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Most of the existing methods for estimating the local intrinsic dimension ofa data distribution do not scale well to high-dimensional data. Many of themrely on a non-parametric nearest neighbors approach which suffers from thecurse of dimensionality. We attempt to address that challenge by proposing anovel approach to the problem: Local Intrinsic Dimension estimation usingapproximate Likelihood (LIDL). Our method relies on an arbitrary densityestimation method as its subroutine and hence tries to sidestep thedimensionality challenge by making use of the recent progress in parametricneural methods for likelihood estimation. We carefully investigate theempirical properties of the proposed method, compare them with our theoreticalpredictions, and show that LIDL yields competitive results on the standardbenchmarks for this problem and that it scales to thousands of dimensions. Whatis more, we anticipate this approach to improve further with the continuingadvances in the density estimation literature.

LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihood