Enhanced SMC$^2$: Leveraging Gradient Information from Differentiable Particle Filters Within Langevin Proposals
<|reference_start|>Enhanced SMC$^2$: Leveraging Gradient Information from Differentiable Particle Filters Within Langevin Proposals: 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.<|reference_end|>
@article{rosato2024enhanced,
    title={Enhanced SMC$^2$: Leveraging Gradient Information from Differentiable
  Particle Filters Within Langevin Proposals},
    author={Conor Rosato, Joshua Murphy, Alessandro Varsi, Paul Horridge, Simon
  Maskell},
    journal={arXiv preprint arXiv:2407.17296},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.17296},
    primaryClass={stat.ML cs.LG stat.AP}
}