Deep Learning and genetic algorithms for cosmological Bayesian inference speed-up

TL;DR

This paper introduces a novel method combining deep learning and genetic algorithms to accelerate cosmological Bayesian inference by dynamically approximating likelihood functions and optimizing neural network architectures during nested sampling.

Contribution

It presents a flexible, on-the-fly neural network approach for likelihood approximation and uses genetic algorithms for hyperparameter optimization, improving efficiency in cosmological Bayesian inference.

Findings

Neural networks effectively replace likelihood functions after training.

Genetic algorithms optimize neural network hyperparameters.

Method accelerates inference on cosmological datasets.

Abstract

In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a robust framework for extracting theoretical insights from observational data. However, its computational demands can be substantial, primarily due to the need for numerous likelihood function evaluations. Our proposed method utilizes the power of deep learning, employing feedforward neural networks to approximate the likelihood function dynamically during the Bayesian inference process. Unlike traditional approaches, our method trains neural networks on-the-fly using the current set of live points as training data, without the need for pre-training. This flexibility enables adaptation to various theoretical models and datasets. We perform simple hyperparameter optimization using genetic algorithms to suggest initial neural network architectures for learning each likelihood function. Once sufficient accuracy is achieved, the neural network replaces the original likelihood function. The implementation integrates with nested sampling algorithms and has been thoroughly evaluated using both simple cosmological dark energy models and diverse observational datasets. Additionally, we explore the potential of genetic algorithms for generating initial live points within nested sampling inference, opening up new avenues for enhancing the efficiency and effectiveness of Bayesian inference methods.