Test of Artificial Neural Networks in Likelihood-free Cosmological Constraints: A Comparison of IMNN and DAE

TL;DR

This paper compares the effectiveness of Information Maximising Neural Networks (IMNN) and Denoising Autoencoders (DAE) in compressing data for cosmological parameter estimation, demonstrating IMNN's superior robustness and non-linear summarization capabilities.

Contribution

The study provides a systematic comparison of IMNN and DAE for data compression in cosmological inference, highlighting IMNN's advantages in robustness and non-linear feature extraction.

Findings

IMNN finds more robust, non-linear summaries than DAE.

IMNN outperforms DAE in compressing data for better parameter constraints.

The comparison uses simulated and real observational data within a Gaussian likelihood framework.

Abstract

In the procedure of constraining the cosmological parameters with the observational Hubble data and the type Ia supernova data, the combination of Masked Autoregressive Flow and Denoising Autoencoder can perform a good result. The above combination extracts the features from OHD with DAE, and estimates the posterior distribution of cosmological parameters with MAF. We ask whether we can find a better tool to compress large data in order to gain better results while constraining the cosmological parameters. Information maximising neural networks, a kind of simulation-based machine learning technique, was proposed at an earlier time. In a series of numerical examples, the results show that IMNN can find optimal, non-linear summaries robustly. In this work, we mainly compare the dimensionality reduction capabilities of IMNN and DAE. We use IMNN and DAE to compress the data into different dimensions and set different learning rates for MAF to calculate the posterior. Meanwhile, the training data and mock OHD are generated with a simple Gaussian likelihood, the spatially flat {\Lambda}CDM model and the real OHD data. To avoid the complex calculation in comparing the posterior directly, we set different criteria to compare IMNN and DAE.