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.

本文介绍了一种新的方法——稀疏哈密顿流，它可以提高贝叶斯核心集合的构建效率，通过代替数据集来减少计算成本，同时在构建后不需要进行次要的推断，并提供与数据边缘证据的界限。理论结果显示，该方法在典型模型中使数据集压缩呈指数级，而准周期动量可以使KL散度降至目标；而实验结果表明，与竞争的基于动力系统的推断方法相比，稀疏哈密顿流提供了准确的后验近似并显著减少了运行时间。

基于稀疏哈密顿流的贝叶斯推断