# Overview of mgcpy¶

mgcpy is a Python package containing tools for multiscale graph correlation and other statistical tests, that is capable of dealing with high dimensional and multivariate data.

## Motivation¶

Examining and identifying relationships between variables is critical for many scientists to definitely establishing causality and deciphering these relationships in further studies. To approach this problem, the most commonly used statistic utilized is Pearson’s Product-Moment Correlation (Pearson, 1895) but the test fails to address some of the issues that data scientists face today (Vogelstein et al., 2016). Other tests conventionally used include "energy statistics" such as Dcorr; kernel-based approaches such as Hilbert Schmidt Independence Criterion (HSIC) (Gretton and GyĂśrfi, 2010) which has recently been shown to be equivalent to "energy statistics" (Sejdinovic et al., 2013)(Shen and Vogelstein, 2018); Heller, Heller, and Gorfine’s test (HHG) (Heller et al., 2012), and many others. These tests perform empirically well on either high dimensional linear data or low dimensional nonlinear data.No approach works well on high dimensional nonlinear data, and no approach addresses issues on how to interpret the data.

Multiscale graph correlation (MGC) attempts to alleviate these issues. The test utilizes features of other techniques such ask-nearest neighbors, kernel methods, and multiscale analysis to detect relationships (Vogelstein et al., 2016) in all types of data, including high dimensional nonlinear data. The test is also computationally efficient, requiring about half or one third of the number of samples to achieve the same statistical power (Vogelstein et al.,2016). In addition, the test provides information about the data’s geometry (Vogelsteinet al., 2016), allowing for more informed decision making of the underlying relationships in the data

mgcpy aims to be a comprehensive independence testing package including all of the commonly used independence tests as mentioned above and additional functionality such as two sample independence testing and a novel random forest-based independence test. These tests are not only included to benchmark MGC but to have a convenient location for users if they would prefer to utilize those tests instead. The package utilizes a simple class structure to enhance usability while also allowing easy extension of the package for developers. The package can be installed on all major platforms (e.g. BSD, GNU/Linux, OS X, Windows)from Python Package Index (PyPI) and GitHub.

## Free software¶

mgcpy is free software; you can redistribute it and/or modify it under the terms of the Apache-2.0. We welcome contributions. Join us on GitHub.

# Documentation¶

mgcpy is a hypothesis testing package in python.