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Showing content from https://github.com/Mamba413/Ball below:

Mamba413/Ball: Statistical Inference and Sure Independence Screening via Ball Statistics

Ball Statistics

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.

Install the Ball package from CRAN:

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)

Install the Ball package from PyPI:

If you use Ball or reference our vignettes in a presentation or publication, we would appreciate citations of our package.

Zhu J, Pan W, Zheng W, Wang X (2021). “Ball: An R Package for Detecting Distribution Difference and Association in Metric Spaces.” Journal of Statistical Software, 97(6), 1–31. doi: 10.18637/jss.v097.i06.

Here is the corresponding Bibtex entry

@Article{ball2021zhu,
  title = {{Ball}: An {R} Package for Detecting Distribution Difference and Association in Metric Spaces},
  author = {Jin Zhu and Wenliang Pan and Wei Zheng and Xueqin Wang},
  journal = {Journal of Statistical Software},
  year = {2021},
  volume = {97},
  number = {6},
  pages = {1--31},
  doi = {10.18637/jss.v097.i06},
}

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
Zhu, Jin, Wenliang Pan, Wei Zheng, and Xueqin Wang. 2021. “Ball: An R Package for Detecting Distribution Difference and Association in Metric Spaces”. Journal of Statistical Software 97 (6):1-31. https://doi.org/10.18637/jss.v097.i06.
Wang, Xueqin, Jin Zhu, Wenliang Pan, Junhao Zhu, and Heping Zhang. 2023. “Nonparametric Statistical Inference via Metric Distribution Function in Metric Spaces.” Journal of the American Statistical Association 119 (548): 2772–84. doi:10.1080/01621459.2023.2277417.

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

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