Local intrinsic dimension (LID) estimation methods have received a lot of attention in recent years thanks to the progress in deep neural networks and generative modeling. In opposition to old non-parametric methods, new methods use generative models to approximate diffused dataset density and scale the methods to high-dimensional datasets like images. In this paper, we investigate the recent state-of-the-art parametric LID estimation methods from the perspective of the Wiener process. We explore how these methods behave when their assumptions are not met. We give an extended mathematical description of those methods and their error as a function of the probability density of the data.

翻译：近年来，随着深度神经网络与生成建模技术的进步，局部本征维数估计方法受到广泛关注。相较于传统的非参数方法，新方法利用生成模型来近似扩散后的数据集密度，并将其扩展至图像等高维数据集。本文从维纳过程的视角，对当前最先进的参数化局部本征维数估计方法进行研究。我们探讨了当这些方法的假设条件不满足时其性能表现。文中对这些方法及其误差随数据概率密度变化的规律给出了扩展的数学描述。