mlsanityData to 13 Oct 2026

Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence

arXiv 2106.15980 ↗First posted 30 Jun 2021stat.ML cs.LG stat.COcited by 29

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Abstract (arXiv)

Variational Inference (VI) is a popular alternative to asymptotically exact sampling in Bayesian inference. Its main workhorse is optimization over a reverse Kullback-Leibler divergence (RKL), which typically underestimates the tail of the posterior leading to miscalibration and potential degeneracy. Importance sampling (IS), on the other hand, is often used to fine-tune and de-bias the estimates of approximate Bayesian inference procedures. The quality of IS crucially depends on the choice of the proposal distribution. Ideally, the proposal distribution has heavier tails than the target, which is rarely achievable by minimizing the RKL. We thus propose a novel combination of optimization and sampling techniques for approximate Bayesian inference by constructing an IS proposal distribution through the minimization of a forward KL (FKL) divergence. This approach guarantees asymptotic consistency and a fast convergence towards both the optimal IS estimator and the optimal variational approximation. We empirically demonstrate on real data that our method is competitive with variational boosting and MCMC.

Key facts. Cited by 29 papers in the map (data through 13 Oct 2026). Builds on 17 of its 60 references that are in the map. First posted on arXiv 30 Jun 2021.

Builds on

17 of 60 references.

References · 17

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,093
  2. 2013Auto-Encoding Variational Bayescited by 4,024
  3. 2016Variational Inference: A Review for Statisticianscited by 1,469
  4. 2015Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networkscited by 295
  5. 2016R'enyi Divergence Variational Inferencecited by 104
  6. 2018Tighter Variational Bounds are Not Necessarily Bettercited by 76
  7. 2014Reweighted Wake-Sleepcited by 66
  8. 2018Importance Weighting and Variational Inferencecited by 55
  9. 2018Yes, but Did It Work?: Evaluating Variational Inferencecited by 52
  10. 2015Pareto Smoothed Importance Samplingcited by 42
  11. 2016Variational Boosting: Iteratively Refining Posterior Approximationscited by 36
  12. 2019Validated Variational Inference via Practical Posterior Error Boundscited by 26
5 more
  1. 2016Boosting Variational Inferencecited by 22
  2. 2019A Contrastive Divergence for Combining Variational Inference and MCMCcited by 20
  3. 2019Universal Boosting Variational Inferencecited by 13
  4. 2017Boosting Variational Inference: an Optimization Perspectivecited by 7
  5. 2016Irreversible Samplers from Jump and Continuous Markov Processescited by 5

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 3; 2022: 5; 2023: 6; 2024: 5; 2025: 5; 2026: 5.

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  1. 2021Understanding Failures in Out-of-Distribution Detection with Deep Generative Modelscited by 89
  2. 2022Variational methods for simulation-based inferencecited by 43
  3. 2021Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergencescited by 41
  4. 2023On Sampling with Approximate Transport Mapscited by 21
  5. 2022Sliced Wasserstein Variational Inferencecited by 17
  6. 2024A theoretical perspective on mode collapse in variational inferencecited by 14
  7. 2024Learned Reference-based Diffusion Sampling for multi-modal distributionscited by 9
  8. 2025Improving the evaluation of samplers on multi-modal targetscited by 9
  9. 2022Transport Score Climbing: Variational Inference Using Forward KL and Adaptive Neural Transportcited by 8
  10. 2023Bridging the Gap Between Variational Inference and Wasserstein Gradient Flowscited by 8
  11. 2022Markov Chain Score Ascent: A Unifying Framework of Variational Inference with Markovian Gradientscited by 6
  12. 2024Stable Training of Normalizing Flows for High-dimensional Variational Inferencecited by 5
17 more
  1. 2023Balanced Training of Energy-Based Models with Adaptive Flow Samplingcited by 4
  2. 2023Forward chi2 Divergence Based Variational Importance Samplingcited by 4
  3. 2024Inclusive KL Gradient Flows: Otto-Wasserstein, Fisher-Rao-Gaussian, and Local-Estimator Dynamicscited by 4
  4. 2021Variational Bayes for high-dimensional proportional hazards models with applications within gene expressioncited by 3
  5. 2022Global convergence of optimized adaptive importance samplerscited by 2
  6. 2023Learning to Generate All Feasible Actionscited by 2
  7. 2025metabeta -- A fast neural model for Bayesian mixed-effects regressioncited by 2
  8. 2024SoftCVI: Contrastive variational inference with self-generated soft labelscited by 1
  9. 2026Amortized Simulation-Based Inference in Generalized Bayes via Neural Posterior Estimationcited by 1
  10. 2026How to Approximate Inference with Subtractive Mixture Modelscited by 1
  11. 2026Even More Guarantees for Variational Inference in the Presence of Symmetriescited by 1
  12. 2023Stochastic automatic differentiation for Monte Carlo processescited by 0
  13. 2025Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functionscited by 0
  14. 2025Two tales for a geometric Jensen--Shannon divergencecited by 0
  15. 2025TinyMusician: On-Device Music Generation with Knowledge Distillation and Mixed Precision Quantizationcited by 0
  16. 2026Total Variation Guarantees for Sampling with Stochastic Localizationcited by 0
  17. 2026Amortized Factor Inference Networks for Posterior Inferencecited by 0