A forward-only scheme for online learning of proposal distributions in particle filters

2026-01-22

AI Summary

This work addresses the limitations of conventional particle filtering approaches that rely on backward recursion for proposal distribution learning, which require access to the entire observation sequence and suffer from numerical instability, thereby hindering online deployment. To overcome these challenges, the authors propose a forward-only online learning mechanism that adaptively refines the proposal distribution by incrementally incorporating future observation information, achieving performance comparable to backward methods while relying solely on forward recursion. This framework constitutes the first fully online approach for proposal distribution learning, substantially improving numerical stability and algorithmic robustness. Experimental results on both synthetic and real-world data demonstrate that the method incurs only a marginal increase in the variance of marginal likelihood estimates while significantly enhancing the reliability of online inference.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Probabilistic Inference

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We introduce a new online approach for constructing proposal distributions in particle filters using a forward scheme. Our method progressively incorporates future observations to refine proposals. This is in contrast to backward-scheme algorithms that require access to the entire dataset, such as the iterated auxiliary particle filters (Guarniero et al., 2017, arXiv:1511.06286) and controlled sequential Monte Carlo (Heng et al., 2020, arXiv:1708.08396) which leverage all future observations through backward recursion. In comparison, our forward scheme achieves a gradual improvement of proposals that converges toward the proposal targeted by these backward methods. We show that backward approaches can be numerically unstable even in simple settings. Our forward method, however, offers significantly greater robustness with only a minor trade-off in performance, measured by the variance of the marginal likelihood estimator. Numerical experiments on both simulated and real data illustrate the enhanced stability of our forward approach.

Problem

• particle filters
• proposal distributions
• online learning
• forward scheme
• numerical stability

Innovation

• forward-only scheme
• online learning
• proposal distribution
• particle filter
• numerical stability