# Neural Networks for Parameter Estimation in Intractable Models

arXiv: https://arxiv.org/abs/2107.14346 · HTML: https://mlsanity.com/paper/2107.14346/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 57 references that are in the map.
- First posted on arXiv 29 Jul 2021.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [BayesFlow: Learning complex stochastic models with invertible neural networks](https://mlsanity.com/paper/2003.06281/) (2020)
- [Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network](https://mlsanity.com/paper/1510.02175/) (2015)
- [Fast covariance parameter estimation of spatial Gaussian process models using neural networks](https://mlsanity.com/paper/2012.15339/) (2020)
- [Parameter Estimation with Dense and Convolutional Neural Networks Applied to the FitzHugh-Nagumo ODE](https://mlsanity.com/paper/2012.06691/) (2020)
- [Deep Gaussian Covariance Network](https://mlsanity.com/paper/1710.06202/) (2017)
- [Full likelihood inference for max-stable data](https://mlsanity.com/paper/1703.08665/) (2017)
- [Likelihood estimators for multivariate extremes](https://mlsanity.com/paper/1411.3448/) (2014)
- [Efficient inference and simulation for elliptical Pareto processes](https://mlsanity.com/paper/1401.0168/) (2013)
- [Bayesian inference for the Brown-Resnick process, with an application to extreme low temperatures](https://mlsanity.com/paper/1506.07836/) (2015)

## Built on by (most cited first, 29 of 29)

- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [Inertial Navigation Meets Deep Learning: A Survey of Current Trends and Future Directions](https://mlsanity.com/paper/2307.00014/) (2023)
- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)
- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networks](https://mlsanity.com/paper/2208.07581/) (2022)
- [Neural Likelihood Surfaces for Spatial Processes with Computationally Intensive or Intractable Likelihoods](https://mlsanity.com/paper/2305.04634/) (2023)
- [Fast parameter estimation of Generalized Extreme Value distribution using Neural Networks](https://mlsanity.com/paper/2305.04341/) (2023)
- [Towards black-box parameter estimation](https://mlsanity.com/paper/2303.15041/) (2023)
- [Neural Bayes estimators for censored inference with peaks-over-threshold models](https://mlsanity.com/paper/2306.15642/) (2023)
- [Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applications](https://mlsanity.com/paper/2404.10899/) (2024)
- [Deep learning the Hurst parameter of linear fractional processes and assessing its reliability](https://mlsanity.com/paper/2401.01789/) (2024)
- [Theoretical guarantees for neural estimators in parametric statistics](https://mlsanity.com/paper/2506.18508/) (2025)
- [Spherical Poisson Point Process Intensity Function Modeling and Estimation with Measure Transport](https://mlsanity.com/paper/2201.09485/) (2022)
- [Efficient Large-scale Nonstationary Spatial Covariance Function Estimation Using Convolutional Neural Networks](https://mlsanity.com/paper/2306.11487/) (2023)
- [Dimension-reduced Reconstruction Map Learning for Parameter Estimation in Likelihood-Free Inference Problems](https://mlsanity.com/paper/2407.13971/) (2024)
- [Modeling Spatial Extremes using Non-Gaussian Spatial Autoregressive Models via Convolutional Neural Networks](https://mlsanity.com/paper/2505.03034/) (2025)
- [LatticeVision: Image to Image Networks for Modeling Non-Stationary Spatial Data](https://mlsanity.com/paper/2505.09803/) (2025)
- [Universal Approximation and the Topological Neural Network](https://mlsanity.com/paper/2305.16639/) (2023)
- [Latent Variable Sequence Identification for Cognitive Models with Neural Network Estimators](https://mlsanity.com/paper/2406.14742/) (2024)
- [Modeling Spatial Extremal Dependence of Precipitation Using Distributional Neural Networks](https://mlsanity.com/paper/2407.08668/) (2024)
- [A Generalized Unified Skew-Normal Process with Neural Bayes Inference](https://mlsanity.com/paper/2411.17400/) (2024)
- [When the whole is greater than the sum of its parts: Scaling black-box inference to large data settings through divide-and-conquer](https://mlsanity.com/paper/2412.20323/) (2024)
- [Neural Bayes estimation and selection for complex bivariate extremal dependence models](https://mlsanity.com/paper/2503.23156/) (2025)
- [Fast Likelihood-Free Parameter Estimation for L'evy Processes](https://mlsanity.com/paper/2505.01639/) (2025)
- [Neural posterior estimation for scalable and accurate inverse parameter inference in Li-ion batteries](https://mlsanity.com/paper/2604.02520/) (2026)
- [Permutation-preserving Functions and Neural Vecchia Covariance Kernels](https://mlsanity.com/paper/2605.05523/) (2026)
- [Keeping Score: Adaptive, Tuning-Free Loss Weighting for Score-Augmented Neural Ratio Estimation](https://mlsanity.com/paper/2605.12118/) (2026)
- [Maximum likelihood, neural networks and posterior mean for inferring fractional Brownian motion parameters](https://mlsanity.com/paper/2610.19888/) (2026)

## 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.