Active Ranking from Pairwise Comparisons and when Parametric Assumptions Don't Help

06/28/2016
by   Reinhard Heckel, et al.
0

We consider sequential or active ranking of a set of n items based on noisy pairwise comparisons. Items are ranked according to the probability that a given item beats a randomly chosen item, and ranking refers to partitioning the items into sets of pre-specified sizes according to their scores. This notion of ranking includes as special cases the identification of the top-k items and the total ordering of the items. We first analyze a sequential ranking algorithm that counts the number of comparisons won, and uses these counts to decide whether to stop, or to compare another pair of items, chosen based on confidence intervals specified by the data collected up to that point. We prove that this algorithm succeeds in recovering the ranking using a number of comparisons that is optimal up to logarithmic factors. This guarantee does not require any structural properties of the underlying pairwise probability matrix, unlike a significant body of past work on pairwise ranking based on parametric models such as the Thurstone or Bradley-Terry-Luce models. It has been a long-standing open question as to whether or not imposing these parametric assumptions allows for improved ranking algorithms. For stochastic comparison models, in which the pairwise probabilities are bounded away from zero, our second contribution is to resolve this issue by proving a lower bound for parametric models. This shows, perhaps surprisingly, that these popular parametric modeling choices offer at most logarithmic gains for stochastic comparisons.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/04/2018

Approximate Ranking from Pairwise Comparisons

A common problem in machine learning is to rank a set of n items based o...
06/20/2014

Spectral Ranking using Seriation

We describe a seriation algorithm for ranking a set of items given pairw...
12/30/2015

Simple, Robust and Optimal Ranking from Pairwise Comparisons

We consider data in the form of pairwise comparisons of n items, with th...
02/01/2019

Graph Resistance and Learning from Pairwise Comparisons

We consider the problem of learning the qualities of a collection of ite...
10/19/2015

Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issues

There are various parametric models for analyzing pairwise comparison da...
04/11/2022

On Top-k Selection from m-wise Partial Rankings via Borda Counting

We analyze the performance of the Borda counting algorithm in a non-para...
06/14/2022

A Truthful Owner-Assisted Scoring Mechanism

Alice (owner) has knowledge of the underlying quality of her items measu...