Batch, match, and patch: low-rank approximations for score-based variational inference
This work addresses computational bottlenecks in variational inference for high-dimensional data, offering an incremental improvement over existing methods.
The paper tackles the scalability issue of black-box variational inference (BBVI) in high-dimensional problems by extending the batch-and-match framework with a low-rank approximation for covariance matrices, achieving improved efficiency and competitive performance on synthetic and real-world datasets.
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.