论文标题
对数Voronoi细胞
Logarithmic Voronoi cells
论文作者
论文摘要
我们通过考虑将开放概率单纯性的最大似然估计量的预先映射来研究统计环境中的Voronoi细胞。通常，对数Voronoi细胞是凸组。但是，对于某些代数模型，即有限的模型，具有ML度1的模型，线性模型和对数线性（或曲折）模型，我们表明对数Voronoi细胞是多面体。作为推论，代数矩图在仅限于单纯形的时具有用于其纤维和图像的多面体。我们还使用数值代数几何形状来计算非聚POPAL对数伏罗尼亚细胞。最后，我们确定有限模型的对数Voronoi多面体，该模型由固定样本量的所有经验分布组成。这些多面体对A型A型的对数根系是双重的，我们表征了它们的脸。
We study Voronoi cells in the statistical setting by considering preimages of the maximum likelihood estimator that tessellate an open probability simplex. In general, logarithmic Voronoi cells are convex sets. However, for certain algebraic models, namely finite models, models with ML degree 1, linear models, and log-linear (or toric) models, we show that logarithmic Voronoi cells are polytopes. As a corollary, the algebraic moment map has polytopes for both its fibres and its image, when restricted to the simplex. We also compute non-polytopal logarithmic Voronoi cells using numerical algebraic geometry. Finally, we determine logarithmic Voronoi polytopes for the finite model consisting of all empirical distributions of a fixed sample size. These polytopes are dual to the logarithmic root polytopes of Lie type A, and we characterize their faces.
