Intrinsic Dimension Estimation Using Wasserstein Distance
Abstract
It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension of a given population distribution from a finite sample. We introduce a new estimator of the intrinsic dimension and provide finite sample, non-asymptotic guarantees. We then apply our techniques to get new sample complexity bounds for Generative Adversarial Networks (GANs) depending only on the intrinsic dimension of the data.
Cite
Text
Block et al. "Intrinsic Dimension Estimation Using Wasserstein Distance." Journal of Machine Learning Research, 2022.Markdown
[Block et al. "Intrinsic Dimension Estimation Using Wasserstein Distance." Journal of Machine Learning Research, 2022.](https://mlanthology.org/jmlr/2022/block2022jmlr-intrinsic/)BibTeX
@article{block2022jmlr-intrinsic,
title = {{Intrinsic Dimension Estimation Using Wasserstein Distance}},
author = {Block, Adam and Jia, Zeyu and Polyanskiy, Yury and Rakhlin, Alexander},
journal = {Journal of Machine Learning Research},
year = {2022},
pages = {1-37},
volume = {23},
url = {https://mlanthology.org/jmlr/2022/block2022jmlr-intrinsic/}
}