# Benchmark of Likelihood-Free Inference Methods based on Neural and Optimal Transport Approaches

arXiv: https://arxiv.org/abs/2605.30516 · HTML: https://mlsanity.com/paper/2605.30516/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 28 May 2026.

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

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Learning Robust Statistics for Simulation-based Inference under Model Misspecification](https://mlsanity.com/paper/2305.15871/) (2023)
- [Likelihood-Free Parameter Estimation with Neural Bayes Estimators](https://mlsanity.com/paper/2208.12942/) (2022)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution](https://mlsanity.com/paper/1609.00066/) (2016)
- [Overview of Approximate Bayesian Computation](https://mlsanity.com/paper/1802.09720/) (2018)
- [Approximating the Likelihood in Approximate Bayesian Computation](https://mlsanity.com/paper/1803.06645/) (2018)

## Abstract (arXiv)

Simulation-based inference (SBI) has become an increasingly important framework for parameter estimation in models for which simulation is feasible, including cases where likelihood evaluation is unavailable or costly. While recent work has introduced benchmark frameworks to compare likelihood-free methods, these studies often do not account for structural features such as heavy-tails or discreteness. In this article, we investigate how the performance of likelihood-free inference methods depends on these structural properties. We consider four approaches: MLE, NBE, EOT and AW--NBE and evaluate them using simulations. This study highlights the importance of carefully selecting evaluation tools in the presence of extremes and discrete data.