Problem
Research questions and friction points this paper is trying to address.
SMC samplers
finite sample bounds
normalising constants
tempering sequences
computational complexity
On the complexity of standard and waste-free SMC samplers
🤖 AI Summary
This work investigates the finite-sample error and computational complexity of Sequential Monte Carlo (SMC) samplers in estimating expectations under a target distribution and its normalizing constant. For both general and annealed sequences of distributions, the study establishes, for the first time, explicit error bounds for standard and waste-free SMC samplers, precisely characterizing their dependence on the number of time steps \(T\) and the ambient dimension \(d\). Leveraging tools from probability theory and statistical learning theory, the authors derive upper bounds that elucidate how estimation error scales with \(T\) and \(d\). Building on these theoretical results, they formulate practical guidelines for algorithm configuration, offering both rigorous theoretical support and actionable recommendations for the efficient deployment of SMC methods in real-world applications.
📝 Abstract
We establish finite sample bounds for the error of standard and waste-free
SMC samplers. Our results cover estimates of both expectations and
normalising constants of the target distributions. We consider first an
arbitrary sequence of distributions, and then specialise our results to
tempering sequences. We use our results to derive the complexity of SMC
samplers with respect to the parameters of the problem, such as $T$, the
number of target distributions, in the general case, or $d$, the dimension
of the ambient space, in the tempering case.
We use these bounds to derive practical recommendations for the implementation
of SMC samplers for end users.
Innovation
Methods, ideas, or system contributions that make the work stand out.
SMC samplers
finite sample bounds
normalising constants
tempering sequences
computational complexity
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