Title: Why We Need New Benchmarks for Local Intrinsic Dimension Estimation
Primary area: datasets and benchmarks
Keywords: Local intrinsic dimension estimation, LIDL, FLIPD, Diffusion Models, Benhamark, Normalizing Flows, ESS, Normal Bundle, NB, LID

Abstract: Recent advancements in algorithms for local intrinsic dimension (LID) estimation have been closely tied to progress in neural networks (NN). However, NN architectures are often tailored to specific domains, such as audio or image data, incorporating inductive biases that limit their transferability across domains. Moreover, existing LID estimation methods leveraging these architectures are typically evaluated on either overly simplistic benchmarks or domain datasets where the true LID is unknown, resulting in potentially erroneous evaluations. To close this research gap, we first isolate problematic aspects of LID estimation and leverage them to analyze the limitations of state-of-the-art methods. Our approach employs several techniques to create LID benchmarks for arbitrary domains, including the introduction of a method to transform any manifold into the domain while preserving the manifold structure, thereby addressing challenges posed by biases in neural network-based methods. Our comparative analysis reveals critical limitations and identifies new directions for future development in LID estimation methods. Code will be available on github when published.

TL;DR: We show that LID estimation community needs new benchmarks for intrinsic dimension estimation and come to interesting conclusions on the performance of existing algorithms.