner. 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 (NPFs) for efficient online inference with convergence guarantees. Applications to realistic models, such as the susceptible-infected-recovered (SIR) and a moving source location task, show that our framework successfully handles both partial observability and online computation.

Problem

• Addresses Bayesian experimental design for partially observed dynamical systems
• Solves intractable likelihood in state-space models with latent variables
• Enables online sequential design selection with computational efficiency

Innovation

• Estimators marginalizing latent states for EIG
• Leveraging nested particle filters for online inference
• Enabling scalable stochastic optimization in nonlinear SSMs