Stochastic Tverberg Theorems With Applications In Multiclass Logistic Regression, Separability, And Centerpoints Of Data

arxiv（2020）

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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.

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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

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