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Poster
Bayesian inference via sparse Hamiltonian flows
Naitong Chen · Zuheng Xu · Trevor Campbell

Wed Nov 30 02:00 PM -- 04:00 PM (PST) @ Hall J #416

A Bayesian coreset is a small, weighted subset of data that replaces the full dataset during Bayesian inference, with the goal of reducing computational cost. Although past work has shown empirically that there often exists a coreset with low inferential error, efficiently constructing such a coreset remains a challenge. Current methods tend to be slow, require a secondary inference step after coreset construction, and do not provide bounds on the data marginal evidence. In this work, we introduce a new method---sparse Hamiltonian flows---that addresses all three of these challenges. The method involves first subsampling the data uniformly, and then optimizing a Hamiltonian flow parametrized by coreset weights and including periodic momentum quasi-refreshment steps. Theoretical results show that the method enables an exponential compression of the dataset in a representative model, and that the quasi-refreshment steps reduce the KL divergence to the target. Real and synthetic experiments demonstrate that sparse Hamiltonian flows provide accurate posterior approximations with significantly reduced runtime compared with competing dynamical-system-based inference methods.

Author Information

Naitong Chen (University of British Columbia)
Zuheng Xu (University of British Columbia)
Trevor Campbell (UBC)

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