Year: 2021
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W3169905676