# Cosmological Analysis with Calibrated Neural Quantile Estimation and Approximate Simulators

arXiv: https://arxiv.org/abs/2411.14748 · HTML: https://mlsanity.com/paper/2411.14748/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 49 references that are in the map.
- First posted on arXiv 22 Nov 2024.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (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)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Likelihood-free inference with emulator networks](https://mlsanity.com/paper/1805.09294/) (2018)
- [Learning to Predict the Cosmological Structure Formation](https://mlsanity.com/paper/1811.06533/) (2018)
- [Robust Field-level Likelihood-free Inference with Galaxies](https://mlsanity.com/paper/2302.14101/) (2023)
- [Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets](https://mlsanity.com/paper/2311.01588/) (2023)
- [Simulation-Based Inference with Quantile Regression](https://mlsanity.com/paper/2401.02413/) (2024)
- [Hybrid Summary Statistics](https://mlsanity.com/paper/2410.07548/) (2024)
- [Simulation-based inference with scattering representations: scattering is all you need](https://mlsanity.com/paper/2410.11883/) (2024)

## Built on by (most cited first, 2 of 2)

- [Tests for model misspecification in simulation-based inference: from local distortions to global model checks](https://mlsanity.com/paper/2412.15100/) (2024)
- [Simulation-Efficient Cosmological Inference with Multi-Fidelity SBI](https://mlsanity.com/paper/2507.00514/) (2025)

## Abstract (arXiv)

A major challenge in extracting information from current and upcoming surveys of cosmological Large-Scale Structure (LSS) is the limited availability of computationally expensive high-fidelity simulations. We introduce calibrated Neural Quantile Estimation (NQE), a new Simulation-Based Inference (SBI) method that leverages a large number of approximate simulations for training and a small number of high-fidelity simulations for calibration. This approach guarantees an unbiased posterior regardless of approximate simulation accuracy, while achieving near-optimal constraining power when the approximate simulations are reasonably accurate. As a proof of concept, we demonstrate that cosmological parameters can be inferred at field level from projected 2-dim dark matter density maps up to krm max~1.5,h/Mpc at z=0 by training on ~104 Particle-Mesh (PM) simulations with transfer function correction and calibrating with ~102 Particle-Particle (PP) simulations. The calibrated posteriors closely match those obtained by directly training on ~104 expensive PP simulations, but at a fraction of the computational cost. Our method offers a practical and scalable framework for SBI of cosmological LSS, enabling precise inference across vast volumes and down to small scales.