论文标题
ISDE的多元密度的非参数估计
Nonparametric estimation of a multivariate density under Kullback-Leibler loss with ISDE
论文作者
论文摘要
在本文中，我们提出了对先前工作中介绍的算法ISDE的理论分析。从数据集中，ISDE将其写入一个密度作为边缘密度估计器的产物，而不是特征的分区。我们表明，在某些假设下，适当的密度和ISDE输出之间的kullback-leibler损失是一个偏差项，加上两个项的总和为零，因为样本数量为无穷大。收敛速度表明，ISD通过将维度从环境空间之一降低到分区中最大的块之一来解决维数的诅咒。常数反映了与ISDE设计相关的组合复杂性降低。
In this paper, we propose a theoretical analysis of the algorithm ISDE, introduced in previous work. From a dataset, ISDE learns a density written as a product of marginal density estimators over a partition of the features. We show that under some hypotheses, the Kullback-Leibler loss between the proper density and the output of ISDE is a bias term plus the sum of two terms which goes to zero as the number of samples goes to infinity. The rate of convergence indicates that ISDE tackles the curse of dimensionality by reducing the dimension from the one of the ambient space to the one of the biggest blocks in the partition. The constants reflect a combinatorial complexity reduction linked to the design of ISDE.
