论文标题
度量空间中缺失质量的浓度
Concentration of the missing mass in metric spaces
论文作者
论文摘要
我们研究了其对观察数据的概率的预期和集中度的估计和集中度。该问题扩展了离散空间中缺失质量的经典问题。我们给出一些有条件缺失质量的估计量，并表明对预期缺失质量的估计通常很困难。确定了良好的估计量和条件缺失的质量集中在其期望下的分布条件。勾勒出对异常检测，编码，真实和经验度量与简单学习范围之间的沃斯坦的距离的应用。
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.
