HESS-MC ² : Sequential Monte Carlo Squared Using Hessian Information and Second Order Proposals

Murphy, Joshua, Rosato, Conor ORCID: 0000-0001-8394-7344, Millard, Andrew, Devlin, Lee ORCID: 0000-0002-2059-7284, Horridge, Paul and Maskell, Simon ORCID: 0000-0003-1917-2913 (2025) HESS-MC ² : Sequential Monte Carlo Squared Using Hessian Information and Second Order Proposals In: 2025 IEEE 35th International Workshop on Machine Learning for Signal Processing (MLSP), 2025-8-31 - 2025-9-3.

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Abstract

When performing Bayesian inference using Sequential Monte Carlo (SMC) methods, two considerations arise: the accuracy of the posterior approximation and computational efficiency. To address computational demands, Sequential Monte Carlo Squared (SMC²) is well-suited for high-performance computing (HPC) environments. The design of the proposal distribution within SMC² can improve accuracy and exploration of the posterior as poor proposals may lead to high variance in importance weights and particle degeneracy. The Metropolis-Adjusted Langevin Algorithm (MALA) uses gradient information so that particles preferentially explore regions of higher probability. In this paper, we extend this idea by incorporating second-order information, specifically the Hessian of the log-target. While second-order proposals have been explored previously in particle Markov Chain Monte Carlo (p-MCMC) methods, we are the first to introduce them within the SMC² framework. Second-order proposals not only use the gradient (first-order derivative), but also the curvature (second-order derivative) of the target distribution. Experimental results on synthetic models highlight the benefits of our approach in terms of step-size selection and posterior approximation accuracy when compared to other proposals.

Item Type:	Conference Item (Unspecified)
Uncontrolled Keywords:	46 Information and Computing Sciences, 4611 Machine Learning, Bioengineering
Divisions:	Faculty of Science & Engineering Faculty of Science & Engineering > School of Engineering Faculty of Science & Engineering > School of Engineering > Electrical Engineering and Electronics
Depositing User:	Symplectic Admin
Date Deposited:	27 Oct 2025 09:31
Last Modified:	24 Nov 2025 14:17
DOI:	10.1109/mlsp62443.2025.11204343
Related Websites:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3195008
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