mlsanityData to 7 Oct 2026

MixFlows: principled variational inference via mixed flows

arXiv 2205.07475 ↗First posted 16 May 2022stat.ML cs.LG stat.COcited by 11

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Abstract (arXiv)

This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling, density evaluation, and unbiased ELBO estimation. We then show that MixFlows have MCMC-like convergence guarantees when the flow map is ergodic and measure-preserving, and provide bounds on the accumulation of error for practical implementations where the flow map is approximated. Finally, we develop an implementation of MixFlows based on uncorrected discretized Hamiltonian dynamics combined with deterministic momentum refreshment. Simulated and real data experiments show that MixFlows can provide more reliable posterior approximations than several black-box normalizing flows, as well as samples of comparable quality to those obtained from state-of-the-art MCMC methods.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 33 of its 89 references that are in the map. First posted on arXiv 16 May 2022.

Builds on

33 of 89 references.

References · 33

  1. 2015Variational Inference with Normalizing Flowscited by 2,161
  2. 2016Density estimation using Real NVPcited by 2,029
  3. 2016Variational Inference: A Review for Statisticianscited by 1,466
  4. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  5. 2013Black Box Variational Inferencecited by 317
  6. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  7. 2016A Kernel Test of Goodness of Fitcited by 143
  8. 2017Measuring Sample Quality with Kernelscited by 119
  9. 2015Measuring Sample Quality with Stein's Methodcited by 94
  10. 2015Hierarchical Variational Modelscited by 89
  11. 2018Hamiltonian Variational Auto-Encodercited by 41
  12. 2021MCMC Variational Inference via Uncorrected Hamiltonian Annealingcited by 39
21 more
  1. 2016Variational Boosting: Iteratively Refining Posterior Approximationscited by 36
  2. 2021Monte Carlo Variational Auto-Encoderscited by 36
  3. 2021Differentiable Annealed Importance Sampling and the Perils of Gradient Noisecited by 36
  4. 2020Blindness of score-based methods to isolated components and mixing proportionscited by 33
  5. 2018Random Feature Stein Discrepanciescited by 23
  6. 2020Sliced Kernelized Stein Discrepancycited by 23
  7. 2016Boosting Variational Inferencecited by 22
  8. 2020Involutive MCMC: a Unifying Frameworkcited by 19
  9. 2016Variational Inference with Hamiltonian Monte Carlocited by 17
  10. 2018Consistency of Variational Bayes Inference for Estimation and Model Selection in Mixturescited by 17
  11. 2018Boosting Black Box Variational Inferencecited by 14
  12. 2021Surrogate Likelihoods for Variational Annealed Importance Samplingcited by 14
  13. 2019Universal Boosting Variational Inferencecited by 13
  14. 2022Bayesian inference via sparse Hamiltonian flowscited by 12
  15. 2021Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Samplingcited by 9
  16. 2017Boosting Variational Inference: an Optimization Perspectivecited by 7
  17. 2020Orbital MCMCcited by 5
  18. 2021Deterministic Gibbs Sampling via Ordinary Differential Equationscited by 5
  19. 2020Deep Involutive Generative Models for Neural MCMCcited by 4
  20. 2018Ergodic Inference: Accelerate Convergence by Optimisationcited by 2
  21. 2021NEO: Non Equilibrium Sampling on the Orbit of a Deterministic Transformcited by 1

Built on by

Cited by year

Citing papers per year: 2023: 4; 2024: 4; 2025: 3.

11 papers.

  1. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  2. 2024Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spacescited by 15
  3. 2023Embracing the chaos: analysis and diagnosis of numerical instability in variational flowscited by 6
  4. 2024Disentangling impact of capacity, objective, batchsize, estimators, and step-size on flow VIcited by 5
  5. 2023Adaptive importance sampling for heavy-tailed distributions via α-divergence minimizationcited by 3
  6. 2025Generalized Guarantees for Variational Inference in the Presence of Even and Elliptical Symmetrycited by 3
  7. 2023Mixed Variational Flows for Discrete Variablescited by 2
  8. 2023Reparameterized Variational Rejection Samplingcited by 2
  9. 2025Fisher meets Feynman: score-based variational inference with a product of expertscited by 2
  10. 2025Asymptotically exact variational flows via involutive MCMC kernelscited by 1
  11. 2024Generative Topological Networkscited by 0