Which Spatial Partition Trees are Adaptive to Intrinsic Dimension?
Abstract
Recent theory work has found that a special type of spatial partition tree - called a random projection tree - is adaptive to the intrinsic dimension of the data from which it is built. Here we examine this same question, with a combination of theory and experiments, for a broader class of trees that includes k-d trees, dyadic trees, and PCA trees. Our motivation is to get a feel for (i) the kind of intrinsic low dimensional structure that can be empirically verified, (ii) the extent to which a spatial partition can exploit such structure, and (iii) the implications for standard statistical tasks such as regression, vector quantization, and nearest neighbor search.
Keywords
Cite
@article{arxiv.1205.2609,
title = {Which Spatial Partition Trees are Adaptive to Intrinsic Dimension?},
author = {Nakul Verma and Samory Kpotufe and Sanjoy Dasgupta},
journal= {arXiv preprint arXiv:1205.2609},
year = {2025}
}
Comments
Appears in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI2009)