HIgh-Dimensional DEsc Metrics (HiDDeM)
This repository stores the code for the HiDDeM project, which aims to develop and characterize metrics for the comparison of multi-dimensional distributions. One common use case for the application of such metrics is validation testing for simulated catalogs, where it is often required to compare simulated and real data distributions in two or more dimensions. There are a number of metrics such as the Kolmogorv-Smirnov (KS) statistic and Kullback–Leibler (KL) divergence that can be adapted to evaluate the overlap between distributions in higher dimensional spaces but, due to their sensitivity to the tails of distributions, they are not always useful. This project will explore other metrics that can be used to compare and characterize the nature of the differences between higher-dimensional distributions. Concrete examples for the use of each metric will be provided by examining their performance in DESCQA validation tests. Other use cases besides catalog validation are envisaged for this work. One example would be the comparison of the results of cosmological inference for two different probes in the full multi-dimensional cosmological parameter space.