Fisher Score Matching for Simulation-Based Forecasting and Inference
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915382189621248 |
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| author | Sui, Ce Pandey, Shivam Wandelt, Benjamin D. |
| author_facet | Sui, Ce Pandey, Shivam Wandelt, Benjamin D. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_07833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fisher Score Matching for Simulation-Based Forecasting and Inference Sui, Ce Pandey, Shivam Wandelt, Benjamin D. Cosmology and Nongalactic Astrophysics Instrumentation and Methods for Astrophysics 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. |
| title | Fisher Score Matching for Simulation-Based Forecasting and Inference |
| topic | Cosmology and Nongalactic Astrophysics Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2507.07833 |