Likelihood-free Inference with the Mixture Density Network

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 ΛCDM and wCDM 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  ( 10 − 2 σ ) . Furthermore, the MDN method can provide accurate parameter estimates with  ( 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.

Machine Learning for Bayesian Experimental Design in the Subsurface

“…The mixing coefficients are trained to smooth out or suppress the unnecessary individual Gaussian components, resulting in a posterior with the desired characteristics. However, excessive component count can slow down the training process and increase the number of trainable parameters, eventually leading to training instability (Wang et al, 2022a). The results are as follows:…”