Black-box variational inference (BBVI) scales poorly to high dimensional problems when it is used to estimate a multivariate Gaussian approximation with a full covariance matrix. In this paper, we extend the batch-and-match (BaM) framework for score-based BBVI to problems where it is prohibitively expensive to store such covariance matrices, let alone to estimate them. Unlike classical algorithms for BBVI, which use gradient descent to minimize the reverse Kullback-Leibler divergence, BaM uses more specialized updates to match the scores of the target density and its Gaussian approximation. We extend the updates for BaM by integrating them with a more compact parameterization of full covariance matrices. In particular, borrowing ideas from factor analysis, we add an extra step to each iteration of BaM -- a patch -- that projects each newly updated covariance matrix into a more efficiently parameterized family of diagonal plus low rank matrices. We evaluate this approach on a variety of synthetic target distributions and real-world problems in high-dimensional inference.

本文解决了黑箱变分推理在高维问题中使用完全协方差矩阵时的扩展性不足的问题。研究提出了将批处理与匹配框架（BaM）结合的新方法，通过引入低秩矩阵的高效参数化，提高了算法的效率和表现。实验证明，该方法在多个合成目标分布和高维推断的真实问题中均取得了显著成效。

批处理、匹配和修补：基于分数的变分推理的低秩近似