mlsanityData to 7 Oct 2026

Sequential Neural Posterior and Likelihood Approximation

arXiv 2102.06522 ↗First posted 12 Feb 2021stat.ML cs.LG stat.MEcited by 30

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Abstract (arXiv)

We introduce the sequential neural posterior and likelihood approximation (SNPLA) algorithm. SNPLA is a normalizing flows-based algorithm for inference in implicit models, and therefore is a simulation-based inference method that only requires simulations from a generative model. SNPLA avoids Markov chain Monte Carlo sampling and correction-steps of the parameter proposal function that are introduced in similar methods, but that can be numerically unstable or restrictive. By utilizing the reverse KL divergence, SNPLA manages to learn both the likelihood and the posterior in a sequential manner. Over four experiments, we show that SNPLA performs competitively when utilizing the same number of model simulations as used in other methods, even though the inference problem for SNPLA is more complex due to the joint learning of posterior and likelihood function. Due to utilizing normalizing flows SNPLA generates posterior draws much faster (4 orders of magnitude) than MCMC-based methods.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Builds on 21 of its 51 references that are in the map. First posted on arXiv 12 Feb 2021.

Builds on

21 of 51 references.

References · 21

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2015Variational Inference with Normalizing Flowscited by 2,161
  4. 2016Density estimation using Real NVPcited by 2,029
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  6. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
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  8. 2019Neural Spline Flowscited by 590
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  10. 2018Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flowscited by 217
  11. 2019Automatic Posterior Transformation for Likelihood-Free Inferencecited by 216
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9 more
  1. 2021Benchmarking Simulation-Based Inferencecited by 160
  2. 2020BayesFlow: Learning complex stochastic models with invertible neural networkscited by 139
  3. 2018Validating Bayesian Inference Algorithms with Simulation-Based Calibrationcited by 118
  4. 2020On Contrastive Learning for Likelihood-free Inferencecited by 96
  5. 2016Likelihood-free inference by ratio estimationcited by 80
  6. 2015Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Modelscited by 61
  7. 2016Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimationcited by 50
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  9. 2018Sequential Neural Methods for Likelihood-free Inferencecited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 5; 2023: 10; 2024: 7; 2025: 4; 2026: 3.

30 papers.

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  1. 2022Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Modelscited by 50
  2. 2021Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networkscited by 48
  3. 2023Learning Robust Statistics for Simulation-based Inference under Model Misspecificationcited by 48
  4. 2022Compositional Score Modeling for Simulation-based Inferencecited by 46
  5. 2022Variational methods for simulation-based inferencecited by 43
  6. 2023JANA: Jointly Amortized Neural Approximation of Complex Bayesian Modelscited by 41
  7. 2024Neural Methods for Amortized Inferencecited by 36
  8. 2025Simulation-Based Inference: A Practical Guidecited by 30
  9. 2024sbi reloaded: a toolkit for simulation-based inference workflowscited by 23
  10. 2023Consistency Models for Scalable and Fast Simulation-Based Inferencecited by 22
  11. 2023Sensitivity-Aware Amortized Bayesian Inferencecited by 20
  12. 2023Generalized Bayesian Inference for Scientific Simulators via Amortized Cost Estimationcited by 17
18 more
  1. 2023Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inferencecited by 14
  2. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  3. 2023Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networkscited by 13
  4. 2025Multifidelity Simulation-based Inference for Computationally Expensive Simulatorscited by 9
  5. 2023Misspecification-robust Sequential Neural Likelihood for Simulation-based Inferencecited by 8
  6. 2024Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigationcited by 8
  7. 2024A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)cited by 5
  8. 2023Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inferencecited by 3
  9. 2024Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappingscited by 3
  10. 2024Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applicationscited by 3
  11. 2022Improving the Accuracy of Marginal Approximations in Likelihood-Free Inference via Localisationcited by 2
  12. 2024Variational Autoencoders for Efficient Simulation-Based Inferencecited by 2
  13. 2025Simulation-based inference for stochastic nonlinear mixed-effects models with applications in systems biologycited by 2
  14. 2026Supercharging Simulation-Based Inference for Bayesian Optimal Experimental Designcited by 1
  15. 2022An Optimal Likelihood Free Method for Biological Model Selectioncited by 0
  16. 2025Misspecification-robust amortised simulation-based inference using variational methodscited by 0
  17. 2026OneFlowSBI: One Model, Many Queries for Simulation-Based Inferencecited by 0
  18. 2026Amortized ratio-estimation importance sampling and localized simulation-based calibration for intractable likelihoodscited by 0