# Hierarchical Neural Simulation-Based Inference Over Event Ensembles

arXiv: https://arxiv.org/abs/2306.12584 · HTML: https://mlsanity.com/paper/2306.12584/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 21 Jun 2023.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Formal Algorithms for Transformers](https://mlsanity.com/paper/2207.09238/) (2022)
- [A Trust Crisis In Simulation-Based Inference? Your Posterior Approximations Can Be Unfaithful](https://mlsanity.com/paper/2110.06581/) (2021)
- [HNPE: Leveraging Global Parameters for Neural Posterior Estimation](https://mlsanity.com/paper/2102.06477/) (2021)
- [Amortized Variational Inference for Simple Hierarchical Models](https://mlsanity.com/paper/2111.03144/) (2021)
- [Mining for Dark Matter Substructure: Inferring subhalo population properties from strong lenses with machine learning](https://mlsanity.com/paper/1909.02005/) (2019)
- [E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once](https://mlsanity.com/paper/2101.07263/) (2021)
- [Hierarchical Inference With Bayesian Neural Networks: An Application to Strong Gravitational Lensing](https://mlsanity.com/paper/2010.13787/) (2020)
- [On the Dynamics of Inference and Learning](https://mlsanity.com/paper/2204.12939/) (2022)
- [Contrastive Neural Ratio Estimation for Simulation-based Inference](https://mlsanity.com/paper/2210.06170/) (2022)
- [Particle Flow Bayes' Rule](https://mlsanity.com/paper/1902.00640/) (2019)
- [Learning Optimal Test Statistics in the Presence of Nuisance Parameters](https://mlsanity.com/paper/2203.13079/) (2022)

## Built on by (most cited first, 10 of 10)

- [Amortized Bayesian Multilevel Models](https://mlsanity.com/paper/2408.13230/) (2024)
- [Amortized Bayesian Mixture Models](https://mlsanity.com/paper/2501.10229/) (2025)
- [metabeta -- A fast neural model for Bayesian mixed-effects regression](https://mlsanity.com/paper/2510.07473/) (2025)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)
- [Tokenised Flow Matching for Hierarchical Simulation Based Inference](https://mlsanity.com/paper/2604.20723/) (2026)
- [It Just Takes Two: Scaling Amortized Inference to Large Sets](https://mlsanity.com/paper/2605.07972/) (2026)
- [Amortized Bayesian Inference on Multilevel Models of Arbitrary Structure](https://mlsanity.com/paper/2609.40024/) (2026)
- [Towards Reliable Simulation-based Inference](https://mlsanity.com/paper/2603.08947/) (2026)
- [Hybrid Neural Simulation-Based Inference for Robust Applications and Limited-Budget Scenarios](https://mlsanity.com/paper/2609.36044/) (2026)
- [Semi-Amortized Bayesian Inference with Reusable Local Posteriors](https://mlsanity.com/paper/2610.18945/) (2026)

## Abstract (arXiv)

When analyzing real-world data it is common to work with event ensembles, which comprise sets of observations that collectively constrain the parameters of an underlying model of interest. Such models often have a hierarchical structure, where "local" parameters impact individual events and "global" parameters influence the entire dataset. We introduce practical approaches for frequentist and Bayesian dataset-wide probabilistic inference in cases where the likelihood is intractable, but simulations can be realized via a hierarchical forward model. We construct neural estimators for the likelihood(-ratio) or posterior and show that explicitly accounting for the model's hierarchical structure can lead to significantly tighter parameter constraints. We ground our discussion using case studies from the physical sciences, focusing on examples from particle physics and cosmology.