相关论文: The many routes to the ubiquitous Bradley-Terry mo…
Most statistical models for pairwise comparisons, including the Bradley-Terry (BT) and Thurstone models and many extensions, make a relatively strong assumption of stochastic transitivity. This assumption imposes the existence of an…
In this paper paired comparison models with stochastic background are investigated. We focus on the models which allow three options for choice and the parameters are estimated by maximum likelihood method. The existence and uniqueness of…
This article introduces the bpcs R package (Bayesian Paired Comparison in Stan) and the statistical models implemented in the package. This package aims to facilitate the use of Bayesian models for paired comparison data in behavioral…
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…
We propose a novel extension of the Bradley-Terry model to multiplayer games and adapt a recent algorithm by Newman [1] to our model. We demonstrate the use of our proposed method on synthetic datasets and on a real dataset of games of…
This paper considers the problem of ranking objects based on their latent merits using data from pairwise interactions. We allow for incomplete observation of these interactions and study what can be inferred about rankings in such…
Over the last few years, there has been a growing interest in the prediction and modelling of competitive sports outcomes, with particular emphasis placed on this area by the Bayesian statistics and machine learning communities. In this…
We propose a novel combinatorial inference framework to conduct general uncertainty quantification in ranking problems. We consider the widely adopted Bradley-Terry-Luce (BTL) model, where each item is assigned a positive preference score…
We provide an algorithm with constant running time that given a weighted tournament $T$, distinguishes with high probability of success between the cases that $T$ can be represented by a Bradley--Terry model, or cannot even be approximated…
A principled approach to cyclicality and intransitivity in paired comparison data is developed. The proposed methodology enables more precise estimation of the underlying preference profile and facilitates the identification of all cyclic…
We study the Stigler model of citation flows among journals adapting the pairwise comparison model of Bradley and Terry to do ranking and selection of journal influence based on nonparametric empirical Bayes procedures. Comparisons with…
Paired comparison models, such as Bradley-Terry and Thurstone-Mosteller, are commonly used to estimate relative strengths of pairwise compared items in tournament-style data. We discuss estimation of paired comparison models with a ridge…
Many applications such as recommendation systems or sports tournaments involve pairwise comparisons within a collection of $n$ items, the goal being to aggregate the binary outcomes of the comparisons in order to recover the latent strength…
We revisit the problem of inferring the overall ranking among entities in the framework of Bradley-Terry-Luce (BTL) model, based on available empirical data on pairwise preferences. By a simple transformation, we can cast the problem as…
Frequently in sporting competitions it is desirable to compare teams based on records of varying schedule strength. Methods have been developed for sports where the result outcomes are win, draw, or loss. In this paper those ideas are…
Pairwise preference learning is central to machine learning, with recent applications in aligning language models with human preferences. A typical dataset consists of triplets $(x, y^+, y^-)$, where response $y^+$ is preferred over…
The standard way to evaluate language models on subjective tasks is through pairwise comparisons: an annotator chooses the "better" of two responses to a prompt. Leaderboards aggregate these comparisons into a single Bradley-Terry (BT)…
The dynamic ranking, due to its increasing importance in many applications, is becoming crucial, especially with the collection of voluminous time-dependent data. One such application is sports statistics, where dynamic ranking aids in…
We address the problem of learning a ranking by using adaptively chosen pairwise comparisons. Our goal is to recover the ranking accurately but to sample the comparisons sparingly. If all comparison outcomes are consistent with the ranking,…
We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates…