A Wiener Process Perspective on Local Intrinsic Dimension Estimation Methods
Abstract
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.
Cite
Text
Tempczyk et al. "A Wiener Process Perspective on Local Intrinsic Dimension Estimation Methods." AAAI Conference on Artificial Intelligence, 2025. doi:10.1609/AAAI.V39I19.34299Markdown
[Tempczyk et al. "A Wiener Process Perspective on Local Intrinsic Dimension Estimation Methods." AAAI Conference on Artificial Intelligence, 2025.](https://mlanthology.org/aaai/2025/tempczyk2025aaai-wiener/) doi:10.1609/AAAI.V39I19.34299BibTeX
@inproceedings{tempczyk2025aaai-wiener,
title = {{A Wiener Process Perspective on Local Intrinsic Dimension Estimation Methods}},
author = {Tempczyk, Piotr and Garncarek, Lukasz and Filipiak, Dominik and Kurpisz, Adam},
booktitle = {AAAI Conference on Artificial Intelligence},
year = {2025},
pages = {20859-20866},
doi = {10.1609/AAAI.V39I19.34299},
url = {https://mlanthology.org/aaai/2025/tempczyk2025aaai-wiener/}
}