提出从非高斯数据中推断条件独立性的新方法。
Conditional Independence Estimates for the Generalized Nonparanormal
- 基于高斯变换的广义非参数正态模型，用精度矩阵推导独立性结构。
- 算法高效，可在合成与真实数据上准确恢复条件独立关系。
- 适合处理非高斯变量间的依赖分析，如生物、金融建模。
对于一般非高斯分布，协方差和精度矩阵不反映变量间的独立性结构，这与多变量高斯分布不同。本文在前人工作基础上，证明对于一类非高斯分布——即由对角变换生成的高斯分布——只要数据满足特定条件，仍可从精度矩阵中推断出条件独立结构。这类变换称为广义非参数正态（generalized nonparanormal）。变换函数在广义上是任意的。本文还提出一种简单且计算高效的算法，用于从广义非参数正态数据中恢复条件独立结构。该算法在合成实验和真实数据应用中均表现出有效性。
原文摘要 · Abstract (English)
For general non-Gaussian distributions, the covariance and precision matrices do not encode the independence structure of the variables, as they do for the multivariate Gaussian. This paper builds on previous work to show that for a class of non-Gaussian distributions -- those derived from diagonal transformations of a Gaussian -- information about the conditional independence structure can still be inferred from the precision matrix, provided the data meet certain criteria, analogous to the Gaussian case. We call such transformations of the Gaussian as the generalized nonparanormal. The functions that define these transformations are, in a broad sense, arbitrary. We also provide a simple and computationally efficient algorithm that leverages this theory to recover conditional independence structure from the generalized nonparanormal data. The effectiveness of the proposed algorithm is demonstrated via synthetic experiments and applications to real-world data.
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