Welcome to Ball’s documentation!¶

Hypothesis tests and sure independence screening (SIS) procedure based on ball statistics, including ball divergence <doi:10.1214/17-AOS1579>, ball covariance <doi:10.1080/01621459.2018.1543600>, and ball correlation <doi:10.1080/01621459.2018.1462709>, are developed to analyze complex data in metric spaces, e.g, shape, directional, compositional and symmetric positive definite matrix data. The ball divergence and ball covariance based distribution-free tests are implemented to detecting distribution difference and association in metric spaces <arXiv:1811.03750>. Furthermore, several generic non-parametric feature selection procedures based on ball correlation, BCor-SIS and all of its variants, are implemented to tackle the challenge in the context of ultra high dimensional data.

Contents:

API List¶

Ball functions¶

A complete list of all ball functions provided by Ball.

Ball divergence, ball covariance, and ball correlation statistics¶

These functions compute the estimators for the ball divergence, ball covariance, and ball correlation.

`Ball.bd`
`Ball.bcov`
`Ball.bcor`

Ball Divergence based Equality of Distributions Test¶

Performs the nonparametric two-sample or K-sample Ball Divergence test for equality of multivariate distributions.

Ball.bd_test

Ball Covariance based (joint) independence Test¶

Ball Covariance test of independence. Ball covariance are generic dependence measures in Banach spaces.

Ball.bcov_test

Ball Correlation based Sure Independence Screening (BCor-SIS)¶

Generic non-parametric sure independence screening (SIS) procedure based on Ball Correlation. Ball correlation is a generic measure of dependence in Banach spaces.

Ball.bcorsis

Ball is developed on Github. Please report issues there as well.