[Paper Review] De-Sequentialized Monte Carlo: a parallel-in-time particle smoother

Adrien Corenflos, Nicolás Chopin+1 more|arXiv (Cornell University)|Feb 4, 2022

Statistical Methods and Bayesian Inference4 citations

TL;DR

This paper introduces dSMC, a parallel-in-time particle smoother that achieves O(log T) span-complexity for T time steps using a de-sequentialized recursive structure based on associative operators and parallel scan algorithms. It enables faster Bayesian smoothing and parameter inference on multi-core hardware, with theoretical Lp convergence bounds and variance reduction via lazy resampling and improved proposal design.

ABSTRACT

Particle smoothers are SMC (Sequential Monte Carlo) algorithms designed to approximate the joint distribution of the states given observations from a state-space model. We propose dSMC (de-Sequentialized Monte Carlo), a new particle smoother that is able to process $T$ observations in $\mathcal{O}(\log T)$ time on parallel architecture. This compares favourably with standard particle smoothers, the complexity of which is linear in $T$. We derive $\mathcal{L}_p$ convergence results for dSMC, with an explicit upper bound, polynomial in $T$. We then discuss how to reduce the variance of the smoothing estimates computed by dSMC by (i) designing good proposal distributions for sampling the particles at the initialization of the algorithm, as well as by (ii) using lazy resampling to increase the number of particles used in dSMC. Finally, we design a particle Gibbs sampler based on dSMC, which is able to perform parameter inference in a state-space model at a $\mathcal{O}(\log(T))$ cost on parallel hardware.

Motivation & Objective

• To address the computational bottleneck of sequential particle smoothers, which scale linearly with time steps T on single-core systems.
• To enable sub-linear span-complexity (O(log T)) for particle smoothing on parallel architectures, overcoming the inherent sequential dependency in standard SMC.
• To develop a scalable, statistically sound particle smoother that maintains convergence properties while drastically reducing wall-clock time.
• To support efficient parameter inference by integrating dSMC into a particle Gibbs sampler with logarithmic time complexity.
• To reduce variance in smoothing estimates through improved proposal distributions and a novel lazy resampling strategy.

Proposed method

• dSMC reformulates the sequential particle smoothing recursion using associative operators to enable parallelization via a parallel scan (prefix sum) algorithm.
• The method constructs a de-sequentialized recursion over time by grouping time steps into a binary tree structure, allowing O(log T) depth computation on parallel hardware.
• It employs a conditional version of dSMC to support unbiased coupling and particle Gibbs sampling for parameter inference.
• A lazy resampling scheme is introduced to reduce memory and computational load by computing weights on-demand and only for active particle pairs.
• Proposal distributions are designed using LGSSM (linear Gaussian state-space model) approximants to improve particle diversity and reduce variance.
• The algorithm leverages the parallel resampling framework of Murray et al. (2016) to further enhance scalability and reduce memory footprint.

Experimental results

Research questions

• RQ1 Can particle smoothing be parallelized in time to achieve O(log T) span-complexity on multi-core systems while maintaining statistical accuracy?
• RQ2 How can the inherent sequential dependency in SMC smoothers be broken using associative operators and recursive decomposition?
• RQ3 What is the theoretical convergence rate of the proposed dSMC algorithm, and can it be bounded in Lp norm with explicit dependence on T?
• RQ4 How can variance in smoothing estimates be reduced without increasing computational cost, especially in high-dimensional or multi-modal posteriors?
• RQ5 Can dSMC be effectively integrated into a particle Gibbs sampler to enable fast, unbiased parameter inference with logarithmic time complexity?

Key findings

• dSMC achieves O(log T) span-complexity for smoothing, representing a significant speedup over standard sequential smoothers that scale linearly with T.
• The algorithm provides explicit Lp convergence bounds that grow polynomially in T, ensuring theoretical consistency as T increases.
• Lazy resampling reduces memory usage and computational overhead by avoiding full weight recomputation, improving scalability in high-dimensional settings.
• The use of LGSSM approximants as proposal distributions significantly improves particle diversity and reduces variance in smoothing estimates.
• dSMC enables a particle Gibbs sampler with O(log T) wall-clock time complexity, making it highly efficient for Bayesian parameter inference in state-space models.
• The method is compatible with the unbiased coupled smoothing framework of Jacob et al. (2019), allowing variance reduction through independent estimation averaging.