Likelihood-free Inference with Mixture Density Network

TL;DR

This paper introduces the use of mixture density networks for likelihood-free inference in cosmology, demonstrating comparable accuracy to traditional methods with fewer simulations, applicable to complex models.

Contribution

The paper presents a novel application of mixture density networks for likelihood-free parameter estimation, achieving high accuracy with fewer simulations in cosmological models.

Findings

MDN achieves similar accuracy to MCMC with fewer samples.

MDN can handle multiple data sets for joint parameter constraints.

The method is extendable to other complex scientific models.

Abstract

In this work, we propose using the mixture density network (MDN) to estimate cosmological parameters. We test the MDN method by constraining parameters of the $\Lambda$CDM and $w$CDM models using Type Ia supernovae and the power spectra of the cosmic microwave background. We find that the MDN method can achieve the same level of accuracy as the Markov Chain Monte Carlo method, with a slight difference of $\mathcal{O}(10^{-2}\sigma)$. Furthermore, the MDN method can provide accurate parameter estimates with $\mathcal{O}(10^3)$ forward simulation samples, which are useful for complex and resource-consuming cosmological models. This method can process either one data set or multiple data sets to achieve joint constraints on parameters, extendable for any parameter estimation of complicated models in a wider scientific field. Thus, the MDN provides an alternative way for likelihood-free inference of parameters.