相关论文: Tractable Ridge Regression for Paired Comparisons

Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments have been proposed in different areas. This paper provides an updated…

We propose a penalized likelihood method to jointly estimate multiple precision matrices for use in quadratic discriminant analysis and model based clustering. A ridge penalty and a ridge fusion penalty are used to introduce shrinkage and…

Ranking a vector of alternatives on the basis of a series of paired comparisons is a relevant topic in many instances. A popular example is ranking contestants in sport tournaments. To this purpose, paired comparison models such as the…

Comparative Judgement is an assessment method where item ratings are estimated based on rankings of subsets of the items. These rankings are typically pairwise, with ratings taken to be the estimated parameters from fitting a Bradley-Terry…

There are various parametric models for analyzing pairwise comparison data, including the Bradley-Terry-Luce (BTL) and Thurstone models, but their reliance on strong parametric assumptions is limiting. In this work, we study a flexible…

Many applications, e.g. in content recommendation, sports, or recruitment, leverage the comparisons of alternatives to score those alternatives. The classical Bradley-Terry model and its variants have been widely used to do so. The…

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…

Several methods of preference modeling, ranking, voting and multi-criteria decision making include pairwise comparisons. It is usually simpler to compare two objects at a time, furthermore, some relations (e.g., the outcome of sports…

Paired comparison models, such as the Bradley-Terry (1952) model and its variants, are commonly used to measure competitor strength in games and sports. Extensions have been proposed to account for order effects (e.g., home-field advantage)…

The linear regression model cannot be fitted to high-dimensional data, as the high-dimensionality brings about empirical non-identifiability. Penalized regression overcomes this non-identifiability by augmentation of the loss function by a…

PageRank and the Bradley-Terry model are competing approaches to ranking entities such as teams in sports tournaments or journals in citation networks. The Bradley-Terry model is a classical statistical method for ranking based on paired…

We present ten different strength-based statistical models that we use to model soccer match outcomes with the aim of producing a new ranking. The models are of four main types: Thurstone-Mosteller, Bradley-Terry, Independent Poisson and…

Separation in logistic regression is a common problem causing failure of the iterative estimation process when finding maximum likelihood estimates. Firth's correction (FC) was proposed as a solution, providing estimates also in presence of…

This paper introduces the Bradley-Terry Regression Trunk model, a novel probabilistic approach for the analysis of preference data expressed through paired comparison rankings. In some cases, it may be reasonable to assume that the…

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…

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced…

Pairwise comparison methods, such as Fuzzy Preference Relations and Saaty's Multiplicative Preference Relations, are widely used to model expert judgments in multi-criteria decision-making. However, their application is limited by the high…

Regularized regression has become very popular nowadays, particularly on high-dimensional problems where the addition of a penalty term to the log-likelihood allows inference where traditional methods fail. A number of penalties have been…

Prediction and modelling of competitive sports outcomes has received much recent attention, especially from the Bayesian statistics and machine learning communities. In the real world setting of outcome prediction, the seminal \'{E}l\H{o}…

We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry…