mlsanityData to 14 Oct 2026

Provable Smoothness Guarantees for Black-Box Variational Inference

arXiv 1901.08431 ↗First posted 24 Jan 2019cs.LG stat.MLcited by 29

Not on the map. Why?

Abstract (arXiv)

Black-box variational inference tries to approximate a complex target distribution though a gradient-based optimization of the parameters of a simpler distribution. Provable convergence guarantees require structural properties of the objective. This paper shows that for location-scale family approximations, if the target is M-Lipschitz smooth, then so is the objective, if the entropy is excluded. The key proof idea is to describe gradients in a certain inner-product space, thus permitting use of Bessel's inequality. This result gives insight into how to parameterize distributions, gives bounds the location of the optimal parameters, and is a key ingredient for convergence guarantees.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 Jan 2019.

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Citing papers per year: 2021: 4; 2022: 1; 2023: 8; 2024: 8; 2025: 4; 2026: 4.

29 papers.

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  1. 2022Variational inference via Wasserstein gradient flowscited by 85
  2. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  3. 2023Provable convergence guarantees for black-box variational inferencecited by 29
  4. 2023On the Convergence of Black-Box Variational Inferencecited by 22
  5. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
  6. 2021Amortized Variational Inference for Simple Hierarchical Modelscited by 19
  7. 2023Variational Inference with Gaussian Score Matchingcited by 17
  8. 2023Towards Understanding the Dynamics of Gaussian-Stein Variational Gradient Descentcited by 13
  9. 2023Linear Convergence of Black-Box Variational Inference: Should We Stick the Landing?cited by 10
  10. 2024Kernel Semi-Implicit Variational Inferencecited by 8
  11. 2024Understanding Stochastic Natural Gradient Variational Inferencecited by 8
  12. 2021Meta-strategy for Learning Tuning Parameters with Guaranteescited by 6
17 more
  1. 2021Mixture weights optimisation for Alpha-Divergence Variational Inferencecited by 6
  2. 2023Practical and Matching Gradient Variance Bounds for Black-Box Variational Bayesian Inferencecited by 6
  3. 2024On Divergence Measures for Training GFlowNetscited by 6
  4. 2021Monotonic Alpha-divergence Minimisation for Variational Inferencecited by 5
  5. 2024Provably Scalable Black-Box Variational Inference with Structured Variational Familiescited by 4
  6. 2025Optimization Guarantees for Square-Root Natural-Gradient Variational Inferencecited by 3
  7. 2025Natural Gradient VI: Guarantees for Non-Conjugate Modelscited by 3
  8. 2024Demystifying SGD with Doubly Stochastic Gradientscited by 2
  9. 2024Variance Control for Black Box Variational Inference Using The James-Stein Estimatorcited by 1
  10. 2024Understanding and mitigating difficulties in posterior predictive evaluationcited by 1
  11. 2025Globally Convergent Variational Inferencecited by 1
  12. 2025Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inferencecited by 1
  13. 2026A Kernel Approach for Semi-implicit Variational Inferencecited by 1
  14. 2024You Only Accept Samples Once: Fast, Self-Correcting Stochastic Variational Inferencecited by 0
  15. 2026Stochastic Gradient Variational Inference with Price's Gradient Estimator from Bures-Wasserstein to Parameter Spacecited by 0
  16. 2026SGD for Variational Inference: Tackling Unbounded Variance via Preconditioning and Dynamic Batchingcited by 0
  17. 2026Large-scale empirical tuning and comparison of default optimizers for variational inferencecited by 0