Nonparametric Functional Graphical Modeling Through Functional Additive Regression Operator
Nonparametric Functional Graphical Modeling Through Functional Additive Regression Operator
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DOI：
10.1080/01621459.2021.2006667
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发表时间：
2021-11
影响因子：
3.7
通讯作者：
Kuang‐Yao Lee;Lexin Li;Bing Li;Hongyu Zhao
中科院分区：
文献类型：
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作者：
Kuang‐Yao Lee;Lexin Li;Bing Li;Hongyu Zhao
摘要本文建立了多元随机函数的非参数图形模型。现有的图形模型大多受多元高斯分布或copula高斯分布假设的限制，这也意味着不同节点上的随机变量或函数之间存在线性关系。我们通过基于一个新的统计对象——函数加性回归算子——构建图形模型来放宽这些假设。通过在算子水平上进行回归和邻域选择，我们的方法可以在不需要任何分布假设的情况下捕获非线性关系。此外，该方法仅使用一维核构建，从而避免了完全非参数方法经常遭受的维数诅咒，并使我们能够处理大规模网络。我们推导了估计回归算子的误差界，并建立了图估计一致性，同时允许函数的数量以样本大小的指数速率发散。我们通过脑电图数据集的模拟和分析证明了我们的方法的有效性。本文的补充材料可在网上获得。
Abstract In this article, we develop a nonparametric graphical model for multivariate random functions. Most existing graphical models are restricted by the assumptions of multivariate Gaussian or copula Gaussian distributions, which also imply linear relations among the random variables or functions on different nodes. We relax those assumptions by building our graphical model based on a new statistical object—the functional additive regression operator. By carrying out regression and neighborhood selection at the operator level, our method can capture nonlinear relations without requiring any distributional assumptions. Moreover, the method is built up using only one-dimensional kernel, thus, avoids the curse of dimensionality from which a fully nonparametric approach often suffers, and enables us to work with large-scale networks. We derive error bounds for the estimated regression operator and establish graph estimation consistency, while allowing the number of functions to diverge at the exponential rate of the sample size. We demonstrate the efficacy of our method by both simulations and analysis of an electroencephalography dataset. Supplementary materials for this article are available online.