Density-Difference Estimation
Density-Difference Estimation
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DOI：
10.1162/neco_a_00492
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发表时间：
2012-06
影响因子：
2.9
通讯作者：
Masashi Sugiyama;T. Kanamori;Taiji Suzuki;M. C. D. Plessis;Song Liu;I. Takeuchi
中科院分区：
文献类型：
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作者：
Masashi Sugiyama;T. Kanamori;Taiji Suzuki;M. C. D. Plessis;Song Liu;I. Takeuchi
我们解决的问题，估计两个概率密度之间的差异。一个简单的方法是一个两步的过程，首先分别估计两个密度，然后计算它们的差异。然而，该过程不一定工作良好，因为执行第一步骤而不考虑第二步骤，并且因此在第一阶段中引起的小估计误差可以在第二阶段中引起大误差。在这封信中，我们提出了一个单一的拍摄过程中直接估计的密度差，而无需单独估计两个密度。我们推导出一个非参数有限样本误差界的建议单次密度差估计，并表明它达到了最佳的收敛速度。然后，我们将展示如何建议的密度差估计可以用于L2距离近似。最后，我们实验证明了所提出的方法在鲁棒分布比较，如类先验估计和变点检测的有用性。
We address the problem of estimating the difference between two probability densities. A naive approach is a two-step procedure of first estimating two densities separately and then computing their difference. However, this procedure does not necessarily work well because the first step is performed without regard to the second step, and thus a small estimation error incurred in the first stage can cause a big error in the second stage. In this letter, we propose a single-shot procedure for directly estimating the density difference without separately estimating two densities. We derive a nonparametric finite-sample error bound for the proposed single-shot density-difference estimator and show that it achieves the optimal convergence rate. We then show how the proposed density-difference estimator can be used in L2-distance approximation. Finally, we experimentally demonstrate the usefulness of the proposed method in robust distribution comparison such as class-prior estimation and change-point detection.