New Lower Bounds for Testing Monotonicity and Log Concavity of Distributions
Machine Learning
2023-08-02 v1 Statistics Theory
Statistics Theory
Abstract
We develop a new technique for proving distribution testing lower bounds for properties defined by inequalities involving the bin probabilities of the distribution in question. Using this technique we obtain new lower bounds for monotonicity testing over discrete cubes and tight lower bounds for log-concavity testing. Our basic technique involves constructing a pair of moment-matching families of distributions by tweaking the probabilities of pairs of bins so that one family maintains the defining inequalities while the other violates them.
Keywords
Cite
@article{arxiv.2308.00089,
title = {New Lower Bounds for Testing Monotonicity and Log Concavity of Distributions},
author = {Yuqian Cheng and Daniel M. Kane and Zhicheng Zheng},
journal= {arXiv preprint arXiv:2308.00089},
year = {2023}
}