论文标题
内核平均嵌入的方差估计
Variance-Aware Estimation of Kernel Mean Embedding
论文作者
论文摘要
内核平均嵌入（KME）的一个重要特征是，经验KME与真实分布KME的收敛速率可以独立于空间的尺寸，核的分布和平滑性特征的尺寸。我们通过利用繁殖内核希尔伯特空间中利用差异信息来展示如何加速融合。此外，我们表明，即使此类信息是先验未知的，我们也可以从数据中有效地估算出来，从而恢复在偶然的环境中享有加速的分布不可知论的持续性。我们将结果从独立数据扩展到固定混合序列，并在假设检验和鲁棒参数估计的背景下说明了我们的方法。
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness features of the kernel. We show how to speed-up convergence by leveraging variance information in the reproducing kernel Hilbert space. Furthermore, we show that even when such information is a priori unknown, we can efficiently estimate it from the data, recovering the desiderata of a distribution agnostic bound that enjoys acceleration in fortuitous settings. We further extend our results from independent data to stationary mixing sequences and illustrate our methods in the context of hypothesis testing and robust parametric estimation.
