Online Rolling Controlled Sequential Monte Carlo

2025-08-01

AI Summary

For real-time filtering in general-state-space hidden Markov models, this paper proposes the Online Rolling Controlled Sequential Monte Carlo (OR-CSMC) method. OR-CSMC employs a dual-particle system to jointly perform state filtering and sequential estimation of nonlinear distortion functions, while incorporating a fixed-length rolling window to ensure bounded computational complexity. It constitutes the first extension of controlled sequential Monte Carlo to strictly online settings, achieving both adaptivity and numerical stability. Experiments on high-dimensional linear-Gaussian, stochastic volatility, and neuroscience dynamical models demonstrate that OR-CSMC significantly outperforms standard particle filters in estimation accuracy and robustness—particularly in high-dimensional nonlinear scenarios—where it exhibits marked advantages in both convergence behavior and resilience to degeneracy.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We introduce methodology for real-time inference in general-state-space hidden Markov models. Specifically, we extend recent advances in controlled sequential Monte Carlo (CSMC) methods-originally proposed for offline smoothing-to the online setting via a rolling window mechanism. Our novel online rolling controlled sequential Monte Carlo (ORCSMC) algorithm employs two particle systems to simultaneously estimate twisting functions and perform filtering, ensuring real-time adaptivity to new observations while maintaining bounded computational cost. Numerical results on linear-Gaussian, stochastic volatility, and neuroscience models demonstrate improved estimation accuracy and robustness in higher dimensions, compared to standard particle filtering approaches. The method offers a statistically efficient and practical solution for sequential and real-time inference in complex latent variable models.

Problem

• Real-time inference in hidden Markov models
• Online adaptation with bounded computational cost
• Improved accuracy in complex latent variable models

Innovation

• Online rolling window mechanism for real-time inference
• Two particle systems estimate twisting functions
• Ensures bounded computational cost adaptively