利用非线性充分维度缩减学习函数图
Learning Functional Graphs with Nonlinear Sufficient Dimension Reduction
AI总结：
本文提出一种基于非线性充分维度缩减的非参数函数图模型，通过避免维度灾难提高估计精度，并保留概率条件独立性作为边不存在的标准。
摘要：
函数图模型近年来得到了广泛的发展，导致了多种模型，如函数高斯图模型、函数皮尔逊高斯图模型、函数贝叶斯图模型、非参数函数加法图模型和条件函数图模型。这些模型要么依赖于随机函数上的某些参数形式分布，要么依赖于加法条件独立性，这是一种不同于概率条件独立性的标准。在本文中，我们引入了一个基于函数充分维度缩减的非参数函数图模型。我们的方法不仅放松了高斯或皮尔逊高斯假设，而且通过避免“维度灾难”提高了估计精度。此外，它保留了概率条件独立性作为确定边不存在的标准。通过模拟研究和f-MRI数据集的分析，我们展示了我们方法的优势。
英文摘要：
Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the functional Bayesian graphical model, the nonparametric functional additive graphical model, and the conditional functional graphical model. These models rely either on some parametric form of distributions on random functions, or on additive conditional independence, a criterion that is different from probabilistic conditional independence. In this paper we introduce a nonparametric functional graphical model based on functional sufficient dimension reduction. Our method not only relaxes the Gaussian or copula Gaussian assumptions, but also enhances estimation accuracy by avoiding the ``curse of dimensionality''. Moreover, it retains the probabilistic conditional independence as the criterion to determine the absence of edges. By doing simulation study and analysis of the f-MRI dataset, we demonstrate the advantages of our method.
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