A SIMPLE MEASURE OF CONDITIONAL DEPENDENCE

• 成果类型: Article
• 署名作者: Azadkia, Mona; Chatterjee, Sourav
• 署名单位: Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2073
• 发表日期: 2021
• 页码: 3070-3102
• 关键词: VARIABLE SELECTION; Dimension Reduction; regression; INDEPENDENCE; copula

摘要

We propose a coefficient of conditional dependence between two random variables Y and Z given a set of other variables X-1, ..., X-p, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in [0, 1], where the limit is 0 if and only if Y and Z are conditionally independent given X-1, ..., X-p, and is 1 if and only if Y is equal to a measurable function of Z given X-1, ..., X-p. Moreover, it has a natural interpretation as a nonlinear generalization of the familiar partial R-2 statistic for measuring conditional dependence by regression. Using this statistic, we devise a new variable selection algorithm, called Feature Ordering by Conditional Independence (FOCI), which is model-free, has no tuning parameters, and is provably consistent under sparsity assumptions. A number of applications to synthetic and real data sets are worked out.