INFERNO: Inference-Aware Neural Optimisation

TL;DR

This paper introduces INFERNO, a method for constructing inference-aware summary statistics using stochastic gradient descent to improve parameter estimation in complex models with nuisance parameters.

Contribution

It presents a novel approach to create non-linear summary statistics that minimize inference-motivated losses, enhancing parameter inference accuracy.

Findings

Outperforms classification-based summary statistics in confidence interval estimation.

Effectively accounts for nuisance parameters in complex models.

Demonstrates improved inference in a multi-dimensional mixture model.

Abstract

Complex computer simulations are commonly required for accurate data modelling in many scientific disciplines, making statistical inference challenging due to the intractability of the likelihood evaluation for the observed data. Furthermore, sometimes one is interested on inference drawn over a subset of the generative model parameters while taking into account model uncertainty or misspecification on the remaining nuisance parameters. In this work, we show how non-linear summary statistics can be constructed by minimising inference-motivated losses via stochastic gradient descent such they provided the smallest uncertainty for the parameters of interest. As a use case, the problem of confidence interval estimation for the mixture coefficient in a multi-dimensional two-component mixture model (i.e. signal vs background) is considered, where the proposed technique clearly outperforms summary statistics based on probabilistic classification, which are a commonly used alternative but do not account for the presence of nuisance parameters.