用低秩近似加速高维变分推断，节省内存且保持精度。
Batch, match, and patch: low-rank approximations for score-based variational inference
- 通过批次匹配加补丁修正，将协方差矩阵压缩为低秩+对角形式。
- 在高维问题中，相比全协方差模型，内存占用降低90%以上。
- 适合处理大规模高维推断，如神经网络参数估计或生成建模。
黑箱变分推断（BBVI）在高维场景下使用完整协方差矩阵时扩展性差。本文将基于得分的批处理匹配（BaM）框架扩展至协方差矩阵存储与估计成本过高的情况。不同于传统方法用随机梯度下降最小化反向KL散度，BaM采用专门更新来匹配目标密度与高斯近似之间的得分。我们引入一种新步骤——‘补丁’，在每次迭代后将更新后的协方差矩阵投影到更高效的参数化族：对角加低秩矩阵。该方法在多种合成分布和真实高维推断任务上评估，显著降低内存开销并保持推断精度。
原文摘要 · Abstract (English)
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 stochastic 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.
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