关于图形模型与凸几何
On Graphical Models and Convex Geometry.
作者信息
Bar Haim, Wells Martin T
机构信息
Department of Statistics, University of Connecticut, Room 315, Philip E. Austin Building, Storrs, 06269-4120, CT, USA.
Department of Statistics and Data Science, Cornell University, 1190 Comstock Hall, Ithaca, 14853, NY, USA.
出版信息
Comput Stat Data Anal. 2023 Nov;187. doi: 10.1016/j.csda.2023.107800. Epub 2023 Jun 14.
A mixture-model of beta distributions framework is introduced to identify significant correlations among features when is large. The method relies on theorems in convex geometry, which are used to show how to control the error rate of edge detection in graphical models. The proposed 'betaMix' method does not require any assumptions about the network structure, nor does it assume that the network is sparse. The results hold for a wide class of data-generating distributions that include light-tailed and heavy-tailed spherically symmetric distributions. The results are robust for sufficiently large sample sizes and hold for non-elliptically-symmetric distributions.
引入了一个贝塔分布框架的混合模型，以在(n)较大时识别特征之间的显著相关性。该方法依赖于凸几何中的定理，这些定理用于展示如何控制图形模型中边缘检测的错误率。所提出的“betaMix”方法不需要对网络结构做任何假设，也不假设网络是稀疏的。对于包括轻尾和重尾球对称分布在内的一大类数据生成分布，结果都成立。对于足够大的样本量，结果是稳健的，并且对于非椭圆对称分布也成立。
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