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:
R install.packages("Ball") Compared with selective R packages available for datasets in metric spaces:

| | fastmit | energy | HHG | Ball | | :-------------------------------- | :----------------------------------------------------------: | :--------------------------------------------------------: | :--------------------------------------------------: | :----------------------------------------------------: | | Test of equal distributions | :x: | :heavycheckmark: | :heavycheckmark: | :heavycheckmark: | | Test of independence | :heavycheckmark: | :heavycheckmark: | :heavycheckmark: | :heavycheckmark: | | Test of joint independence | :x: | :x: | :x: | :heavycheckmark: | | Feature screening / Sure Independence Screening (SIS) | :x: | :x: | :x: | :heavycheckmark: | | Iterative Feature screening / Iterative SIS | :x: | :x: | :x: | :heavycheckmark: | | Datasets in metric spaces | :heavycheckmark: | SNT | :heavycheckmark: | :heavycheckmark: | | Robustness | :heavycheckmark: | :x: | :heavycheckmark: | :heavycheckmark: | | Parallel programming | :x: | :x: | :heavycheckmark: | :heavycheckmark: | | Computational efficiency | :running::running::running: | :running::running::running: | :running::running: | :running::running::walking: |

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:
shell pip install Ball

Citation

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}, }

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
• 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.

Bug report

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