A Bayesian pseudocoreset is a compact synthetic dataset summarizing essential information of a large-scale dataset and thus can be used as a proxy dataset for scalable Bayesian inference. Typically, a Bayesian pseudocoreset is constructed by minimizing a divergence measure between the posterior conditioning on the pseudocoreset and the posterior conditioning on the full dataset. However, evaluating the divergence can be challenging, particularly for the models like deep neural networks having high-dimensional parameters. In this paper, we propose a novel Bayesian pseudocoreset construction method that operates on a function space. Unlike previous methods, which construct and match the coreset and full data posteriors in the space of model parameters (weights), our method constructs variational approximations to the coreset posterior on a function space and matches it to the full data posterior in the function space. By working directly on the function space, our method could bypass several challenges that may arise when working on a weight space, including limited scalability and multi-modality issue. Through various experiments, we demonstrate that the Bayesian pseudocoresets constructed from our method enjoys enhanced uncertainty quantification and better robustness across various model architectures.

通过在函数空间上构造变分逼近，我们的方法能够在构建贝叶斯伪核心集并将其与完整数据后验匹配时绕过几个可能出现的挑战，包括可扩展性有限和多模态问题。通过各种实验证明，我们方法构建的贝叶斯伪核心集在各种模型架构下具有增强的不确定度量化能力和更好的稳健性。

函数空间贝叶斯伪核心集的贝叶斯神经网络