Convergence rates for ordinal embedding
Statistics Theory
2019-05-01 v1 Machine Learning
Statistics Theory
Abstract
We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number theory on sets of integers with no three-term arithmetic progressions. We also carry out some computational experiments aimed at developing a sense of what the convergence rate for ordinal embedding might look like in higher dimensions.
Cite
@article{arxiv.1904.12994,
title = {Convergence rates for ordinal embedding},
author = {Jordan S. Ellenberg and Lalit Jain},
journal= {arXiv preprint arXiv:1904.12994},
year = {2019}
}