Ranking recommendation algorithms across datasets using Bradley-Terry model
problem Comparing recommendation algorithms across different datasets
method Introduce a novel data-driven ranking methodology based on Bradley-Terry model
result The obtained ranking depends on key dataset statistics
We propose a time-varying generalization of the Bradley-Terry model that allows for nonparametric modeling of dynamic global rankings of distinct teams. We develop a novel estimator that relies on kernel smoothing to pre-process the pairwise comparisons over time and is applicable in sparse settings where the Bradley-T…
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 extensions are estimated by maximizing the log-likelihood, or an appropriately penalize…
A new method sorts projects using Quicksort and Bradley-Terry model for uncertain long-term benefits.
problem Selecting projects with uncertain long-term benefits.
method Combining Quicksort and Bradley-Terry model for ranking projects based on uncertain long-term benefits.
result Proposed methods outperform existing aggregation methods and can be combined with sampling techniques.
The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess ranking and multiclass classification. Numerous extensions of the basic model have a…
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.
New models ensure monotonicity in preference learning, improving accuracy especially with limited data.
problem Failure of widely used preference learning models to maintain monotonicity.
method Proposed Linear Generalized Bradley-Terry models with Diffusion Priors.
result New models improve accuracy, especially with limited data.
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.
A faster algorithm for ranking from pairwise comparisons.
problem Efficiently ranking individuals or objects from pairwise comparisons.
method An alternative and simpler iterative algorithm for ranking that converges faster.
result The new algorithm is over 100 times faster in some cases.
Algorithm learns similarity metrics for individual fairness.
problem Difficulty in learning similarity metrics for individual fairness.
method Gradient descent and Bradley-Terry model for pairwise comparisons.
result Algorithm converges to ground truth metric for individual fairness.
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 Élő update still remains, after more than 50 years, a valuable baseline which is difficult to…
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.
Paper establishes statistical inference for pairwise comparison models.
problem Statistical inference for pairwise comparison models when the number of subjects diverges.
method Identifies Fisher information matrix as a weighted graph Laplacian for asymptotic normality.
result Near-optimal asymptotic normality result for maximum likelihood estimator.
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.
Introduces AMLB, an open benchmark for AutoML frameworks.
problem Challenges in comparing AutoML frameworks.
method Open benchmark with 9 AutoML frameworks, 71 classification, 33 regression tasks, multi-faceted analysis, Bradley-Terry trees.
result Differences in AutoML frameworks' performance and trade-offs.
Bayesian model compares ML algorithms on various datasets.
problem Comparing multiple machine learning algorithms across multiple datasets.
method Bayesian Bradley-Terry model, defining regions of practical equivalence (ROPE).
result Allows nuanced statements and ROPE definitions for algorithm comparison.
A new method resolves non-identifiability in reward modeling using anchor labels.
problem Non-identifiability in reward modeling from pairwise preferences alone.
method Anchor-guided Variance-aware Reward Modeling (AVRM) framework.
result AVRM resolves non-identifiability and improves reward modeling performance.
Paper introduces a novel framework for recognizing dynamic ranking structures in preference-based data.
problem Complex and noisy preference-based data often hide underlying homogeneous structures.
method Developed an approach to identify dynamic ranking groups using temporal penalties and spectral estimation. Introduced an objective function for detecting structural changes.
result Consistent recognition of ranking groups and structural changes in preference-based data.
New method ranks competitors from multiple types of comparisons.
problem Ranking individuals or teams from multiple conflicting comparison types.
method Combination of expectation-maximization algorithm and modified Bradley-Terry model.
result A ranking can be computed from multiple conflicting comparison types.
Direct Density Ratio Optimization aligns LLMs with human preferences without assuming specific models.
problem Statistical inconsistency in aligning LLMs with human preferences.
method Direct Density Ratio Optimization (DDRO) estimates density ratio directly.
result DDRO is statistically consistent, converging to true human preferences as data grows.
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 K-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.
Dropping a tiny fraction of preferences can significantly alter the rankings of top LLMs.
problem Robustness of LLM ranking systems to small changes in preference data.
method A computational method based on the Bradley-Terry model to evaluate robustness.
result Top LLM rankings can be highly sensitive to the removal of a small fraction of preferences.
Paper proposes using pairwise feature comparisons to infer modification costs for user recourse.
problem Learning and inferring user preferences for modifying features in black-box models.
method Bradley-Terry model for inferring feature-wise costs from non-exhaustive human comparison surveys.
result Non-exhaustive human surveys can efficiently learn feature costs, enabling recourse finding.
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.
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 of making personalized recommendations. In particular, we assume that there are …
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).
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 Bradley-Terry model of paired comparisons, the Rao-Kupper model of paired comparison…
Duel-Evolve uses LLM self-preferences for test-time optimization of discrete outputs.
problem Optimizing LLM outputs at test time with limited or unreliable scalar rewards.
method Duel-Evolve uses pairwise comparisons from the LLM to guide optimization, aggregating them via a Bayesian Bradley-Terry model.
result Achieves significant improvement over existing methods in accuracy.
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.
Best-of-N sampling reveals reward targets from preference data, influencing N and base distribution choices.
problem Understanding reward extraction from Best-of-N preference data and optimal N and base distribution choices.
method Specialized analysis of preference data via induced conditional distribution, deriving reward targets and design principles.
result Reward targets are explicit functions of N and base distribution, and bounded-class minimizers approach these targets as N grows.
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 ℓ∞-loss under general graphs. method Novel upper bounds on ℓ∞ estimation error dependent on algebraic connectivity and graph topology. result Upper bounds on ℓ∞ 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.
The paper proposes a new method for learning reward models from ordinal feedback, improving upon binary feedback.
problem Learning reward models from human preferences using binary feedback discards useful samples and loses fine-grained information.
method The paper introduces a framework for learning reward models under ordinal feedback, generalizing the Bradley-Terry model.
result Ordinal feedback reduces the Rademacher complexity compared to binary feedback, leading to better reward learning.
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.
In this paper we present a hybrid active sampling strategy for pairwise preference aggregation, which aims at recovering the underlying rating of the test candidates from sparse and noisy pairwise labelling. Our method employs Bayesian optimization framework and Bradley-Terry model to construct the utility function, th…
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 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, the optimal solution is to use an efficient sorting algorithm, such as Quicksor…
Proposes a robust algorithm for aligning large language models with human preferences.
problem Misspecification in preference models, reference policies, and reward functions.
method Doubly robust preference optimization algorithm.
result Superior and more robust performance compared to state-of-the-art algorithms.
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.
Paper proposes a robust RLHF algorithm for LLMs, improving response preference over baselines.
problem Reward model misspecifications in RLHF for LLMs.
method Proposes a robust algorithm to reduce reward and policy estimator variance, theoretically and empirically validated.
result Consistently outperforms existing methods on LLM benchmark datasets, favoring 77-81% of responses over baselines.