mlsanityData to 14 Oct 2026

Likelihood-Free Frequentist Inference: Bridging Classical Statistics and Machine Learning for Reliable Simulator-Based Inference

arXiv 2107.03920 ↗First posted 8 Jul 2021stat.ML cs.LGcited by 11

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Abstract (arXiv)

Many areas of science rely on simulators that implicitly encode intractable likelihood functions of complex systems. Classical statistical methods are poorly suited for these so-called likelihood-free inference (LFI) settings, especially outside asymptotic and low-dimensional regimes. At the same time, popular LFI methods - such as Approximate Bayesian Computation or more recent machine learning techniques - do not necessarily lead to valid scientific inference because they do not guarantee confidence sets with nominal coverage in general settings. In addition, LFI currently lacks practical diagnostic tools to check the actual coverage of computed confidence sets across the entire parameter space. In this work, we propose a modular inference framework that bridges classical statistics and modern machine learning to provide (i) a practical approach for constructing confidence sets with near finite-sample validity at any value of the unknown parameters, and (ii) interpretable diagnostics for estimating empirical coverage across the entire parameter space. We refer to this framework as likelihood-free frequentist inference (LF2I). Any method that defines a test statistic can leverage LF2I to create valid confidence sets and diagnostics without costly Monte Carlo or bootstrap samples at fixed parameter settings. We study two likelihood-based test statistics (ACORE and BFF) and demonstrate their performance on high-dimensional complex data. Code is available at https://github.com/lee-group-cmu/lf2i.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 27 of its 94 references that are in the map. First posted on arXiv 8 Jul 2021.

Builds on

27 of 94 references.

References · 27

  1. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  2. 2019The frontier of simulation-based inferencecited by 502
  3. 2018Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flowscited by 221
  4. 2019Automatic Posterior Transformation for Likelihood-Free Inferencecited by 219
  5. 2017Flexible statistical inference for mechanistic models of neural dynamicscited by 163
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  7. 2018Validating Bayesian Inference Algorithms with Simulation-Based Calibrationcited by 124
  8. 2020On Contrastive Learning for Likelihood-free Inferencecited by 98
  9. 2015Approximating Likelihood Ratios with Calibrated Discriminative Classifierscited by 90
  10. 2016Likelihood-free inference by ratio estimationcited by 81
  11. 2015Bayesian Optimization for Likelihood-Free Inference of Simulator-Based Statistical Modelscited by 61
  12. 2018Likelihood-free inference with emulator networkscited by 61
15 more
  1. 2018Mining gold from implicit models to improve likelihood-free inferencecited by 60
  2. 2019Universal Inferencecited by 44
  3. 2021Diagnostics for Conditional Density Models and Bayesian Inference Algorithmscited by 28
  4. 2020Fast covariance parameter estimation of spatial Gaussian process models using neural networkscited by 25
  5. 2014High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computationcited by 19
  6. 2019Parallel Gaussian process surrogate Bayesian inference with noisy likelihood evaluationscited by 18
  7. 2020Confidence Sets and Hypothesis Testing in a Likelihood-Free Inference Settingcited by 18
  8. 2014GPS-ABC: Gaussian Process Surrogate Approximate Bayesian Computationcited by 17
  9. 2017Frequentist coverage and sup-norm convergence rate in Gaussian process regressioncited by 17
  10. 2016ABC random forests for Bayesian parameter inferencecited by 11
  11. 2018ABC-CDE: Towards Approximate Bayesian Computation with Complex High-Dimensional Data and Limited Simulationscited by 8
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  13. 2019Adaptive Gaussian Copula ABCcited by 7
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  15. 2019Approximating posteriors with high-dimensional nuisance parameters via integrated rotated Gaussian approximationcited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 4; 2026: 4.

11 papers.

  1. 2024Neural Methods for Amortized Inferencecited by 39
  2. 2025Epistemic Uncertainty in Conformal Scores: A Unified Approachcited by 9
  3. 2025Simulation-based Bayesian inference under model misspecificationcited by 9
  4. 2024A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)cited by 7
  5. 2025CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inferencecited by 6
  6. 2024Conformal Calibration of Statistical Confidence Setscited by 3
  7. 2025Trustworthy scientific inference with generative modelscited by 1
  8. 2026An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learningcited by 1
  9. 2026Likelihood-free inference with nuisance parameters through normalizing flowscited by 0
  10. 2026A Three-Way Testing Framework for Quantifying Epistemic Calibration Uncertainty in SBIcited by 0
  11. 2026SLICE: Sequential Likelihood-Free Inference via Conformal E-Valuescited by 0