论文标题
高斯模型的对数Voronoi细胞
Logarithmic Voronoi Cells for Gaussian Models
论文作者
论文摘要
我们将对数Voronoi细胞的理论扩展到高斯统计模型。通常，高斯模型上一个点上的对数伏罗尼元细胞是其对数正常谱中包含的凸集。我们表明，对于ML学位的模型，线性协方差模型两组一致。特别是，对于定向和无向图形模型，它们都是相等的。我们为后一个家族介绍了对数Voronoi细胞的分解理论。我们还研究了协方差模型，该模型通常严格包含在对数正态光谱中的对数Voronoi细胞。我们为双变量相关模型提供了对数Voronoi细胞的明确描述，并表明它们是半代数集。最后，我们指出一个猜想认为，用于无限制相关模型的对数伏罗尼元细胞不是半代数。
We extend the theory of logarithmic Voronoi cells to Gaussian statistical models. In general, a logarithmic Voronoi cell at a point on a Gaussian model is a convex set contained in its log-normal spectrahedron. We show that for models of ML degree one and linear covariance models the two sets coincide. In particular, they are equal for both directed and undirected graphical models. We introduce decomposition theory of logarithmic Voronoi cells for the latter family. We also study covariance models, for which logarithmic Voronoi cells are, in general, strictly contained in log-normal spectrahedra. We give an explicit description of logarithmic Voronoi cells for the bivariate correlation model and show that they are semi-algebraic sets. Finally, we state a conjecture that logarithmic Voronoi cells for unrestricted correlation models are not semi-algebraic.
