Parallel resampling in the particle filter

TL;DR

This paper investigates parallel resampling methods for particle filters on GPUs, comparing alternative schemes to standard ones, and finds that some alternatives are faster and less biased in single precision, especially with large particle sets.

Contribution

It introduces and evaluates alternative resampling schemes that avoid collective operations, improving speed and numerical stability in parallel implementations of particle filters.

Findings

Alternative resamplers can outperform standard schemes on GPUs.

Standard schemes exhibit bias in single precision with many particles.

Proposed auxiliary functions facilitate in-place propagation implementations.

Abstract

Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to data-parallel algorithms such as the particle filter, or more generally Sequential Monte Carlo (SMC), which are increasingly used in statistical inference. SMC methods carry a set of weighted particles through repeated propagation, weighting and resampling steps. The propagation and weighting steps are straightforward to parallelise, as they require only independent operations on each particle. The resampling step is more difficult, as standard schemes require a collective operation, such as a sum, across particle weights. Focusing on this resampling step, we analyse two alternative schemes that do not involve a collective operation (Metropolis and rejection resamplers), and compare them to standard schemes (multinomial, stratified and systematic resamplers). We find that, in certain circumstances, the alternative resamplers can perform significantly faster on a GPU, and to a lesser extent on a CPU, than the standard approaches. Moreover, in single precision, the standard approaches are numerically biased for upwards of hundreds of thousands of particles, while the alternatives are not. This is particularly important given greater single- than double-precision throughput on modern devices, and the consequent temptation to use single precision with a greater number of particles. Finally, we provide auxiliary functions useful for implementation, such as for the permutation of ancestry vectors to enable in-place propagation.