mlsanityData to 14 Oct 2026

Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds

arXiv 2105.04379 ↗First posted 10 May 2021stat.ML cs.LG stat.COcited by 27

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Abstract (arXiv)

We introduce a framework for Bayesian experimental design (BED) with implicit models, where the data-generating distribution is intractable but sampling from it is still possible. In order to find optimal experimental designs for such models, our approach maximises mutual information lower bounds that are parametrised by neural networks. By training a neural network on sampled data, we simultaneously update network parameters and designs using stochastic gradient-ascent. The framework enables experimental design with a variety of prominent lower bounds and can be applied to a wide range of scientific tasks, such as parameter estimation, model discrimination and improving future predictions. Using a set of intractable toy models, we provide a comprehensive empirical comparison of prominent lower bounds applied to the aforementioned tasks. We further validate our framework on a challenging system of stochastic differential equations from epidemiology.

Key facts. Cited by 27 papers in the map (data through 14 Oct 2026). Builds on 26 of its 62 references that are in the map. First posted on arXiv 10 May 2021.

Builds on

26 of 62 references.

References · 26

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  2. 2018Representation Learning with Contrastive Predictive Codingcited by 7,777
  3. 2018Learning deep representations by mutual information estimation and maximizationcited by 1,273
  4. 2018MINE: Mutual Information Neural Estimationcited by 683
  5. 2019On Variational Bounds of Mutual Informationcited by 559
  6. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 506
  7. 2019The frontier of simulation-based inferencecited by 502
  8. 2019Monte Carlo Gradient Estimation in Machine Learningcited by 283
  9. 2020Scalable Gradients for Stochastic Differential Equationscited by 271
  10. 2020CLUB: A Contrastive Log-ratio Upper Bound of Mutual Informationcited by 235
  11. 2018Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flowscited by 221
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14 more
  1. 2019Understanding the Limitations of Variational Mutual Information Estimatorscited by 140
  2. 2019Variational Bayesian Optimal Experimental Designcited by 116
  3. 2021Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Designcited by 106
  4. 2016Likelihood-free inference by ratio estimationcited by 81
  5. 2020Neural Approximate Sufficient Statistics for Implicit Modelscited by 74
  6. 2015Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Modelscited by 61
  7. 2020Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimationcited by 56
  8. 2018Efficient Bayesian Experimental Design for Implicit Modelscited by 34
  9. 2020Sequential Bayesian Experimental Design for Implicit Models via Mutual Informationcited by 23
  10. 2018Bayesian design of experiments for intractable likelihood models using coupled auxiliary models and multivariate emulationcited by 10
  11. 2019Adaptive Gaussian Copula ABCcited by 7
  12. 2021A Scalable Gradient-Free Method for Bayesian Experimental Design with Implicit Modelscited by 7
  13. 2016Gaussian process modeling in approximate Bayesian computation to estimate horizontal gene transfer in bacteriacited by 3
  14. 2018Optimal Bayesian design for model discrimination via classificationcited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 3; 2023: 9; 2024: 4; 2025: 5; 2026: 3.

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  1. 2023Modern Bayesian Experimental Designcited by 125
  2. 2021Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoodscited by 61
  3. 2021Tight Mutual Information Estimation With Contrastive Fenchel-Legendre Optimizationcited by 18
  4. 2022Policy-Based Bayesian Experimental Design for Non-Differentiable Implicit Modelscited by 16
  5. 2023Differentiable Multi-Target Causal Bayesian Experimental Designcited by 15
  6. 2025Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Designcited by 12
  7. 2024Bayesian Experimental Design via Contrastive Diffusionscited by 11
  8. 2023Variational Sequential Optimal Experimental Design using Reinforcement Learningcited by 8
  9. 2022Statistical applications of contrastive learningcited by 5
  10. 2023On Estimating the Gradient of the Expected Information Gain in Bayesian Experimental Designcited by 5
  11. 2024PASOA- PArticle baSed Bayesian Optimal Adaptive designcited by 5
  12. 2023CO-BED: Information-Theoretic Contextual Optimization via Bayesian Experimental Designcited by 4
15 more
  1. 2023Online simulator-based experimental design for cognitive model selectioncited by 3
  2. 2023Designing Optimal Behavioral Experiments Using Machine Learningcited by 3
  3. 2025Performance Comparisons of Reinforcement Learning Algorithms for Sequential Experimental Designcited by 3
  4. 2025A Geometric Approach to Optimal Experimental Designcited by 3
  5. 2024Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalitiescited by 2
  6. 2024A Likelihood-Free Approach to Goal-Oriented Bayesian Optimal Experimental Designcited by 2
  7. 2025Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Designcited by 2
  8. 2026Action-BED: Task-Driven Bayesian Experimental Design with Singly Intractable Objectivescited by 2
  9. 2021MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectoriescited by 1
  10. 2023Stochastic Gradient Bayesian Optimal Experimental Designs for Simulation-based Inferencecited by 1
  11. 2023Amortised Experimental Design and Parameter Estimation for User Models of Pointingcited by 1
  12. 2025Online Bayesian Experimental Design for Partially Observed Dynamical Systemscited by 1
  13. 2022An Optimal Likelihood Free Method for Biological Model Selectioncited by 0
  14. 2026Case-Guided Sequential Assay Planning in Drug Discoverycited by 0
  15. 2026Goal-driven Bayesian Optimal Experimental Design for Robust Decision-Making Under Model Uncertaintycited by 0