Fisher Score Matching for Simulation-Based Forecasting and Inference

2025/07/10 by Ce Sui, Sui, Ce, Shivam Pandey +3
Computer Science · Physics and Astronomy · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Galaxies: Formation, Evolution, Phenomena #Gaussian Processes and Bayesian Inference #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2507.07833

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Hybrid Summary Statistics
• A Parameter-Masked Mock Data Challenge for Beyond-Two-Point Galaxy Clustering Statistics
• A point cloud approach to generative modeling for galaxy surveys at the field level
• pmwd: A Differentiable Cosmological Particle-Mesh N-body Library
• Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models
• Score-Based Generative Modeling through Stochastic Differential Equations
• Generative Modeling by Estimating Gradients of the Data Distribution
• Mining gold from implicit models to improve likelihood-free inference
• MontePython 3: boosted MCMC sampler and other features

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• Direct Fisher Score Estimation for Likelihood Maximization

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