LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihood

TL;DR

LIDL introduces a scalable method for estimating local intrinsic dimension in high-dimensional data by leveraging approximate likelihood estimation with neural density models, outperforming traditional approaches.

Contribution

The paper proposes a novel likelihood-based approach for local intrinsic dimension estimation that scales to high dimensions, addressing limitations of non-parametric methods.

Findings

LIDL achieves competitive results on standard benchmarks.

The method scales to thousands of dimensions.

It benefits from advances in neural density estimation.

Abstract

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of dimensionality. We attempt to address that challenge by proposing a novel approach to the problem: Local Intrinsic Dimension estimation using approximate Likelihood (LIDL). Our method relies on an arbitrary density estimation method as its subroutine and hence tries to sidestep the dimensionality challenge by making use of the recent progress in parametric neural methods for likelihood estimation. We carefully investigate the empirical properties of the proposed method, compare them with our theoretical predictions, and show that LIDL yields competitive results on the standard benchmarks for this problem and that it scales to thousands of dimensions. What is more, we anticipate this approach to improve further with the continuing advances in the density estimation literature.