# Massive data compression for parameter-dependent covariance matrices

arXiv: https://arxiv.org/abs/1707.06529 · HTML: https://mlsanity.com/paper/1707.06529/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2017.

## Built on by (most cited first, 4 of 4)

- [Robust Simulation-Based Inference in Cosmology with Bayesian Neural Networks](https://mlsanity.com/paper/2207.08435/) (2022)
- [Robust Field-level Likelihood-free Inference with Galaxies](https://mlsanity.com/paper/2302.14101/) (2023)
- [DeepLSS: breaking parameter degeneracies in large scale structure with deep learning analysis of combined probes](https://mlsanity.com/paper/2203.09616/) (2022)
- [Field-level simulation-based inference with galaxy catalogs: the impact of systematic effects](https://mlsanity.com/paper/2310.15234/) (2023)

## Abstract (arXiv)

We show how the massive data compression algorithm MOPED can be used to reduce, by orders of magnitude, the number of simulated datasets that are required to estimate the covariance matrix required for the analysis of gaussian-distributed data. This is relevant when the covariance matrix cannot be calculated directly. The compression is especially valuable when the covariance matrix varies with the model parameters. In this case, it may be prohibitively expensive to run enough simulations to estimate the full covariance matrix throughout the parameter space. This compression may be particularly valuable for the next-generation of weak lensing surveys, such as proposed for Euclid and LSST, for which the number of summary data (such as band power or shear correlation estimates) is very large, ~ 104, due to the large number of tomographic redshift bins that the data will be divided into. In the pessimistic case where the covariance matrix is estimated separately for all points in an MCMC analysis, this may require an unfeasible 109 simulations. We show here that MOPED can reduce this number by a factor of 1000, or a factor of ~ 106 if some regularity in the covariance matrix is assumed, reducing the number of simulations required to a manageable 103, making an otherwise intractable analysis feasible.