# Direct Amortized Likelihood Ratio Estimation

arXiv: https://arxiv.org/abs/2311.10571 · HTML: https://mlsanity.com/paper/2311.10571/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 17 Nov 2023.

## Builds on (most cited first, 9 of 9)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [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)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimation](https://mlsanity.com/paper/2208.13624/) (2022)
- [Introducing an Explicit Symplectic Integration Scheme for Riemannian Manifold Hamiltonian Monte Carlo](https://mlsanity.com/paper/1910.06243/) (2019)

## Built on by (most cited first, 5 of 5)

- [Neural Methods for Amortized Inference](https://mlsanity.com/paper/2404.12484/) (2024)
- [A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2602.00834/) (2026)
- [Do Diffusion Models Dream of Electric Planes? Discrete and Continuous Simulation-Based Inference for Aircraft Design](https://mlsanity.com/paper/2603.13284/) (2026)
- [On the Dataless Training of Neural Networks](https://mlsanity.com/paper/2510.25962/) (2025)
- [FUSE: FK-Steered Multi-Modal Flow Matching for Efficient Simulation-Based Posterior Estimation](https://mlsanity.com/paper/2607.05252/) (2026)

## Abstract (arXiv)

We introduce a new amortized likelihood ratio estimator for likelihood-free simulation-based inference (SBI). Our estimator is simple to train and estimates the likelihood ratio using a single forward pass of the neural estimator. Our approach directly computes the likelihood ratio between two competing parameter sets which is different from the previous approach of comparing two neural network output values. We refer to our model as the direct neural ratio estimator (DNRE). As part of introducing the DNRE, we derive a corresponding Monte Carlo estimate of the posterior. We benchmark our new ratio estimator and compare to previous ratio estimators in the literature. We show that our new ratio estimator often outperforms these previous approaches. As a further contribution, we introduce a new derivative estimator for likelihood ratio estimators that enables us to compare likelihood-free Hamiltonian Monte Carlo (HMC) with random-walk Metropolis-Hastings (MH). We show that HMC is equally competitive, which has not been previously shown. Finally, we include a novel real-world application of SBI by using our neural ratio estimator to design a quadcopter. Code is available at https://github.com/SRI-CSL/dnre.