Ball Statistics

Introdution

The fundamental problems for data mining, statistical analysis, and machine learning are:

• whether several distributions are different?
• whether random variables are dependent?
• how to pick out useful variables/features from a high-dimensional data?

These issues can be tackled by Ball statistics, which enjoy following admirable advantages:

• available for most of datasets (e.g., traditional tabular data, brain shape, functional connectome, wind direction and so on)
• insensitive to outliers, distribution-free and model-free;
• theoretically guaranteed and computationally efficient.

Softwares

R package

Install the Ball package from CRAN:

install.packages("Ball")

Compared with selective R packages available for datasets in metric spaces:

	fastmit	energy	HHG	Ball
Test of equal distributions	❌	✔️	✔️	✔️
Test of independence	✔️	✔️	✔️	✔️
Test of joint independence	❌	❌	❌	✔️
Feature screening / Sure Independence Screening (SIS)	❌	❌	❌	✔️
Iterative Feature screening / Iterative SIS	❌	❌	❌	✔️
Datasets in metric spaces	✔️	SNT	✔️	✔️
Robustness	✔️	❌	✔️	✔️
Parallel programming	❌	❌	✔️	✔️
Computational efficiency	🏃🏃🏃	🏃🏃🏃	🏃🏃	🏃🏃🚶

SNT is the abbreviation of strong negative type.

See the following documents for more details about the Ball package:

• github page (short)
• vignette (moderate)
• JSS paper (detailed)

Python package

Install the Ball package from PyPI:

pip install Ball

References

• Pan, Wenliang; Tian, Yuan; Wang, Xueqin; Zhang, Heping. Ball Divergence: Nonparametric two sample test. Ann. Statist. 46 (2018), no. 3, 1109--1137. doi:10.1214/17-AOS1579. https://projecteuclid.org/euclid.aos/1525313077
• Wenliang Pan, Xueqin Wang, Weinan Xiao & Hongtu Zhu (2018) A Generic Sure Independence Screening Procedure, Journal of the American Statistical Association, DOI: 10.1080/01621459.2018.1462709
• Wenliang Pan, Xueqin Wang, Heping Zhang, Hongtu Zhu & Jin Zhu (2019) Ball Covariance: A Generic Measure of Dependence in Banach Space, Journal of the American Statistical Association, DOI: 10.1080/01621459.2018.1543600
• Jin, Z., Wenliang P., Wei Z., and Xueqin W. (2018). Ball: An R package for detecting distribution difference and association in metric spaces. arXiv preprint arXiv:1811.03750. URL http://arxiv.org/abs/1811.03750.

Bug report

Open an issue or send an email to Jin Zhu at zhuj37@mail2.sysu.edu.cn