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Hierarchical Variational Models

arXiv 1511.02386 ↗First posted 7 Nov 2015stat.ML cs.LG stat.COcited by 89

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Abstract (arXiv)

Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive variational distribution that maintains efficient computation? To address this, we develop hierarchical variational models (HVMs). HVMs augment a variational approximation with a prior on its parameters, which allows it to capture complex structure for both discrete and continuous latent variables. The algorithm we develop is black box, can be used for any HVM, and has the same computational efficiency as the original approximation. We study HVMs on a variety of deep discrete latent variable models. HVMs generalize other expressive variational distributions and maintains higher fidelity to the posterior.

Key facts. Cited by 89 papers in the map (data through 14 Oct 2026). First posted on arXiv 7 Nov 2015.

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Citing papers per year: 2020: 1; 2021: 24; 2022: 14; 2023: 19; 2024: 15; 2025: 8; 2026: 8.

89 papers.

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  1. 2022GFlowNets and variational inferencecited by 106
  2. 2025DIME:Diffusion-Based Maximum Entropy Reinforcement Learningcited by 58
  3. 2023Local Search GFlowNetscited by 48
  4. 2021Monte Carlo Variational Auto-Encoderscited by 36
  5. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusionscited by 29
  6. 2025Beyond Verifiable Rewards: Scaling Reinforcement Learning for Language Models to Unverifiable Datacited by 29
  7. 2022Efficient-VDVAE: Less is morecited by 26
  8. 2022Unifying Generative Models with GFlowNets and Beyondcited by 24
  9. 2024Contrasting with Symile: Simple Model-Agnostic Representation Learning for Unlimited Modalitiescited by 24
  10. 2021Multiresolution Equivariant Graph Variational Autoencodercited by 20
  11. 2023Learning to Jump: Thinning and Thickening Latent Counts for Generative Modelingcited by 18
  12. 2020Non-Adversarial Imitation Learning and its Connections to Adversarial Methodscited by 17
38 more
  1. 2021Sparse Uncertainty Representation in Deep Learning with Inducing Weightscited by 16
  2. 2022Amortized Variational Inference: A Systematic Reviewcited by 16
  3. 2023Hierarchical Semi-Implicit Variational Inference with Application to Diffusion Model Accelerationcited by 14
  4. 2023Unified Brain MR-Ultrasound Synthesis using Multi-Modal Hierarchical Representationscited by 13
  5. 2023Order-Preserving GFlowNetscited by 13
  6. 2023Learning Energy-Based Prior Model with Diffusion-Amortized MCMCcited by 13
  7. 2021VAE Approximation Error: ELBO and Exponential Familiescited by 12
  8. 2021A unified view of likelihood ratio and reparameterization gradientscited by 12
  9. 2021On Incorporating Inductive Biases into VAEscited by 11
  10. 2022MixFlows: principled variational inference via mixed flowscited by 11
  11. 2022Alleviating Adversarial Attacks on Variational Autoencoders with MCMCcited by 10
  12. 2023Tree Variational Autoencoderscited by 10
  13. 2021Efficient Semi-Implicit Variational Inferencecited by 9
  14. 2021Automatic variational inference with cascading flowscited by 9
  15. 2021Variational Predictive Routing with Nested Subjective Timescalescited by 9
  16. 2024Unified Cross-Modal Medical Image Synthesis with Hierarchical Mixture of Product-of-Expertscited by 9
  17. 2022Recursive Monte Carlo and Variational Inference with Auxiliary Variablescited by 8
  18. 2024Combining Hierachical VAEs with LLMs for clinically meaningful timeline summarisation in social mediacited by 8
  19. 2024Hierarchical VAE with a Diffusion-based VampPriorcited by 8
  20. 2021Structured Dropout Variational Inference for Bayesian Neural Networkscited by 7
  21. 2021Diagnosing Vulnerability of Variational Auto-Encoders to Adversarial Attackscited by 7
  22. 2021Variational Inference with NoFAS: Normalizing Flow with Adaptive Surrogate for Computationally Expensive Modelscited by 7
  23. 2021Multi-Task Neural Processescited by 7
  24. 2024What's the score? Automated Denoising Score Matching for Nonlinear Diffusionscited by 7
  25. 2021Variational Marginal Particle Filterscited by 6
  26. 2024A Review of Bayesian Uncertainty Quantification in Deep Probabilistic Image Segmentationcited by 6
  27. 2025Reinforced sequential Monte Carlo for amortised samplingcited by 6
  28. 2023Variational Inference for Bayesian Neural Networks under Model and Parameter Uncertaintycited by 5
  29. 2024A Probabilistic Model Behind Self-Supervised Learningcited by 5
  30. 2025Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutionscited by 5
  31. 2021ADAVI: Automatic Dual Amortized Variational Inference Applied To Pyramidal Bayesian Modelscited by 4
  32. 2022Black-box Coreset Variational Inferencecited by 4
  33. 2023Predictive World Models from Real-World Partial Observationscited by 4
  34. 2023Calibrating the Rigged Lottery: Making All Tickets Reliablecited by 4
  35. 2024Provably Scalable Black-Box Variational Inference with Structured Variational Familiescited by 4
  36. 2024Probabilistic Programming with Programmable Variational Inferencecited by 4
  37. 2026f-Trajectory Balance: A Loss Family for Tuning GFlowNets, Generative Models, and LLMs with Off- and On-Policy Datacited by 4
  38. 2021Interpolating between sampling and variational inference with infinite stochastic mixturescited by 3

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