From Distance Correlation to Multiscale Graph Correlation
From Distance Correlation to Multiscale Graph Correlation
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DOI：
10.1080/01621459.2018.1543125
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发表时间：
2019-04-08
影响因子：
3.7
通讯作者：
Vogelstein, Joshua T.
中科院分区：
文献类型：
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作者：
Shen, Cencheng;Priebe, Carey E.;Vogelstein, Joshua T.
理解和开发一种可以检测一般依赖关系的相关性度量不仅对统计学和机器学习至关重要，而且对大数据时代的一般科学发现也至关重要。在本文中，我们建立了一个新的框架，推广距离相关性（Dcorr）-一个相关性的措施，最近提出的，并证明是普遍一致的依赖测试对所有联合分布的有限时刻-多尺度图相关性（MGC）。通过使用的特征函数，并结合最近邻机，我们正式的人口版本的局部距离相关性，定义在一个给定的依赖的最佳规模，并命名为MGC的最佳局部相关性。新的理论框架激发了一个理论上健全的样本MGC，并允许一些理想的属性被证明，包括普遍的一致性，收敛性，几乎无偏的样本版本。MGC的优点是通过一组全面的模拟与线性，非线性，单变量，多变量和噪声的依赖关系，其中它失去了几乎没有权力在单调的依赖关系，同时实现更好的性能在一般的依赖关系，相比Dcorr和其他流行的方法。可以在网上找到。
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we establish a new framework that generalizes distance correlation (Dcorr)-a correlation measure that was recently proposed and shown to be universally consistent for dependence testing against all joint distributions of finite moments-to the multiscale graph correlation (MGC). By using the characteristic functions and incorporating the nearest neighbor machinery, we formalize the population version of local distance correlations, define the optimal scale in a given dependency, and name the optimal local correlation as MGC. The new theoretical framework motivates a theoretically sound sample MGC and allows a number of desirable properties to be proved, including the universal consistency, convergence, and almost unbiasedness of the sample version. The advantages of MGC are illustrated via a comprehensive set of simulations with linear, nonlinear, univariate, multivariate, and noisy dependencies, where it loses almost no power in monotone dependencies while achieving better performance in general dependencies, compared to Dcorr and other popular methods. for this article are available online.