Intrinsic Dimension Estimation Using Wasserstein Distances
Machine Learning
2022-06-01 v2 Machine Learning
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
@article{arxiv.2106.04018,
title = {Intrinsic Dimension Estimation Using Wasserstein Distances},
author = {Adam Block and Zeyu Jia and Yury Polyanskiy and Alexander Rakhlin},
journal= {arXiv preprint arXiv:2106.04018},
year = {2022}
}