Estimating a density near an unknown manifold: A Bayesian nonparametric approach
研究数据位于欧氏空间未知子流形偏移区域时的贝叶斯密度估计，提出新的各向异性Hölder条件，获得适应密度正则性、流形内在维度和偏移大小的最优后验速率，方法基于高斯位置尺度混合，易于实现且对奇异数据有效。
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.