# A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks

arXiv: https://arxiv.org/abs/1802.06153 · HTML: https://mlsanity.com/paper/1802.06153/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2018.

## Built on by (most cited first, 30 of 31)

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- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
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- [Posterior SBC: Simulation-Based Calibration Checking Conditional on Data](https://mlsanity.com/paper/2502.03279/) (2025)
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- [Spatial Bayesian Neural Networks](https://mlsanity.com/paper/2311.09491/) (2023)
- [Latent Target Score Matching, with an application to Simulation-Based Inference](https://mlsanity.com/paper/2602.07189/) (2026)
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- [JIR-Arena: The First Benchmark Dataset for Just-in-time Information Recommendation](https://mlsanity.com/paper/2505.13550/) (2025)
- [Exchangeability in Neural Network and its Application to Dynamic Pruning](https://mlsanity.com/paper/2506.02210/) (2025)

## Abstract (arXiv)

An explosion of high-throughput DNA sequencing in the past decade has led to a surge of interest in population-scale inference with whole-genome data. Recent work in population genetics has centered on designing inference methods for relatively simple model classes, and few scalable general-purpose inference techniques exist for more realistic, complex models. To achieve this, two inferential challenges need to be addressed: (1) population data are exchangeable, calling for methods that efficiently exploit the symmetries of the data, and (2) computing likelihoods is intractable as it requires integrating over a set of correlated, extremely high-dimensional latent variables. These challenges are traditionally tackled by likelihood-free methods that use scientific simulators to generate datasets and reduce them to hand-designed, permutation-invariant summary statistics, often leading to inaccurate inference. In this work, we develop an exchangeable neural network that performs summary statistic-free, likelihood-free inference. Our framework can be applied in a black-box fashion across a variety of simulation-based tasks, both within and outside biology. We demonstrate the power of our approach on the recombination hotspot testing problem, outperforming the state-of-the-art.