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Butterfly resampling - convergence and central limit theorems for particle filters with constrained interactions

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If you have a question about this talk, please contact Fredrik Lindsten .

We describe a novel class of particle filters that generalizes the classical bootstrap filter in a manner of introducing constraints on the interaction pattern of the particles. In some instances, the conditional independence structure of the new algorithm can be expressed as a graph with the same structure as the butterfly diagram of the Cooley-Tukey fast Fourier transform. The main motivation for the interest in these algorithms with sparse independence structure is to lay rigorous foundations for the design of algorithms better suited to modern computing architectures.

The law of large numbers and the central limit theorem (CLT) are established for specific instances of the new particle filters. It turns out, that the price to pay for the sparseness of the conditional independence structure is increased asymptotic variance in the CLT , and, in some cases, slower rate of convergence that manifests itself as a non-standard scaling in the CLT .

This talk is part of the Probabilistic Systems, Information, and Inference Group Seminars series.

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