# Set-based Implicit Likelihood Inference of Galaxy Cluster Mass

arXiv: https://arxiv.org/abs/2507.20378 · HTML: https://mlsanity.com/paper/2507.20378/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 39 references that are in the map.
- First posted on arXiv 27 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Sampling-Based Accuracy Testing of Posterior Estimators for General Inference](https://mlsanity.com/paper/2302.03026/) (2023)
- [Invertible Generative Modeling using Linear Rational Splines](https://mlsanity.com/paper/2001.05168/) (2020)
- [Robust Field-level Likelihood-free Inference with Galaxies](https://mlsanity.com/paper/2302.14101/) (2023)
- [Mass Estimation of Galaxy Clusters with Deep Learning I: Sunyaev-Zel'dovich Effect](https://mlsanity.com/paper/2003.06135/) (2020)
- [Predicting the Thermal Sunyaev-Zel'dovich Field using Modular and Equivariant Set-Based Neural Networks](https://mlsanity.com/paper/2203.00026/) (2022)
- [Mass Estimation of Galaxy Clusters with Deep Learning II: CMB Cluster Lensing](https://mlsanity.com/paper/2005.13985/) (2020)
- [Estimating Dark Matter Halo Masses in Simulated Galaxy Clusters with Graph Neural Networks](https://mlsanity.com/paper/2411.12629/) (2024)

## Abstract (arXiv)

We present a set-based machine learning framework that infers posterior distributions of galaxy cluster masses from projected galaxy dynamics. Our model combines Deep Sets and conditional normalizing flows to incorporate both positional and velocity information of member galaxies to predict residual corrections to the M-σ relation for improved interpretability. Trained on the Uchuu-UniverseMachine simulation, our approach significantly reduces scatter and provides well-calibrated uncertainties across the full mass range compared to traditional dynamical estimates.