A SIMPLE MEASURE OF CONDITIONAL DEPENDENCE
A SIMPLE MEASURE OF CONDITIONAL DEPENDENCE
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DOI：
10.1214/21-aos2073
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发表时间：
2021-12-01
影响因子：
4.5
通讯作者：
Chatterjee, Sourav
中科院分区：
文献类型：
--
作者：
Azadkia, Mona;Chatterjee, Sourav
在给定一组其他变量X-1，…，X-p的情况下，基于I.I.D.，我们提出了两个随机变量Y和Z之间的条件依赖系数。样本。该系数具有一长串理想的性质，其中最重要的是在绝对没有分布假设的情况下，它收敛于[0，1]中的一个极限，其中极限为0当且仅当Y和Z在给定X-1，…，X-p时是条件独立的，当且仅当Y等于给定X-1，…，X-p的Z的一个可测函数。此外，它有一个自然的解释，作为常见的部分R-2统计量的非线性推广，用于通过回归来衡量条件相关性。利用这个统计量，我们设计了一种新的变量选择算法，称为按条件独立性的特征排序(FOCI)，该算法不需要模型，没有调整参数，并且在稀疏性假设下可证明是一致的。对合成数据集和真实数据集进行了大量的应用。
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.