论文标题
BESOV IPM损失下的强大密度估计
Robust Density Estimation under Besov IPM Losses
论文作者
论文摘要
我们研究了Huber污染模型中非参数密度估计的最小值收敛速率，其中一部分数据来自未知的异常分布。我们在大量损失家族中为此问题提供了第一个结果，称为BESOV一体概率指标（IPMS），其中包括$ \ Mathcal {l}^p $，Wasserstein，Kolmogorov-Smirnov以及概率分布之间的其他常见距离。具体而言，在对种群和异常分布的一系列平稳性假设下，我们表明，重新标准的阈值小波序列估计器在多种损失下达到了最小的最佳收敛速率。最后，基于最近在IPM损失下的非参数密度估计与生成对抗网络（GAN）之间显示的连接，我们表明某些GAN体系结构也达到了这些最小值。
We study minimax convergence rates of nonparametric density estimation in the Huber contamination model, in which a proportion of the data comes from an unknown outlier distribution. We provide the first results for this problem under a large family of losses, called Besov integral probability metrics (IPMs), that includes $\mathcal{L}^p$, Wasserstein, Kolmogorov-Smirnov, and other common distances between probability distributions. Specifically, under a range of smoothness assumptions on the population and outlier distributions, we show that a re-scaled thresholding wavelet series estimator achieves minimax optimal convergence rates under a wide variety of losses. Finally, based on connections that have recently been shown between nonparametric density estimation under IPM losses and generative adversarial networks (GANs), we show that certain GAN architectures also achieve these minimax rates.
