Particle filter efficiency under limited communication
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Sequential Monte Carlo (SMC) methods are typically not straightforward to implement on parallel architectures. This is because standard resampling schemes involve communication between all particles in the system. In this article, we consider the α-SMC algorithm, a generalised particle filter algorithm with limited communications between particles. The communication between different particles is controlled through the so-called α-matrices. We study the influence of the communication structure on the convergence and stability properties of the resulting algorithms. We prove that under standard assumptions, it is possible to use randomised communication structures where each particle only communicates with a small number of neighbouring particles while still having good mixing properties, and this ensures that the resulting algorithms are stable in time and converge at the usual Monte Carlo rate. A particularly simple approach to implement these ideas consists of choosing the α-matrices as the Markov transition matrices of random walks on Ramanujan graphs.
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