Concentration Inequality for Distance Covariances and Applications in Feature Screening

• Activity Number: 259 - Recent Developments in Statistical Inference Using Distance Correlation and Related Dependence Metrics
• Type: Invited
• Date/Time: Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xiaoming Huo*
• Companies: Georgia Institute of Technology
• Keywords: Distance covariance; Feature selection; Concentration inequality; Symmetric inequality; U-statistics; Non-asymptotic error bounds

Abstract

Minimizing the distance covariance can be utilized to screen out independent features. The statistical property of such an approach can be assessed by deriving the upper bound of the corresponding errors. These upper bounds are often derived via applying the concentration inequality to some sample means. A challenge of such an approach regarding the distance covariance is that the distance covariance is not a sample mean, however a U-statistic. A recent advance in applied probability provides a tool to derive some concentration inequalities when the estimators are U-statistics. We apply this new technique and derived some non-asymptotic error bounds of a distance-covariance-based statistics, when the distance covariance is used as a criterion function in the feature screening. Some numerical studies are carried out to evaluate the applicability of these concentration-inequality-based bounds.