Intrinsic Dimension Estimation Using Wasserstein Distance

Adam Block, Zeyu Jia, Yury Polyanskiy, Alexander Rakhlin.

Year: 2022, Volume: 23, Issue: 313, Pages: 1−37


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.