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.

翻译：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。该图模型本质上具有非参数性质，因为它不依赖于高斯分布或Copula高斯分布等分布假设。然而，与依赖高维核来表征条件独立性的完全非参数图模型不同，我们的图模型基于在降维后的充分预测变量集合上的条件独立性，从而避免了高维核带来的维度灾难问题。我们建立了估计量的总体性质、收敛速率以及变量选择一致性。通过模拟比较和对DREAM 4挑战数据集的分析，我们证明：在高斯或Copula高斯假设被违反时，我们的方法优于现有方法，且在高维场景下仍保持优异的性能表现。