Intrinsic Dimension Estimation with Optimal Transport

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. In this talk, I will introduce a new estimator of the intrinsic dimension and provide finite sample, non-asymptotic guarantees under weak assumptions on the geometry of the support. If time permits, I will then describe how to apply the techniques to get new sample complexity bounds for Generative Adversarial Networks (GANs) depending only on the intrinsic dimension of the data.