  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.
