On the Use of Bagging for Local Intrinsic Dimensionality Estimation

TL;DR

This paper introduces a bagging ensemble method for Local Intrinsic Dimensionality estimation that reduces variance and improves accuracy by carefully balancing sampling rate and neighborhood size, with theoretical and experimental validation.

Contribution

It proposes a novel ensemble approach using subbagging for LID estimation, analyzing its effects on bias and variance, and offers practical guidance for hyper-parameter selection.

Findings

Bagging significantly reduces variance and mean squared error in LID estimation.

The interplay between sampling rate and neighborhood size critically affects estimation performance.

Combining bagging with neighborhood smoothing yields further improvements.

Abstract

The theory of Local Intrinsic Dimensionality (LID) has become a valuable tool for characterizing local complexity within and across data manifolds, supporting a range of data mining and machine learning tasks. Accurate LID estimation requires samples drawn from small neighborhoods around each query to avoid biases from nonlocal effects and potential manifold mixing, yet limited data within such neighborhoods tends to cause high estimation variance. As a variance reduction strategy, we propose an ensemble approach that uses subbagging to preserve the local distribution of nearest neighbor (NN) distances. The main challenge is that the uniform reduction in total sample size within each subsample increases the proximity threshold for finding a fixed number k of NNs around the query. As a result, in the specific context of LID estimation, the sampling rate has an additional, complex interplay with the neighborhood size, where both combined determine the sample size as well as the locality and resolution considered for estimation. We analyze both theoretically and experimentally how the choice of the sampling rate and the k-NN size used for LID estimation, alongside the ensemble size, affects performance, enabling informed prior selection of these hyper-parameters depending on application-based preferences. Our results indicate that within broad and well-characterized regions of the hyper-parameters space, using a bagged estimator will most often significantly reduce variance as well as the mean squared error when compared to the corresponding non-bagged baseline, with controllable impact on bias. We additionally propose and evaluate different ways of combining bagging with neighborhood smoothing for substantial further improvements on LID estimation performance.