Bayesian inference via sparse Hamiltonian flows

• URL: http://arxiv.org/abs/2203.05723v1
• Date: Fri, 11 Mar 2022 02:36:59 GMT
• Title: Bayesian inference via sparse Hamiltonian flows
• Authors: Naitong Chen, Zuheng Xu, Trevor Campbell
• Abstract summary: A Bayesian coreset is a small, weighted subset of data that replaces the full dataset during Bayesian inference. Current methods tend to be slow, require a secondary inference step after coreset construction, and do not provide bounds on the data marginal evidence. We introduce a new method -- sparse Hamiltonian flows -- that addresses all three of these challenges.
• Score: 16.393322369105864
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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