# Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network

arXiv: https://arxiv.org/abs/1510.02175 · HTML: https://mlsanity.com/paper/1510.02175/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2015.

## Built on by (most cited first, 30 of 39)

- [Lossy Compression for Lossless Prediction](https://mlsanity.com/paper/2106.10800/) (2021)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models](https://mlsanity.com/paper/2302.09125/) (2023)
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- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Neural Networks for Parameter Estimation in Intractable Models](https://mlsanity.com/paper/2107.14346/) (2021)
- [Group equivariant neural posterior estimation](https://mlsanity.com/paper/2111.13139/) (2021)
- [Robustness to Label Noise Depends on the Shape of the Noise Distribution in Feature Space](https://mlsanity.com/paper/2206.01106/) (2022)
- [Black-box Bayesian inference for economic agent-based models](https://mlsanity.com/paper/2202.00625/) (2022)
- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [Learning Summary Statistics for Bayesian Inference with Autoencoders](https://mlsanity.com/paper/2201.12059/) (2022)
- [Approximate Bayesian Computation with Domain Expert in the Loop](https://mlsanity.com/paper/2201.12090/) (2022)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [Hessian Geometry of Latent Space in Generative Models](https://mlsanity.com/paper/2506.10632/) (2025)
- [TIP: Task-Informed Motion Prediction for Intelligent Vehicles](https://mlsanity.com/paper/2110.08750/) (2021)
- [Amortised Likelihood-free Inference for Expensive Time-series Simulators with Signatured Ratio Estimation](https://mlsanity.com/paper/2202.11585/) (2022)
- [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)
- [Preconditioned Neural Posterior Estimation for Likelihood-free Inference](https://mlsanity.com/paper/2404.13557/) (2024)
- [Efficient identification of informative features in simulation-based inference](https://mlsanity.com/paper/2210.11915/) (2022)
- [Robust and integrative Bayesian neural networks for likelihood-free parameter inference](https://mlsanity.com/paper/2102.06521/) (2021)
- [Simulation-Based Inference with Quantile Regression](https://mlsanity.com/paper/2401.02413/) (2024)
- [Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inference](https://mlsanity.com/paper/2311.10671/) (2023)
- [Generative Bayesian Computation for Maximum Expected Utility](https://mlsanity.com/paper/2408.16101/) (2024)
- [Approximate Bayesian Computation via Classification](https://mlsanity.com/paper/2111.11507/) (2021)
- [Unifying Summary Statistic Selection for Approximate Bayesian Computation](https://mlsanity.com/paper/2206.02340/) (2022)
- [Kernel-Based Tests for Likelihood-Free Hypothesis Testing](https://mlsanity.com/paper/2308.09043/) (2023)
- [Deep Generative Quantile Bayes](https://mlsanity.com/paper/2410.08378/) (2024)
- [Generative Modeling: A Review](https://mlsanity.com/paper/2501.05458/) (2024)
- [ConDiSim: Conditional Diffusion Models for Simulation Based Inference](https://mlsanity.com/paper/2505.08403/) (2025)

## Abstract (arXiv)

Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary statistic, but outside of special cases where the optimal summary statistics are known, it is unclear which guiding principles can be used to construct effective summary statistics. In this paper we explore the possibility of automating the process of constructing summary statistics by training deep neural networks to predict the parameters from artificially generated data: the resulting summary statistics are approximately posterior means of the parameters. With minimal model-specific tuning, our method constructs summary statistics for the Ising model and the moving-average model, which match or exceed theoretically-motivated summary statistics in terms of the accuracies of the resulting posteriors.