Automatically adapting the number of state particles in SMC$^2$

TL;DR

This paper introduces an adaptive method for automatically selecting the number of state particles in SMC$^2$ algorithms, improving efficiency and automation in parameter inference for complex state-space models.

Contribution

The paper presents novel adaptive techniques for choosing the number of state particles in SMC$^2$, enhancing efficiency and making the process fully automatic.

Findings

Significant improvement in SMC$^2$ efficiency.

Fully automatic adaptation of particle number.

Open-source implementation available.

Abstract

Sequential Monte Carlo squared (SMC$^2$) methods can be used for parameter inference of intractable likelihood state-space models. These methods replace the likelihood with an unbiased particle filter estimator, similarly to particle Markov chain Monte Carlo (MCMC). As with particle MCMC, the efficiency of SMC$^2$ greatly depends on the variance of the likelihood estimator, and therefore on the number of state particles used within the particle filter. We introduce novel methods to adaptively select the number of state particles within SMC$^2$ using the expected squared jumping distance to trigger the adaptation, and modifying the exchange importance sampling method of \citet{Chopin2012a} to replace the current set of state particles with the new set of state particles. The resulting algorithm is fully automatic, and can significantly improve current methods. Code for our methods is available at https://github.com/imkebotha/adaptive-exact-approximate-smc.