LIDL: Local Intrinsic Dimension estimation using approximate Likelihood

Understanding how neural networks work is one of the most important questions in machine learning research. Their performance is connected with the shape of the data manifold. The structure of this manifold can be explored with local intrinsic dimension (LID) estimation methods. Unfortunately, they do not scale well to high-dimensional datasets and give inaccurate estimates for complex manifolds. We address those challenges by proposing a new method -- LIDL -- that uses novel normalizing flow models. Our method yields accurate estimates on complex manifolds and scales well to problems with thousands of dimensions. We use our algorithm to show that LID is connected with neural networks performance in supervised and unsupervised settings.