We study the estimation and concentration on its expectation of the probability to observe data further than a specified distance from a given iid sample in a metric space. The problem extends the classical problem of estimation of the missing mass in discrete spaces. We give some estimators for the conditional missing mass and show that estimation of the expected missing mass is difficult in general. Conditions on the distribution, under which the Good-Turing estimator and the conditional missing mass concentrate on their expectations are identified. Applications to anomaly detection, coding, the Wasserstein distance between true and empirical measure and simple learning bounds are sketched.
翻译:我们研究对数据观察概率的估计和集中,其估计和集中的预期值大于在计量空间中某一特定基点样本的一定距离。问题扩大了在离散空间估计缺失质量的典型问题。我们给有条件缺失质量的一些估计者以有条件缺失质量的某种估计,并表明对预期缺失质量的估算总体上是困难的。分布条件,根据这种条件,确定良好试验测算员和有条件缺失质量的集中度以其预期值为主。应用异常探测、编码、瓦瑟斯坦在真实和实证测量与简单学习界限之间的距离。