mlsanityData to 7 Oct 2026

Neural Networks for Parameter Estimation in Intractable Models

arXiv 2107.14346 ↗First posted 29 Jul 2021stat.ME stat.MLcited by 28

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Abstract (arXiv)

We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is exceptionally challenging even with small datasets but simulation is straightforward. We use data from model simulations as input and train deep neural networks to learn statistical parameters. Our neural-network-based method provides a competitive alternative to current approaches, as demonstrated by considerable accuracy and computational time improvements. It serves as a proof of concept for deep learning in statistical parameter estimation and can be extended to other estimation problems.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 13 of its 57 references that are in the map. First posted on arXiv 29 Jul 2021.

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13 of 57 references.

References · 13

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challengescited by 813
  3. 2019The frontier of simulation-based inferencecited by 490
  4. 2021Benchmarking Simulation-Based Inferencecited by 160
  5. 2020BayesFlow: Learning complex stochastic models with invertible neural networkscited by 139
  6. 2015Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Networkcited by 39
  7. 2020Fast covariance parameter estimation of spatial Gaussian process models using neural networkscited by 25
  8. 2020Parameter Estimation with Dense and Convolutional Neural Networks Applied to the FitzHugh-Nagumo ODEcited by 19
  9. 2017Deep Gaussian Covariance Networkcited by 9
  10. 2017Full likelihood inference for max-stable datacited by 5
  11. 2014Likelihood estimators for multivariate extremescited by 3
  12. 2013Efficient inference and simulation for elliptical Pareto processescited by 2
1 more
  1. 2015Bayesian inference for the Brown-Resnick process, with an application to extreme low temperaturescited by 2

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Citing papers per year: 2022: 4; 2023: 8; 2024: 8; 2025: 5; 2026: 3.

28 papers.

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  1. 2024Neural Methods for Amortized Inferencecited by 36
  2. 2022Likelihood-Free Parameter Estimation with Neural Bayes Estimatorscited by 31
  3. 2023Inertial Navigation Meets Deep Learning: A Survey of Current Trends and Future Directionscited by 20
  4. 2022Statistical Deep Learning for Spatial and Spatio-Temporal Datacited by 15
  5. 2023Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networkscited by 13
  6. 2022Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networkscited by 11
  7. 2023Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoodscited by 10
  8. 2023Fast parameter estimation of Generalized Extreme Value distribution using Neural Networkscited by 7
  9. 2023Towards black-box parameter estimationcited by 6
  10. 2023Neural Bayes estimators for censored inference with peaks-over-threshold modelscited by 6
  11. 2024Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applicationscited by 3
  12. 2024Deep learning the Hurst parameter of linear fractional processes and assessing its reliabilitycited by 2
16 more
  1. 2022Spherical Poisson Point Process Intensity Function Modeling and Estimation with Measure Transportcited by 1
  2. 2023Efficient Large-scale Nonstationary Spatial Covariance Function Estimation Using Convolutional Neural Networkscited by 1
  3. 2024Dimension-reduced Reconstruction Map Learning for Parameter Estimation in Likelihood-Free Inference Problemscited by 1
  4. 2025Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networkscited by 1
  5. 2025LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Datacited by 1
  6. 2025Theoretical guarantees for neural estimators in parametric statisticscited by 1
  7. 2023Universal Approximation and the Topological Neural Networkcited by 0
  8. 2024Latent Variable Sequence Identification for Cognitive Models with Neural Network Estimatorscited by 0
  9. 2024Modeling Spatial Extremal Dependence of Precipitation Using Distributional Neural Networkscited by 0
  10. 2024A Generalized Unified Skew-Normal Process with Neural Bayes Inferencecited by 0
  11. 2024When the whole is greater than the sum of its parts: Scaling black-box inference to large data settings through divide-and-conquercited by 0
  12. 2025Neural Bayes estimation and selection for complex bivariate extremal dependence modelscited by 0
  13. 2025Fast Likelihood-Free Parameter Estimation for L'evy Processescited by 0
  14. 2026Neural posterior estimation for scalable and accurate inverse parameter inference in Li-ion batteriescited by 0
  15. 2026Permutation-preserving Functions and Neural Vecchia Covariance Kernelscited by 0
  16. 2026Keeping Score: Adaptive, Tuning-Free Loss Weighting for Score-Augmented Neural Ratio Estimationcited by 0