Nested Sequential Monte Carlo Methods
This provides a method for researchers and practitioners in statistics and machine learning to apply SMC to high-dimensional filtering problems, though it is an incremental extension of existing SMC frameworks.
The authors tackled the problem of sampling from sequences of high-dimensional probability distributions by proposing nested sequential Monte Carlo (NSMC), which generalizes SMC to allow approximate samples and arbitrary nesting, enabling efficient handling of complex models with dimensions up to 1,000.
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. Furthermore, NSMC can in itself be used to produce such properly weighted samples. Consequently, one NSMC sampler can be used to construct an efficient high-dimensional proposal distribution for another NSMC sampler, and this nesting of the algorithm can be done to an arbitrary degree. This allows us to consider complex and high-dimensional models using SMC. We show results that motivate the efficacy of our approach on several filtering problems with dimensions in the order of 100 to 1 000.