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On Contrastive Learning for Likelihood-free Inference

arXiv 2002.03712 ↗First posted 10 Feb 2020stat.ML cs.LGcited by 96

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Abstract (arXiv)

Likelihood-free methods perform parameter inference in stochastic simulator models where evaluating the likelihood is intractable but sampling synthetic data is possible. One class of methods for this likelihood-free problem uses a classifier to distinguish between pairs of parameter-observation samples generated using the simulator and pairs sampled from some reference distribution, which implicitly learns a density ratio proportional to the likelihood. Another popular class of methods fits a conditional distribution to the parameter posterior directly, and a particular recent variant allows for the use of flexible neural density estimators for this task. In this work, we show that both of these approaches can be unified under a general contrastive learning scheme, and clarify how they should be run and compared.

Key facts. Cited by 96 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Feb 2020.

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Citing papers per year: 2021: 16; 2022: 17; 2023: 18; 2024: 14; 2025: 18; 2026: 13.

96 papers.

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  1. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  2. 2021Benchmarking Simulation-Based Inferencecited by 160
  3. 2023Flow Matching for Scalable Simulation-Based Inferencecited by 97
  4. 2024All-in-one simulation-based inferencecited by 71
  5. 2022From Denoising Diffusions to Denoising Markov Modelscited by 58
  6. 2021Robot Learning from Randomized Simulations: A Reviewcited by 56
  7. 2022Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Modelscited by 50
  8. 2021Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networkscited by 48
  9. 2023Learning Robust Statistics for Simulation-based Inference under Model Misspecificationcited by 48
  10. 2022Robust Neural Posterior Estimation and Statistical Model Criticismcited by 45
  11. 2023Sampling-Based Accuracy Testing of Posterior Estimators for General Inferencecited by 45
  12. 2022Discrete Contrastive Diffusion for Cross-Modal Music and Image Generationcited by 44
38 more
  1. 2022Investigating the Impact of Model Misspecification in Neural Simulation-based Inferencecited by 44
  2. 2022Variational methods for simulation-based inferencecited by 43
  3. 2025Advancing Reasoning in Large Language Models: Promising Methods and Approachescited by 43
  4. 2023JANA: Jointly Amortized Neural Approximation of Complex Bayesian Modelscited by 41
  5. 2022Truncated proposals for scalable and hassle-free simulation-based inferencecited by 40
  6. 2022GATSBI: Generative Adversarial Training for Simulation-Based Inferencecited by 36
  7. 2021Sequential Neural Posterior and Likelihood Approximationcited by 30
  8. 2021Truncated Marginal Neural Ratio Estimationcited by 30
  9. 2025Simulation-Based Inference: A Practical Guidecited by 30
  10. 2021A Trust Crisis In Simulation-Based Inference? Your Posterior Approximations Can Be Unfaithfulcited by 27
  11. 2022Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimationcited by 27
  12. 2023Consistency Models for Scalable and Fast Simulation-Based Inferencecited by 22
  13. 2021HNPE: Leveraging Global Parameters for Neural Posterior Estimationcited by 17
  14. 2022Astronomia ex machina: a history, primer, and outlook on neural networks in astronomycited by 17
  15. 2022Likelihood-Free Inference with Generative Neural Networks via Scoring Rule Minimizationcited by 14
  16. 2021Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimationcited by 13
  17. 2022Black-box Bayesian inference for economic agent-based modelscited by 13
  18. 2025Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Modelscited by 13
  19. 2021On Contrastive Representations of Stochastic Processescited by 12
  20. 2021Likelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning for Reliable Simulator-Based Inferencecited by 10
  21. 2023Balancing Simulation-based Inference for Conservative Posteriorscited by 10
  22. 2023Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probabilitycited by 10
  23. 2022Neural Posterior Estimation with Differentiable Simulatorscited by 9
  24. 2025Multifidelity Simulation-based Inference for Computationally Expensive Simulatorscited by 9
  25. 2025Simulation-based Bayesian inference under model misspecificationcited by 9
  26. 2022Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimationcited by 8
  27. 2023Misspecification-robust Sequential Neural Likelihood for Simulation-based Inferencecited by 8
  28. 2023Reliable Gradient-free and Likelihood-free Prompt Tuningcited by 8
  29. 2023Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimationcited by 8
  30. 2024Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigationcited by 8
  31. 2024Compositional simulation-based inference for time seriescited by 8
  32. 2021Deep Bayesian Active Learning for Accelerating Stochastic Simulationcited by 7
  33. 2022Contrastive Neural Ratio Estimation for Simulation-based Inferencecited by 7
  34. 2026BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Pythoncited by 7
  35. 2024Cost-aware simulation-based inferencecited by 6
  36. 2022Statistical applications of contrastive learningcited by 5
  37. 2022Generative Bayesian Inference with GANscited by 5
  38. 2023Variational Inference with Coverage Guarantees in Simulation-Based Inferencecited by 5

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