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. 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…
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…
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.
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.
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 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…
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.
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…
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.
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.
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 O(nlog(n)) samples are needed to rank well when there is no feature information present. However, this might be sub-optimal in the presence of associat…
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).
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 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.
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 w∗∈Rd that represents the "qualities" of the d 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…
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.
We consider data in the form of pairwise comparisons of n items, with the goal of precisely identifying the top k items for some value of k < n, or alternatively, recovering a ranking of all the items. We analyze the Copeland counting algorithm that ranks the items in order of the number of pairwise comparisons won, an…
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…
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.
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.
This paper explores the preference-based top-K 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-K ranked items, based on partially revealed preferences. We focus on the Bradley-Terry-Luce (BTL) model…
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 designs tests for comparing ranked preference data and finds significant differences.
problem Comparing pairwise comparison and ranking data in various applications.
method Developed two-sample tests for pairwise comparison and ranking data, proving upper and lower bounds.
result Upper and lower bounds show tightness of the proposed tests, and significant differences in preferences were found.
The paper introduces BCART models for aggregate claim amount, improving frequency-severity and joint modeling.
problem Modeling aggregate claim amount with frequency-severity and joint dependencies.
method Developed three types of BCART models: frequency-severity, sequential, and joint models. Used various distributions for claim severity data.
result Weibull distribution outperforms gamma and lognormal for right-skewed, heavy-tailed claim severity data.
The paper uses model-based trees to create interpretable surrogate models for complex machine learning models.
problem Interpreting complex machine learning models.
method Using model-based trees to partition feature space and create interpretable models.
result Model-based trees generate optimal surrogate models that balance interpretability and performance.
Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.
problem Improving generative model performance.
method Integrates a learnable Gauge Field into Flow ODEs.
result Gauge Flow Models outperform traditional Flow Models in Flow Matching experiments.
The study examines how model predictions hold up under model extensions.
problem Model predictions may not be robust under model extensions, limiting their applicability.
method The study uses causal ordering to assess robustness of qualitative model predictions and characterizes model extensions that preserve predictions.
result Conditions and techniques are provided to assess robustness of model predictions under model extensions.
Revises Bayesian model averaging for foundation models.
problem Ensemble pre-trained and lightly-finetuned foundation models for improved classification performance.
method Introduces trainable linear classifiers and computationally cheaper model averaging scheme (OMA).
result Ensembled models can better predict on various datasets.
Paper introduces symmetric divergence link models for probability distributions.
problem Symmetric divergence measures for probability distributions.
method Two general classes of link models: one for survival functions and another for cumulative probability distribution functions.
result Advantages of symmetric divergence measures over asymmetric measures for model averaging and feature assessment.
New method to handle credit portfolio model uncertainties.
problem Model risk in credit portfolio models.
method Demonstrates comprehensive yet easy-to-implement approach to uncertainty in model parameters.
result Comprehensive method to deal with model uncertainties.
The paper tests stock return models and uses LSTM to predict stock returns.
problem Validating stock return models and predicting stock returns.
method Used Fama-French three-factor, four-factor, and five-factor models; also used LSTM model.
result Fama-French five-factor model shows better validity for stock returns.
Researchers review challenges in interpreting additive models, especially neural additive models.
problem Challenges in interpreting additive models, particularly neural additive models.
method Review of generalized additive models and discussion of nonidentifiability.
result Challenges in claiming interpretability or suitability for safety-critical applications of additive models.
Novel hybrid modeling combines ML and physics for real-time diagnosis.
problem Real-time diagnosis of complex systems.
method Combines machine learning and physics-based models to create reduced-order models.
result Generated models are two orders of magnitude simpler, improving efficiency.
CRS model improves ranking data modeling with theoretical guarantees.
problem Lack of rich, multimodal models for ranking data.
method Contextual Repeated Selection (CRS) model for multimodal ranking data.
result CRS model significantly outperforms existing methods in various ranking contexts.
Sigma models linked to Gross-Neveu models via quiver varieties.
problem Understanding the relationship between sigma models and Gross-Neveu models.
method Exploring the mathematical correspondence between sigma models and Gross-Neveu models, including their geometric and trigonometric/elliptic deformations.
result Sigma models are mathematically equivalent to Gross-Neveu models under certain conditions.
Interpretable machine learning has become a strong competitor for traditional black-box models. However, the possible loss of the predictive performance for gaining interpretability is often inevitable, putting practitioners in a dilemma of choosing between high accuracy (black-box models) and interpretability (interpr…
Simple models are preferred over complex models, but over-simplistic models could lead to erroneous interpretations. The classical approach is to start with a simple model, whose shortcomings are assessed in residual-based model diagnostics. Eventually, one increases the complexity of this initial overly simple model a…
Matryoshka hides secret models in a carrier model, achieving high capacity and robustness.
problem Stealing functionality of private ML data by hiding models in a carrier model.
method Parameter sharing approach exploiting the learning capacity of the carrier model.
result Hides a 26x larger secret model or 8 secret models in the carrier model.
Eigen-stratified models reduce model size and improve performance.
problem Large model size in Laplacian-regularized stratified models.
method Formulate eigen-stratified models with linear combinations of bottom eigenvectors of the graph Laplacian.
result Significant reduction in model size with eigen-stratified models.
Seq2Seq models speed up epidemic model predictions.
problem Complex epidemic models are computationally expensive.
method Used deep seq2seq models as surrogates for complex models.
result Surrogates predict scenarios up to several thousand times faster.
This work develops scalable model selection methods with fast update and selection.
problem Efficient model selection for large pools of candidate models.
method Isolated model embedding, which supports asymptotically fast update and selection.
result Standardized Embedder achieves competitive model selection performances.
Paper proposes BMPO to optimize policies using bidirectional models.
problem Model-based reinforcement learning's reliance on forward model accuracy.
method Develops BMPO using both forward and backward models for policy optimization.
result BMPO outperforms state-of-the-art methods in sample efficiency and asymptotic performance.
Copulas outperform marginal models in multivariate risk forecasting, reducing model risk by narrowing down the set of models.
problem Model risk in multivariate risk forecasting, especially during crises.
method Comprehensive empirical study comparing Copula-GARCH models with fixed marginals, copulas, or neither.
result Model risk is almost entirely due to copula choice, not marginal models.
BayesBlend blends multiple models' predictions for better insurance loss predictions.
problem Improving insurance loss predictions by combining multiple models.
method Pseudo-Bayesian model averaging, stacking, and hierarchical stacking.
result BayesBlend provides a user-friendly way to blend model predictions and estimate weights.
The paper identifies when larger models improve predictions and proposes a switcher model.
problem Understanding when larger models benefit from added complexity.
method Numerical studies on T5 architecture to analyze predictive uncertainty and model performance.
result Large models improve on examples where small models are uncertain, but not on certain examples.