Stochastic Tverberg Theorems With Applications in Multiclass Logistic Regression, Separability, and Centerpoints of Data

被引：3
作者：
De Loera, Jesus A. [1 ]
Hogan, Thomas [1 ]
机构：
[1] Univ Calif Davis, Dept Math, Davis, CA 95616 USA
来源：
SIAM JOURNAL ON MATHEMATICS OF DATA SCIENCE | 2020年 / 2卷 / 04期
关键词：
logistic regression; generalized linear models; maximum likelihood estimation; high-dimensional logistic regression; Tverberg's theorem; separability of data; geometric probability; combinatorial convexity; computational geometry in statistics; depth of data point; centerpoints; Tukey median; EXISTENCE; CARATHEODORY; POINTS; DEPTH; TIME;
D O I：
10.1137/19M1277102
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present new stochastic geometry theorems that give bounds on the probability that m random data classes all contain a point in common in their convex hulls. These theorems relate to the existence of maximum likelihood estimators in multinomial logistic regression, to the separability of data, and to the computation of centerpoints of data clouds.
引用
收藏
页码：1151 / 1166
页数：16
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