Achievability and Impossibility of Exact Pairwise Ranking

TL;DR

This paper investigates the fundamental limits of exactly recovering item rankings from noisy pairwise comparisons within the SST model, providing sharp bounds and improved algorithms.

Contribution

It offers the first sharp information-theoretic bounds for exact ranking and improves the minimax rate constants using a moment method-based algorithm.

Findings

Sharp bounds for exact ranking under SST model

Improved constants in minimax optimal rate

Algorithmic contribution with better performance

Abstract

We consider the problem of recovering the rank of a set of $n$ items based on noisy pairwise comparisons. We assume the SST class as the family of generative models. Our analysis gave sharp information theoretic upper and lower bound for the exact requirement, which matches exactly in the parametric limit. Our tight analysis on the algorithm induced by the moment method gave better constant in Minimax optimal rate than ~\citet{shah2017simple} and contribute to their open problem. The strategy we used in this work to obtain information theoretic bounds is based on combinatorial arguments and is of independent interest.