关于充分图模型

AI总结：

本文提出一种基于非线性充分降维的充分图模型，用低维充分预测变量刻画条件独立性以避免维数灾难，并在非高斯高维场景下优于现有方法。

摘要：

我们通过将最近发展的非线性充分降维技术应用于条件独立性评估，引入了一种充分图模型。该图模型本质上是非参数的，因为它不做高斯或高斯 copula 之类的分布假设。然而，与依赖高维核来刻画条件独立性的完全非参数图模型不同，我们的图模型基于给定一组维度大幅降低的充分预测变量的条件独立性。通过这种方式，我们避免了高维核带来的维数灾难。我们建立了估计量的总体性质、收敛速率和变量选择一致性。通过模拟比较和对 DREAM 4 Challenge 数据集的分析，我们证明当高斯或高斯 copula 假设被违反时，我们的方法优于现有方法，并且其在高维设置下的表现依然出色。

英文摘要：

We introduce a sufficient graphical model by applying the recently developed nonlinear sufficient dimension reduction techniques to the evaluation of conditional independence. The graphical model is nonparametric in nature, as it does not make distributional assumptions such as the Gaussian or copula Gaussian assumptions. However, unlike a fully nonparametric graphical model, which relies on the high-dimensional kernel to characterize conditional independence, our graphical model is based on conditional independence given a set of sufficient predictors with a substantially reduced dimension. In this way we avoid the curse of dimensionality that comes with a high-dimensional kernel. We develop the population-level properties, convergence rate, and variable selection consistency of our estimate. By simulation comparisons and an analysis of the DREAM 4 Challenge data set, we demonstrate that our method outperforms the existing methods when the Gaussian or copula Gaussian assumptions are violated, and its performance remains excellent in the high-dimensional setting.

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