边际化破坏分布的核均值估计
Kernel Mean Estimation by Marginalized Corrupted Distributions
摘要：
在再生核希尔伯特空间中估计核均值是许多核学习算法中的关键组成部分。给定有限样本，目标核均值的标准估计值是经验平均值。以前的工作表明，更好的估计，可以构建收缩方法。在这项工作中，我们提出了腐败的数据的例子与噪声从已知的分布，并提出了一个新的核均值估计，称为边缘化核均值估计，估计核均值下损坏的分布。理论上，我们证明了边缘化核均值估计在核均值估计中引入了隐正则化。经验上，我们在各种数据集上证明了边缘化核均值估计比现有的估计获得了更低的估计误差。
英文摘要：
Estimating the kernel mean in a reproducing kernel Hilbert space is a critical component in many kernel learning algorithms. Given a finite sample, the standard estimate of the target kernel mean is the empirical average. Previous works have shown that better estimators can be constructed by shrinkage methods. In this work, we propose to corrupt data examples with noise from known distributions and present a new kernel mean estimator, called the marginalized kernel mean estimator, which estimates kernel mean under the corrupted distribution. Theoretically, we show that the marginalized kernel mean estimator introduces implicit regularization in kernel mean estimation. Empirically, we show on a variety of datasets that the marginalized kernel mean estimator obtains much lower estimation error than the existing estimators.
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