A semi-model-independent approach to describe a cosmological database

TL;DR

This paper presents a semi-model-independent method combining Gaussian linear models with neural networks to reconstruct functions from cosmological data, offering advantages over previous approaches including straightforward uncertainty estimation.

Contribution

It introduces a novel semi-model-independent approach that integrates neural networks with Gaussian linear models for flexible and efficient cosmological data reconstruction.

Findings

Provides a closed-form posterior distribution and Bayesian evidence.

Removes drawbacks of previous non-parametric methods.

Enables straightforward uncertainty quantification.

Abstract

A model-independent or non-parametric approach for modeling a database has been widely used in cosmology. In these scenarios, the data has been used directly to reconstruct an underlying function. In this work, we introduce a novel semi-model-independent method to do the task. The new approach not only removes some drawbacks of previous methods but also has some remarkable advantages. We combine the well-known Gaussian linear model with a neural network and introduce a procedure for the reconstruction of an arbitrary function. In the scenario, the neural network produces some arbitrary base functions which subsequently are fed to the Gaussian linear model. Given a prior distribution on the free parameters, the Gaussian linear model provides a close form for the posterior distribution as well as the Bayesian evidence. In addition, contrary to other methods, it is straightforward to compute the uncertainty.