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Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…

General Economics · Economics 2026-02-27 Salvatore Greco , Sajid Siraj , Michele Lundy

Process reward models (PRMs) have shown success in complex reasoning tasks for large language models (LLMs). However, their application to machine translation (MT) remains underexplored due to the lack of systematic methodologies and…

Computation and Language · Computer Science 2025-09-22 Zhaopeng Feng , Jiahan Ren , Jiayuan Su , Jiamei Zheng , Hongwei Wang , Zuozhu Liu

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…

Optimization and Control · Mathematics 2025-09-04 László Gyarmati , Éva Orbán-Mihálykó , Csaba Mihálykó , Sándor Bozóki , Zsombor Szádoczki

Multileaved comparison methods generalize interleaved comparison methods to provide a scalable approach for comparing ranking systems based on regular user interactions. Such methods enable the increasingly rapid research and development of…

Information Retrieval · Computer Science 2017-11-28 Harrie Oosterhuis , Maarten de Rijke

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…

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…

Machine Learning · Statistics 2015-12-18 Rui Wu , Jiaming Xu , R. Srikant , Laurent Massoulié , Marc Lelarge , Bruce Hajek

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…

Methodology · Statistics 2024-10-03 Cristiano Varin , David Firth

This paper presents an advanced mathematical problem-solving framework, LLaMA-Berry, for enhancing the mathematical reasoning ability of Large Language Models (LLMs). The framework combines Monte Carlo Tree Search (MCTS) with iterative…

Artificial Intelligence · Computer Science 2024-11-22 Di Zhang , Jianbo Wu , Jingdi Lei , Tong Che , Jiatong Li , Tong Xie , Xiaoshui Huang , Shufei Zhang , Marco Pavone , Yuqiang Li , Wanli Ouyang , Dongzhan Zhou

Deliberative tree search is a cornerstone of modern Large Language Model (LLM) research, driving the pivot from brute-force scaling toward algorithmic efficiency. This single paradigm unifies two critical frontiers: \textbf{Test-Time…

We introduce an approach aimed at enhancing the reasoning capabilities of Large Language Models (LLMs) through an iterative preference learning process inspired by the successful strategy employed by AlphaZero. Our work leverages Monte…

Artificial Intelligence · Computer Science 2024-06-19 Yuxi Xie , Anirudh Goyal , Wenyue Zheng , Min-Yen Kan , Timothy P. Lillicrap , Kenji Kawaguchi , Michael Shieh

Lowering the numerical precision of model parameters and computations is widely adopted to improve the efficiency of retrieval systems. However, when computing relevance scores between the query and documents in low-precision, we observe…

Information Retrieval · Computer Science 2026-04-14 Kisu Yang , Yoonna Jang , Hwanseok Jang , Kenneth Choi , Isabelle Augenstein , Heuiseok Lim

Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess…

Computation and Language · Computer Science 2024-07-02 Mingqian He , Yongliang Shen , Wenqi Zhang , Zeqi Tan , Weiming Lu

Tool-augmented large language models (LLMs) leverage tools, often in the form of APIs, to improve their reasoning capabilities on complex tasks. This enables them to act as intelligent agents interacting with the real world. The recently…

Computation and Language · Computer Science 2025-03-24 Sijia Chen , Yibo Wang , Yi-Feng Wu , Qing-Guo Chen , Zhao Xu , Weihua Luo , Kaifu Zhang , Lijun Zhang

We present a novel preference learning framework to capture participant preferences efficiently within limited interaction rounds. It involves three main contributions. First, we develop a variational Bayesian approach to infer the…

Machine Learning · Computer Science 2025-03-20 Yan Wang , Jiapeng Liu , Milosz Kadziński , Xiuwu Liao

Pairwise comparisons are a well-known method for modelling of the subjective preferences of a decision maker. A popular implementation of the method is based on solving an eigenvalue problem for M - the matrix of pairwise comparisons. This…

Discrete Mathematics · Computer Science 2015-09-25 Konrad Kułakowski

The Bradley-Terry (BT) model is a common and successful practice in reward modeling for Large Language Model (LLM) alignment. However, it remains unclear why this model -- originally developed for multi-player stochastic game matching --…

Artificial Intelligence · Computer Science 2025-01-28 Hao Sun , Yunyi Shen , Jean-Francois Ton

Decision trees are a commonly used class of machine learning models valued for their interpretability and versatility, capable of both classification and regression. We propose ZTree, a novel decision tree learning framework that replaces…

Machine Learning · Computer Science 2025-09-17 Eric Cheng , Jie Cheng

Pairwise comparison matrices are widely used in Multicriteria Decision Making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad…

Applications · Statistics 2019-06-20 László Csató

How to predict precise user preference and how to make efficient retrieval from a big corpus are two major challenges of large-scale industrial recommender systems. In tree-based methods, a tree structure T is adopted as index and each item…

Information Retrieval · Computer Science 2021-09-23 Daqing Chang , Jintao Liu , Ziru Xu , Han Li , Han Zhu , Xiaoqiang Zhu

Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…

Methodology · Statistics 2026-04-14 Soham Bakshi , Snigdha Panigrahi
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