Direct Amortized Likelihood Ratio Estimation

TL;DR

This paper introduces a new neural likelihood ratio estimator called DNRE for likelihood-free inference, demonstrating improved performance, enabling comparison of HMC and MH, and applying it to quadcopter design.

Contribution

The paper presents the DNRE, a simple, efficient neural likelihood ratio estimator, along with a Monte Carlo posterior estimate, and compares HMC and MH in likelihood-free inference.

Findings

DNRE often outperforms previous ratio estimators.

HMC is shown to be competitive with MH for likelihood-free inference.

Application to quadcopter design demonstrates real-world utility.

Abstract

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.