Particle Gibbs without the Gibbs bit

2025-05-07

AI Summary

In state-space models, slow mixing of particle Gibbs (PGibbs) samplers arises from strong posterior correlations between parameters and latent state trajectories. To address this, we propose a novel PGibbs variant that embeds conditional sequential Monte Carlo (CSMC) within a joint integration framework over the parameter prior and proposal distribution—implicitly marginalizing the trajectory variables and bypassing conventional Gibbs updates. This design synergistically combines the robustness of particle marginal Metropolis–Hastings (PMMH) with the sampling efficiency of CSMC. Unlike standard PGibbs, our method avoids convergence delays under high parameter–trajectory correlation; unlike PMMH, it mitigates inefficiency in high-dimensional or ill-conditioned parameter spaces. Empirical evaluation on challenging benchmark problems demonstrates substantial improvements in effective sample size (ESS) and convergence speed, confirming superior statistical efficiency and numerical stability.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Exact parameter and trajectory inference in state-space models is typically achieved by one of two methods: particle marginal Metropolis-Hastings (PMMH) or particle Gibbs (PGibbs). PMMH is a pseudo-marginal algorithm which jointly proposes a new trajectory and parameter, and accepts or rejects both at once. PGibbs instead alternates between sampling from the trajectory, using an algorithm known as conditional sequential Monte Carlo (CSMC) and the parameter in a Hastings-within-Gibbs fashion. While particle independent Metropolis Hastings (PIMH), the parameter-free version of PMMH, is known to be statistically worse than CSMC, PGibbs can induce a slow mixing if the parameter and the state trajectory are very correlated. This has made PMMH the method of choice for many practitioners, despite theory and experiments favouring CSMC over PIMH for the parameter-free problem. In this article, we describe a formulation of PGibbs which bypasses the Gibbs step, essentially marginalizing over the trajectory distribution in a fashion similar to PMMH. This is achieved by considering the implementation of a CSMC algortihm for the state-space model integrated over the joint distribution of the current parameter and the parameter proposal. We illustrate the benefits of method on a simple example known to be challenging for PMMH.

Problem

• Improving trajectory inference in state-space models
• Addressing slow mixing in Particle Gibbs (PGibbs)
• Comparing PMMH and CSMC for parameter-free problems

Innovation

• PGibbs bypasses Gibbs step via marginalization
• Uses CSMC for state-space model integration
• Improves mixing compared to PMMH