论文标题
估计未知歧管附近的密度：贝叶斯非参数方法
Estimating a density near an unknown manifold: a Bayesian nonparametric approach
论文作者
论文摘要
我们研究了生活在欧几里得空间未知亚货中的数据的贝叶斯密度估计。从这个角度来看，我们引入了一种针对潜在密度的各向异性Hölder的新概念，并获得最小值的后率，这些率是最佳的，并且适应了密度的规律性，以偏移的内在维度，以及偏移的大小，前提是后者不太小的偏移量。我们的贝叶斯程序基于高斯的位置尺度混合物，似乎方便实施并产生良好的实际结果，即使对于相当奇异的数据也是如此。
We study the Bayesian density estimation of data living in the offset of an unknown submanifold of the Euclidean space. In this perspective, we introduce a new notion of anisotropic Hölder for the underlying density and obtain posterior rates that are minimax optimal and adaptive to the regularity of the density, to the intrinsic dimension of the manifold, and to the size of the offset, provided that the latter is not too small -- while still allowed to go to zero. Our Bayesian procedure, based on location-scale mixtures of Gaussians, appears to be convenient to implement and yields good practical results, even for quite singular data.
