# Likelihood-free inference with an improved cross-entropy estimator

arXiv: https://arxiv.org/abs/1808.00973 · HTML: https://mlsanity.com/paper/1808.00973/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2018.

## Built on by (most cited first, 11 of 11)

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- [Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models](https://mlsanity.com/paper/2210.04872/) (2022)
- [E Pluribus Unum Ex Machina: Learning from Many Collider Events at Once](https://mlsanity.com/paper/2101.07263/) (2021)
- [Learning Likelihood Ratios with Neural Network Classifiers](https://mlsanity.com/paper/2305.10500/) (2023)
- [Inferring dark matter substructure with astrometric lensing beyond the power spectrum](https://mlsanity.com/paper/2110.01620/) (2021)
- [New Machine Learning Techniques for Simulation-Based Inference: InferoStatic Nets, Kernel Score Estimation, and Kernel Likelihood Ratio Estimation](https://mlsanity.com/paper/2210.01680/) (2022)
- [Neural Quasiprobabilistic Likelihood Ratio Estimation with Negatively Weighted Data](https://mlsanity.com/paper/2410.10216/) (2024)
- [Neural simulation-based inference of the Higgs trilinear self-coupling via off-shell Higgs production](https://mlsanity.com/paper/2507.02032/) (2025)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)
- [Correcting Sensor-Induced Distribution Drift with Wasserstein Adversarial Learning](https://mlsanity.com/paper/2606.18561/) (2026)
- [GIST: Generator-state-Informed Supervision for Tabular Foundation Models](https://mlsanity.com/paper/2610.12904/) (2026)

## Abstract (arXiv)

We extend recent work (Brehmer, et. al., 2018) that use neural networks as surrogate models for likelihood-free inference. As in the previous work, we exploit the fact that the joint likelihood ratio and joint score, conditioned on both observed and latent variables, can often be extracted from an implicit generative model or simulator to augment the training data for these surrogate models. We show how this augmented training data can be used to provide a new cross-entropy estimator, which provides improved sample efficiency compared to previous loss functions exploiting this augmented training data.