Enhanced SMC$^2$: Leveraging Gradient Information from Differentiable Particle Filters Within Langevin Proposals

TL;DR

This paper introduces an enhanced SMC$^2$ method that uses gradient information from differentiable particle filters within Langevin proposals, improving efficiency and accuracy in high-dimensional Bayesian inference.

Contribution

The paper presents a novel approach integrating gradient-based Langevin proposals into SMC$^2$, leveraging differentiable particle filters and parallel computing for significant speed-ups.

Findings

Higher effective sample size with Langevin proposals

More accurate parameter estimates compared to random-walk

51x speed-up using 64 cores

Abstract

Sequential Monte Carlo Squared (SMC$^2$) is a Bayesian method which can infer the states and parameters of non-linear, non-Gaussian state-space models. The standard random-walk proposal in SMC$^2$ faces challenges, particularly with high-dimensional parameter spaces. This study outlines a novel approach by harnessing first-order gradients derived from a Common Random Numbers - Particle Filter (CRN-PF) using PyTorch. The resulting gradients can be leveraged within a Langevin proposal without accept/reject. Including Langevin dynamics within the proposal can result in a higher effective sample size and more accurate parameter estimates when compared with the random-walk. The resulting algorithm is parallelized on distributed memory using Message Passing Interface (MPI) and runs in $\mathcal{O}(\log_2N)$ time complexity. Utilizing 64 computational cores we obtain a 51x speed-up when compared to a single core. A GitHub link is given which provides access to the code.