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Black Box Variational Inference

arXiv 1401.0118 ↗First posted 31 Dec 2013stat.ML cs.LG stat.COcited by 317

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Abstract (arXiv)

Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm generally requires significant model-specific analysis, and these efforts can hinder and deter us from quickly developing and exploring a variety of models for a problem at hand. In this paper, we present a "black box" variational inference algorithm, one that can be quickly applied to many models with little additional derivation. Our method is based on a stochastic optimization of the variational objective where the noisy gradient is computed from Monte Carlo samples from the variational distribution. We develop a number of methods to reduce the variance of the gradient, always maintaining the criterion that we want to avoid difficult model-based derivations. We evaluate our method against the corresponding black box sampling based methods. We find that our method reaches better predictive likelihoods much faster than sampling methods. Finally, we demonstrate that Black Box Variational Inference lets us easily explore a wide space of models by quickly constructing and evaluating several models of longitudinal healthcare data.

Key facts. Cited by 317 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 Dec 2013.

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Citing papers per year: 2016: 1; 2017: 0; 2018: 0; 2019: 1; 2020: 2; 2021: 61; 2022: 53; 2023: 60; 2024: 54; 2025: 47; 2026: 38.

317 papers.

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  1. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  2. 2022Trusted Multi-View Classification with Dynamic Evidential Fusioncited by 167
  3. 2022GFlowNets and variational inferencecited by 103
  4. 2021Trusted Multi-View Classificationcited by 94
  5. 2022Variational inference via Wasserstein gradient flowscited by 84
  6. 2021Comparing Test Sets with Item Response Theorycited by 55
  7. 2024Improved off-policy training of diffusion samplerscited by 47
  8. 2022Variational methods for simulation-based inferencecited by 43
  9. 2022A Variational Perspective on Generative Flow Networkscited by 39
  10. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  11. 2021Order Matters: Probabilistic Modeling of Node Sequence for Graph Generationcited by 32
  12. 2023Provable convergence guarantees for black-box variational inferencecited by 29
38 more
  1. 2025KL-Regularized Reinforcement Learning is Designed to Mode Collapsecited by 29
  2. 2021Auto-differentiable Ensemble Kalman Filterscited by 28
  3. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusionscited by 27
  4. 2025On a few pitfalls in KL divergence gradient estimation for RLcited by 27
  5. 2021Pathfinder: Parallel quasi-Newton variational inferencecited by 26
  6. 2022Hybrid Predictive Coding: Inferring, Fast and Slowcited by 25
  7. 2022FiLM-Ensemble: Probabilistic Deep Learning via Feature-wise Linear Modulationcited by 24
  8. 2021Pulling back information geometrycited by 23
  9. 2023Efficient Attention via Control Variatescited by 23
  10. 2021Tractable structured natural gradient descent using local parameterizationscited by 22
  11. 2022Gradient Estimation with Discrete Stein Operatorscited by 22
  12. 2022SIXO: Smoothing Inference with Twisted Objectivescited by 22
  13. 2022Bayesian Learning for Neural Networks: an algorithmic surveycited by 22
  14. 2023On the Convergence of Black-Box Variational Inferencecited by 22
  15. 2023Prototype-based Aleatoric Uncertainty Quantification for Cross-modal Retrievalcited by 22
  16. 2023Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Modelscited by 22
  17. 2024Batch and match: black-box variational inference with a score-based divergencecited by 22
  18. 2022Image-based Treatment Effect Heterogeneitycited by 20
  19. 2022Particle-based Variational Inference with Preconditioned Functional Gradient Flowcited by 20
  20. 2023Reparameterized Policy Learning for Multimodal Trajectory Optimizationcited by 20
  21. 2024LoRA-Ensemble: Efficient Uncertainty Modelling for Self-Attention Networkscited by 20
  22. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 20
  23. 2021Amortized Variational Inference for Simple Hierarchical Modelscited by 19
  24. 2022Mean-field Variational Inference via Wasserstein Gradient Flowcited by 19
  25. 2023Semi-Implicit Variational Inference via Score Matchingcited by 19
  26. 2021Variational inference with a quantum computercited by 18
  27. 2021Differentiable Particle Filtering without Modifying the Forward Passcited by 18
  28. 2025A Comedy of Estimators: On KL Regularization in RL Training of LLMscited by 18
  29. 2022Sliced Wasserstein Variational Inferencecited by 17
  30. 2023Black Box Variational Inference with a Deterministic Objective: Faster, More Accurate, and Even More Black Boxcited by 17
  31. 2023Variational Inference with Gaussian Score Matchingcited by 17
  32. 2022Markovian Gaussian Process Variational Autoencoderscited by 16
  33. 2022Amortized Variational Inference: A Systematic Reviewcited by 16
  34. 2021Mind the Gap when Conditioning Amortised Inference in Sequential Latent-Variable Modelscited by 14
  35. 2021AttDMM: An Attentive Deep Markov Model for Risk Scoring in Intensive Care Unitscited by 14
  36. 2021Nested Variational Inferencecited by 14
  37. 2021Surrogate Likelihoods for Variational Annealed Importance Samplingcited by 14
  38. 2023Hierarchical Semi-Implicit Variational Inference with Application to Diffusion Model Accelerationcited by 14

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