论文标题
降级和室内检测问题
Denoising and Interior Detection Problems
论文作者
论文摘要
令$ \ mathcal {m} $为$ \ mathbb {r}^d $的紧凑型歧管。本文的目的是根据点样本来决定$ \ Mathcal {M} $的内部是否为空。我们将这项工作分为两个主要部分。首先，在可能包含或可能不包含某些噪声的因样本下，我们根据对依赖性的适当控制来表征内部检测试验的渐近性特性。之后，我们删除依赖性，并考虑一个模型，其中将从歧管采样的点与从不同度量采样的某些点混合（嘈杂的观察值）。我们研究了有关嘈杂观测的数量的行为，引入了一种方法来识别真正的多种歧视点，表征收敛性能。
Let $\mathcal{M}$ be a compact manifold of $\mathbb{R}^d$. The goal of this paper is to decide, based on a sample of points, whether the interior of $\mathcal{M}$ is empty or not. We divide this work in two main parts. Firstly, under a dependent sample which may or may not contain some noise within, we characterize asymptotic properties of an interior detection test based on a suitable control of the dependence. Afterwards, we drop the dependence and consider a model where the points sampled from the manifold are mixed with some points sampled from a different measure (noisy observations). We study the behaviour with respect to the amount of noisy observations, introducing a methodology to identify true manifold points, characterizing convergence properties.
