随机Tverberg定理及其在多类逻辑斯谛回归、数据可分性和数据中心点中的应用
Stochastic Tverberg theorems and their applications in multi-class logistic regression, data separability, and centerpoints of data
摘要：
我们提出了新的随机几何定理，给界的概率，$m$随机数据类都包含一个点，在其凸包。我们应用这些随机分离定理得到了多项式逻辑斯谛回归中极大似然估计存在概率的界。我们还讨论了连接到条件数的分析最速下降算法在逻辑斯谛回归和数据云的中心点的计算。
英文摘要：
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. We apply these stochastic separation theorems to obtain bounds on the probability of existence of maximum likelihood estimators in multinomial logistic regression. We also discuss connections to condition numbers for analysis of steepest descent algorithms in logistic regression and to the computation of centerpoints of data clouds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
