Inapproximability of VC Dimension and Littlestone’s Dimension
Abstract
We study the complexity of computing the VC Dimension and Littlestone’s Dimension. Given an explicit description of a finite universe and a concept class (a binary matrix whose $(x,C)$-th entry is $1$ iff element $x$ belongs to concept $C$), both can be computed exactly in quasi-polynomial time ($n^O(\log n)$). Assuming the randomized Exponential Time Hypothesis (ETH), we prove nearly matching lower bounds on the running time, that hold even for \em approximation algorithms.
Cite
Text
Manurangsi and Rubinstein. "Inapproximability of VC Dimension and Littlestone’s Dimension." Proceedings of the 2017 Conference on Learning Theory, 2017.Markdown
[Manurangsi and Rubinstein. "Inapproximability of VC Dimension and Littlestone’s Dimension." Proceedings of the 2017 Conference on Learning Theory, 2017.](https://mlanthology.org/colt/2017/manurangsi2017colt-inapproximability/)BibTeX
@inproceedings{manurangsi2017colt-inapproximability,
title = {{Inapproximability of VC Dimension and Littlestone’s Dimension}},
author = {Manurangsi, Pasin and Rubinstein, Aviad},
booktitle = {Proceedings of the 2017 Conference on Learning Theory},
year = {2017},
pages = {1432-1460},
volume = {65},
url = {https://mlanthology.org/colt/2017/manurangsi2017colt-inapproximability/}
}