DeepAI

# Intrinsic Dimension Estimation

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.

• 10 publications
• 6 publications
• 42 publications
• 58 publications
01/11/2019

### Non-Parametric Inference Adaptive to Intrinsic Dimension

We consider non-parametric estimation and inference of conditional momen...
07/06/2022

### The Union of Manifolds Hypothesis and its Implications for Deep Generative Modelling

Deep learning has had tremendous success at learning low-dimensional rep...
03/15/2020

### Hierarchical Models: Intrinsic Separability in High Dimensions

It has long been noticed that high dimension data exhibits strange patte...
04/18/2021

### The Intrinsic Dimension of Images and Its Impact on Learning

It is widely believed that natural image data exhibits low-dimensional s...
06/01/2019

### Graph-based Discriminators: Sample Complexity and Expressiveness

A basic question in learning theory is to identify if two distributions ...
10/30/2020

### Empirical or Invariant Risk Minimization? A Sample Complexity Perspective

Recently, invariant risk minimization (IRM) was proposed as a promising ...
05/04/2022

### A Manifold Two-Sample Test Study: Integral Probability Metric with Neural Networks

Two-sample tests are important areas aiming to determine whether two col...