Fisher Score Matching for Simulation-Based Forecasting and Inference

TL;DR

This paper introduces a neural network-based method to estimate Fisher scores from simulation models, enabling gradient-based inference even with non-differentiable simulators, with applications demonstrated in cosmology.

Contribution

The authors develop a score matching approach to estimate Fisher scores using neural networks, extending gradient-based inference to non-differentiable simulation models.

Findings

Scores closely match ground truth in toy and cosmological models

Method enables Fisher forecasts for non-differentiable simulators

Validated on linear Gaussian and cosmological examples

Abstract

We propose a method for estimating the Fisher score--the gradient of the log-likelihood with respect to model parameters--using score matching. By introducing a latent parameter model, we show that the Fisher score can be learned by training a neural network to predict latent scores via a mean squared error loss. We validate our approach on a toy linear Gaussian model and a cosmological example using a differentiable simulator. In both cases, the learned scores closely match ground truth for plausible data-parameter pairs. This method extends the ability to perform Fisher forecasts, and gradient-based Bayesian inference to simulation models, even when they are not differentiable; it therefore has broad potential for advancing cosmological analyses.