Elo ratings learn model parameters quickly using Markov chains.
problem Ranking players in online settings.
method Bradley--Terry--Luce model and Markov chain theory.
result Elo learns model parameters at a competitive rate.
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44 results for “Bradley-Terry-Luce”
Paper quantifies uncertainty in pairwise comparison models.
problem Uncertainty quantification in sparse Bradley-Terry-Luce models.
method Unified proof strategy for MLE and spectral estimator.
result Sharp and uniform non-asymptotic expansions for estimators.
Researchers show mixtures of ranking models are generally identifiable.
problem Understanding when and how parameters of mixtures of ranking models can be uniquely determined.
method Algebraic geometry framework applied to verify the number of solutions in polynomial systems.
result Popular mixtures of ranking models with two components are generically identifiable.
The paper improves ranking by integrating covariates and sparse intrinsic scores.
problem Ranking items with incomplete preference scores explained by covariates.
method Extends BTL model with covariate information and sparse intrinsic scores, using penalized MLE.
result Developed debiased estimator for penalized MLE with distributional properties.
Spectral ranking methods are improved against semi-random graph sampling.
problem Improving spectral ranking methods in semi-random graph sampling.
method Investigating entry-wise error of spectral algorithms against a semi-random adversary.
result Asymptotic performance can be recovered by reweighting observed edges.
Proposes a method to infer ranking properties and top-K rankings with uncertainty quantification.
problem General uncertainty quantification in ranking problems.
method Combinatorial inference framework for the Bradley-Terry-Luce model, generalized to multiple testing.
result Minimax optimal method for inferring top-K rankings with FDR control.
A new framework evaluates LLMs by considering judge reliability.
problem Evaluating LLMs without ground truth labels can lead to biased results.
method Introduces judge-specific discrimination parameters and estimates model quality and judge reliability.
result Improves agreement with human preferences and produces calibrated uncertainty quantification.
Paper proposes a fair grading method for randomized exams.
problem Ensuring fairness in grading for randomized exams.
method Maximum-likelihood estimator for Bradley-Terry-Luce model on student-question graph.
result Maximum-likelihood estimator is consistent and outperforms simple averaging in fairness and accuracy.
The paper analyzes RLHF with human feedback and provides convergence results for MLE and pessimistic MLE.
problem Improving RLHF with human feedback from pairwise or -wise comparisons.
method Theoretical framework for RLHF with convergence analysis of MLE and pessimistic MLE.
result MLE fails but pessimistic MLE provides improved policies under certain coverage assumptions.
RLHF uses human feedback to train AI models, posing statistical challenges.
problem Aligning AI models with human preferences using noisy, subjective feedback.
method Supervised fine-tuning, reward modeling, policy optimization, statistical ideas.
result Statistical methods for reward function learning and policy optimization.
Optimizes ranking of top-k players from partial comparison data.
problem Identifying the top-k players from incomplete pairwise comparisons.
method Maximum Likelihood Estimator (MLE) and Spectral Method.
result MLE achieves optimal partial and exact recovery, while Spectral Method is sub-optimal.
The paper improves spectral ranking methods for diverse comparison graphs.
problem Estimating preference scores from multiway comparisons with heterogeneous sizes.
method Develops a two-step spectral method for estimating preference scores and their uncertainties.
result The two-step spectral method achieves the same asymptotic efficiency as the Maximum Likelihood Estimator (MLE).
New RLHF approach mitigates bias in aligning LLMs with human preferences.
problem Algorithmic bias in RLHF leading to preference collapse.
method Preference Matching (PM) RLHF, using PM regularizer and conditional variant.
result 29% to 41% improvement in alignment with human preferences.
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 that of solving a noisy linear system, for which a ready algorithm is available in …
The paper derives upper bounds on the MLE error for BTL model under general graphs.
problem Estimating the MLE of BTL model parameters with -loss under general graphs.
method Novel upper bounds on estimation error dependent on algebraic connectivity and graph topology.
result Upper bounds on error are sharp and match minimax lower bounds under certain graph topologies.
Paper proposes CARE model for ranking with covariates, improving MLE accuracy.
problem Statistical estimation and inference for ranking with covariate information.
method Covariate-Assisted Ranking Estimation (CARE) model, extending Bradley-Terry-Luce (BTL) model.
result Derives optimal rates and asymptotic distributions for MLE of latent scores and covariates.
This research tackles multiclass classification by introducing a method for label ranking.
problem The challenge is to predict a sorted list of labels based on input features.
method Inspired by ranking median regression, the One-Versus-One (OVO) approach is used to achieve optimal ranking.
result The OVO approach yields an optimal ranking of labels with overwhelming probability under noise conditions.
The paper uses belief propagation to analyze rankings and partial orders from partial information.
problem Analyzing rankings and partial orders from incomplete data.
method Continuous spin system and belief propagation algorithm.
result Computes marginal distribution and approximates number of linear extensions.
Paper learns skill distributions from game outcomes, proving minimax optimality.
problem Learning skill distributions from noisy pairwise game outcomes.
method Proposes a simple algorithm using kernel density estimation and minimax techniques.
result Near-optimal minimax mean squared error scaling for skill density estimation.
We propose the Heterogeneous Thurstone Model (HTM) for aggregating ranked data, which can take the accuracy levels of different users into account. By allowing different noise distributions, the proposed HTM model maintains the generality of Thurstone's original framework, and as such, also extends the Bradley-Terry-Lu…
We propose a novel ranking model that combines the Bradley-Terry-Luce probability model with a nonnegative matrix factorization framework to model and uncover the presence of latent variables that influence the performance of top tennis players. We derive an efficient, provably convergent, and numerically stable majori…
Study preference-based reinforcement learning in episodic kernel MDPs.
problem Learning from episodic human preferences in reinforcement learning.
method Developed preference-based value estimation and confidence sets for kernel-based MDPs.
result Proved high-probability regret bounds that converge to optimal policy value.
In this paper, we aim to learn a low-dimensional Euclidean representation from a set of constraints of the form "item j is closer to item i than item k". Existing approaches for this "ordinal embedding" problem require expensive optimization procedures, which cannot scale to handle increasingly larger datasets. To addr…
We consider the problem of learning the qualities of a collection of items by performing noisy comparisons among them. Following the standard paradigm, we assume there is a fixed "comparison graph" and every neighboring pair of items in this graph is compared times according to the Bradley-Terry-Luce model (where t…
We study the problem of ranking a set of items from nonactively chosen pairwise preferences where each item has feature information with it. We propose and characterize a very broad class of preference matrices giving rise to the Feature Low Rank (FLR) model, which subsumes several models ranging from the classic Bradl…
Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector that represents the "qualities" of the ite…
When eliciting judgements from humans for an unknown quantity, one often has the choice of making direct-scoring (cardinal) or comparative (ordinal) measurements. In this paper we study the relative merits of either choice, providing empirical and theoretical guidelines for the selection of a measurement scheme. We pro…
A number of applications (e.g., AI bot tournaments, sports, peer grading, crowdsourcing) use pairwise comparison data and the Bradley-Terry-Luce (BTL) model to evaluate a given collection of items (e.g., bots, teams, students, search results). Past work has shown that under the BTL model, the widely-used maximum-likeli…
New algorithm ranks players from partial comparisons with optimal rate.
problem Ranking players from partial pairwise comparisons.
method Divide-and-conquer approach, local MLE within groups.
result Optimal ranking algorithm with minimax rate.
We study the top- ranking problem where the goal is to recover the set of top- ranked items out of a large collection of items based on partially revealed preferences. We consider an adversarial crowdsourced setting where there are two population sets, and pairwise comparison samples drawn from one of the populat…
The paper explores game-theoretic alignment of LLMs with human preferences, finding limitations and conditions.
problem Aligning LLMs with human preferences using game theory.
method Systematic study of payoff choices in a two-player zero-sum game for desirable alignment properties.
result Impossibility of preference matching in game-theoretic LLM alignment under standard assumptions.
Score attack method provides a lower bound on privacy-constrained minimax risk.
problem Characterizing the optimality of privacy-constrained statistical models.
method Score attack based on tracing attack concept.
result Optimally lower bounds the minimax risk of estimating unknown model parameters.
Stochastically Transitive Models for Pairwise Comparisons: Statistical and Computational Issuesstat.ML
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 model for pairwise comparisons, under which the probabilities of outcomes are requir…
Automates debiasing for large language model evaluations through Fisher random walk.
problem Rigorous and scalable evaluation of large language models.
method Semiparametric efficient estimator using Fisher random walk for weighted residual balancing.
result Efficient estimation of contextual preference scores for large language models.
The report studies ranking from pairwise comparisons in graphs, achieving optimal error bounds and proposing efficient algorithms.
problem Ranking items from pairwise comparisons in general graphs and graphs with locality.
method Maximum likelihood estimation (MLE) and preconditioned gradient descent for general graphs; divide-and-conquer algorithms for graphs with locality.
result MLE achieves optimal error bounds in general graphs and identifies conditions for locality.
There is a growing need for discrete choice models that account for the complex nature of human choices, escaping traditional behavioral assumptions such as the transitivity of pairwise preferences. Recently, several parametric models of intransitive comparisons have been proposed, but in all cases the maximum likeliho…
We explore the top- rank aggregation problem. Suppose a collection of items is compared in pairs repeatedly, and we aim to recover a consistent ordering that focuses on the top- ranked items based on partially revealed preference information. We investigate the Bradley-Terry-Luce model in which one ranks items ac…
We consider the problem of ranking a set of items from pairwise comparisons in the presence of features associated with the items. Recent works have established that samples are needed to rank well when there is no feature information present. However, this might be sub-optimal in the presence of associat…
This paper explores the preference-based top- rank aggregation problem. Suppose that a collection of items is repeatedly compared in pairs, and one wishes to recover a consistent ordering that emphasizes the top- ranked items, based on partially revealed preferences. We focus on the Bradley-Terry-Luce (BTL) model…
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 …
The paper ranks items based on top choices in multiway comparisons.
problem Ranking items based on top choices in multiway comparisons.
method Uniform sampling scheme, statistical rates of convergence, asymptotic normality, maximum likelihood estimator, Gaussian multiplier bootstrap.
result Proposed inference framework for ranking items through maximum pairwise difference statistic.
This paper is concerned with the problem of top- ranking from pairwise comparisons. Given a collection of items and a few pairwise comparisons across them, one wishes to identify the set of items that receive the highest ranks. To tackle this problem, we adopt the logistic parametric model --- the Bradley-Te…
The question of aggregating pair-wise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR's TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In mo…
A method for dynamic ranking using BTL model and nearest neighbor rank centrality.
problem Aggregating evolving pairwise comparisons to recover item strengths over time.
method Adapting Rank Centrality method to handle dynamic pairwise outcomes.
result Consistency of the method in estimating latent strengths over time.