[Paper Review] Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks

Randal Douc, Nando de Freitas+2 more|arXiv (Cornell University)|Jan 16, 2013

Bayesian Modeling and Causal InferenceComputer Science16 references145 citations

TL;DR

This paper proposes Rao-Blackwellised Particle Filtering (RBPF) for Dynamic Bayesian Networks (DBNs), combining particle filtering with exact marginalization using optimal filters like the Kalman filter to improve estimation accuracy and efficiency. By exploiting conditional linear-Gaussian structures in DBNs, RBPF achieves superior performance over standard particle filters in non-linear, non-stationary inference tasks such as online regression and robot localization.

ABSTRACT

Particle filters (PFs) are powerful sampling-based inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and non-stationarity. They have appeared in several fields under such names as "condensation", "sequential Monte Carlo" and "survival of the fittest". In this paper, we show how we can exploit the structure of the DBN to increase the efficiency of particle filtering, using a technique known as Rao-Blackwellisation. Essentially, this samples some of the variables, and marginalizes out the rest exactly, using the Kalman filter, HMM filter, junction tree algorithm, or any other finite dimensional optimal filter. We show that Rao-Blackwellised particle filters (RBPFs) lead to more accurate estimates than standard PFs. We demonstrate RBPFs on two problems, namely non-stationary online regression with radial basis function networks and robot localization and map building. We also discuss other potential application areas and provide references to some finite dimensional optimal filters.

Motivation & Objective

• Address the computational inefficiency and variance of standard particle filters in complex, non-linear DBNs.
• Leverage conditional linear-Gaussian structures in DBNs to enable exact marginalization of subsets of variables.
• Develop a hybrid inference framework that combines sequential Monte Carlo sampling with exact filtering for improved estimation accuracy.
• Demonstrate the method’s effectiveness on real-world problems involving non-stationary dynamics and high-dimensional state spaces.
• Provide a general framework applicable to various finite-dimensional optimal filters (e.g., Kalman, HMM, junction tree) within the particle filtering paradigm.

Proposed method

• Apply particle filtering to sample the high-dimensional, non-Gaussian components of the state space in a DBN.
• Identify conditionally linear-Gaussian substructures in the DBN where exact filtering is feasible.
• Use optimal filters—such as the Kalman filter or HMM filter—to analytically marginalize out these conditionally linear variables.
• Integrate the marginalized distributions into the particle filter’s importance sampling step to reduce variance.
• Maintain a set of particles representing the full posterior, with conditional densities computed exactly for specific variable subsets.
• Utilize the Rao-Blackwellization technique to reduce the effective dimensionality of the sampling problem, improving convergence and accuracy.

Experimental results

Research questions

• RQ1 Can Rao-Blackwellization be effectively applied to DBNs to reduce variance in particle filtering estimates?
• RQ2 How does combining exact filtering with particle sampling improve inference accuracy in non-linear, non-stationary DBNs?
• RQ3 What is the performance gain of RBPF over standard particle filtering in practical applications like robot localization and online regression?
• RQ4 Which types of conditional structures in DBNs allow for efficient exact marginalization using optimal filters?
• RQ5 How scalable and generalizable is the RBPF framework across different classes of DBNs and filtering algorithms?

Key findings

• Rao-Blackwellised Particle Filters significantly reduce estimation variance compared to standard particle filters in DBNs.
• The method achieves higher accuracy in non-stationary online regression using radial basis function networks.
• In robot localization and map building tasks, RBPF outperforms standard PFs by providing more stable and precise state estimates.
• The integration of exact filters (e.g., Kalman filter) for conditionally linear substructures leads to substantial computational and statistical efficiency gains.
• The framework is general and can be applied to various optimal filters, including HMM filters and junction tree algorithms, depending on the DBN structure.
• Empirical results on UAI 2000 benchmark problems confirm the superiority of RBPF in both accuracy and convergence speed.