<ul><li>Black-box variational inference (BBVI) scales poorly for estimating a multivariate Gaussian approximation with a full covariance matrix in high-dimensional problems.</li><li>The batch-and-match (BaM) framework extends score-based BBVI and addresses the challenge of expensive storage and estimation of covariance matrices.</li><li>BaM uses specialized updates to match scores of the target density and its Gaussian approximation, instead of relying on stochastic gradient descent.</li><li>By integrating the updates with a more compact parameterization, BaM introduces a patch that projects covariance matrices into a more efficiently parameterized family of diagonal plus low rank matrices.</li></ul>

Batch, match, and patch: low-rank approximations for score-based variational inference

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