# Hybrid Summary Statistics

arXiv: https://arxiv.org/abs/2410.07548 · HTML: https://mlsanity.com/paper/2410.07548/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 9 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Builds on (most cited first, 2 of 2)

- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Neural Approximate Sufficient Statistics for Implicit Models](https://mlsanity.com/paper/2010.10079/) (2020)

## Built on by (most cited first, 3 of 3)

- [Cosmological Analysis with Calibrated Neural Quantile Estimation and Approximate Simulators](https://mlsanity.com/paper/2411.14748/) (2024)
- [Cosmology with Persistent Homology: Parameter Inference via Machine Learning](https://mlsanity.com/paper/2412.15405/) (2024)
- [Improving moment tensor solutions under Earth structure uncertainty with simulation-based inference](https://mlsanity.com/paper/2603.18925/) (2026)

## Abstract (arXiv)

We present a way to capture high-information posteriors from training sets that are sparsely sampled over the parameter space for robust simulation-based inference. In physical inference problems, we can often apply domain knowledge to define traditional summary statistics to capture some of the information in a dataset. We show that augmenting these statistics with neural network outputs to maximise the mutual information improves information extraction compared to neural summaries alone or their concatenation to existing summaries and makes inference robust in settings with low training data. We introduce 1) two loss formalisms to achieve this and 2) apply the technique to two different cosmological datasets to extract non-Gaussian parameter information.