English
Related papers

Related papers: Estimation from Pairwise Comparisons: Sharp Minima…

200 papers

Multi-label ranking, which returns multiple top-ranked labels for each instance, has a wide range of applications for visual tasks. Due to its complicated setting, prior arts have proposed various measures to evaluate model performances.…

Machine Learning · Computer Science 2024-07-10 Zitai Wang , Qianqian Xu , Zhiyong Yang , Peisong Wen , Yuan He , Xiaochun Cao , Qingming Huang

Ranking items based on pairwise comparisons is common, from using match outcomes to rank sports teams to using purchase or survey data to rank consumer products. Statistical inference-based methods such as the Bradley-Terry model, which…

Physics and Society · Physics 2026-01-09 Sebastian Morel-Balbi , Alec Kirkley

In this work we study the metric distortion problem in voting theory under a limited amount of ordinal information. Our primary contribution is threefold. First, we consider mechanisms which perform a sequence of pairwise comparisons…

Computer Science and Game Theory · Computer Science 2021-07-07 Ioannis Anagnostides , Dimitris Fotakis , Panagiotis Patsilinakos

A number of applications require two-sample testing on ranked preference data. For instance, in crowdsourcing, there is a long-standing question of whether pairwise comparison data provided by people is distributed similar to…

Machine Learning · Statistics 2020-11-20 Charvi Rastogi , Sivaraman Balakrishnan , Nihar B. Shah , Aarti Singh

We consider the problem of estimating latent positions in a one-dimensional torus from pairwise affinities. The observed affinity between a pair of items is modeled as a noisy observation of a function $f(x^*_{i},x^*_{j})$ of the latent…

Statistics Theory · Mathematics 2023-08-15 Christophe Giraud , Yann Issartel , Nicolas Verzelen

Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…

Methodology · Statistics 2017-04-28 Valeria Vitelli , Øystein Sørensen , Marta Crispino , Arnoldo Frigessi , Elja Arjas

We study methods for aggregating pairwise comparison data in order to estimate outcome probabilities for future comparisons among a collection of n items. Working within a flexible framework that imposes only a form of strong stochastic…

Machine Learning · Computer Science 2016-03-23 Nihar B. Shah , Sivaraman Balakrishnan , Martin J. Wainwright

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…

Machine Learning · Computer Science 2016-09-26 Reinhard Heckel , Nihar B. Shah , Kannan Ramchandran , Martin J. Wainwright

Given a set of pairwise comparisons, the classical ranking problem computes a single ranking that best represents the preferences of all users. In this paper, we study the problem of inferring individual preferences, arising in the context…

Machine Learning · Statistics 2015-12-18 Rui Wu , Jiaming Xu , R. Srikant , Laurent Massoulié , Marc Lelarge , Bruce Hajek

We consider a simple model of imprecise comparisons: there exists some $\delta>0$ such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least $\delta$, then the…

Data Structures and Algorithms · Computer Science 2015-01-14 Miklos Ajtai , Vitaly Feldman , Avinatan Hassidim , Jelani Nelson

In this paper, we study a popular method for inference of the Bradley-Terry model parameters, namely the MM algorithm, for maximum likelihood estimation and maximum a posteriori probability estimation. This class of models includes the…

Machine Learning · Statistics 2020-12-29 Milan Vojnovic , Seyoung Yun , Kaifang Zhou

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…

Statistics Theory · Mathematics 2021-03-29 Michael Bell , Yuval Kochman

We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to…

Optimization and Control · Mathematics 2016-01-18 Nikolai Krivulin

We consider the problem of evaluating designs for a two-arm randomized experiment with an incidence (binary) outcome under a nonparametric general response model. Our two main results are that the priori pair matching design of Greevy et…

Methodology · Statistics 2022-09-02 Adam Kapelner , Abba M. Krieger , David Azriel

We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…

Statistics Theory · Mathematics 2008-12-02 Michel Broniatowski , Amor Keziou

Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate…

Econometrics · Economics 2024-06-19 Matthew D. Cocci , Mikkel Plagborg-Møller

Incomplete pairwise comparison matrices contain some missing judgements. A natural approach to estimate these values is provided by minimising a reasonable measure of inconsistency after unknown entries are replaced by variables. Two widely…

Optimization and Control · Mathematics 2024-02-07 László Csató , Kolos Csaba Ágoston , Sándor Bozóki

In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided.…

Logic · Mathematics 2018-07-12 Waldemar W. Koczkodaj , Jean-Pierre Magnot

Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\epsilon$-stationary point with…

Optimization and Control · Mathematics 2025-12-01 Lesi Chen , Jingzhao Zhang

We consider the fundamental problem of matching a template to a signal. We do so by M-estimation, which encompasses procedures that are robust to gross errors (i.e., outliers). Using standard results from empirical process theory, we derive…

Statistics Theory · Mathematics 2020-09-10 Ery Arias-Castro , Lin Zheng