Divide-and-Conquer Fusion
| Autor: | Chan, Ryan S. Y., Pollock, Murray, Johansen, Adam M., Roberts, Gareth O. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Combining several (sample approximations of) distributions, which we term sub-posteriors, into a single distribution proportional to their product, is a common challenge. Occurring, for instance, in distributed 'big data' problems, or when working under multi-party privacy constraints. Many existing approaches resort to approximating the individual sub-posteriors for practical necessity, then find either an analytical approximation or sample approximation of the resulting (product-pooled) posterior. The quality of the posterior approximation for these approaches is poor when the sub-posteriors fall out-with a narrow range of distributional form, such as being approximately Gaussian. Recently, a Fusion approach has been proposed which finds an exact Monte Carlo approximation of the posterior, circumventing the drawbacks of approximate approaches. Unfortunately, existing Fusion approaches have a number of computational limitations, particularly when unifying a large number of sub-posteriors. In this paper, we generalise the theory underpinning existing Fusion approaches, and embed the resulting methodology within a recursive divide-and-conquer sequential Monte Carlo paradigm. This ultimately leads to a competitive Fusion approach, which is robust to increasing numbers of sub-posteriors. Comment: 73 pages, 14 figures |
| Databáze: | arXiv |
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