论文标题
平面Mondrian Tessellations的二阶特性
Second-order properties for planar Mondrian tessellations
论文作者
论文摘要
在本文中，考虑了带有加权轴平行切割方向的平面stit缝线。它们在机器学习文献中也被称为加权平面蒙德里亚镶嵌，它们在随机的森林学习和内核方法中使用。得出了此类随机镶嵌的各种二阶特性，特别是，对于适当适当的版本，在边缘骨架和顶点点过程中获得了长度测量的合适版本的显式公式。同样，详细讨论了方差的显式公式和方差的渐近行为。
In this paper planar STIT tesselations with weighted axis-parallel cutting directions are considered. They are known also as weighted planar Mondrian tesselations in the machine learning literature, where they are used in random forest learning and kernel methods. Various second-order properties of such random tessellations are derived, in particular, explicit formulas are obtained for suitably adapted versions of the pair- and cross-correlation functions of the length measure on the edge skeleton and the vertex point process. Also, explicit formulas and the asymptotic behaviour of variances are discussed in detail.
