A Wiener Process Perspective on Local Intrinsic Dimension Estimation Methods
This work addresses the reliability of LID estimation methods for researchers in machine learning, particularly in high-dimensional data analysis, but it appears incremental as it focuses on theoretical analysis without introducing new methods.
The paper investigates state-of-the-art parametric local intrinsic dimension estimation methods from a Wiener process perspective, analyzing their behavior when assumptions are violated and providing a mathematical description of their errors based on data probability density.
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 to scale the methods to high-dimensional datasets (e.g. 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.