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Large language models (LLMs) are often confidently wrong, making reliable uncertainty estimation (UE) essential. Output-based heuristics are cheap but brittle, while probing internal representations is effective yet high-dimensional and…

Machine Learning · Computer Science 2026-03-25 Zvi N. Badash , Yonatan Belinkov , Moti Freiman

[Abridged] Production LLM deployments receive feedback from a non-random fraction of users: thumbs sit mostly in the tails of the satisfaction distribution, and a naive average over them can land 40-50 percentage points away from true…

Computation and Language · Computer Science 2026-05-13 Andrea Morandi , Mahesh Viswanathan

The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…

Statistics Theory · Mathematics 2019-06-05 Paulo Orenstein

Recently, large language models (LLMs) have exhibited significant progress in language understanding and generation. By leveraging textual features, customized LLMs are also applied for recommendation and demonstrate improvements across…

Information Retrieval · Computer Science 2023-11-07 Zhenrui Yue , Sara Rabhi , Gabriel de Souza Pereira Moreira , Dong Wang , Even Oldridge

We introduce a novel Bayesian estimator for the class proportion in an unlabeled dataset, based on the targeted learning framework. Our procedure requires the specification of a prior (and outputs a posterior) only for the target of…

Methodology · Statistics 2019-11-26 Iván Díaz , Oleksander Savenkov , Hooman Kamel

In inverse problems, the parameters of a model are estimated based on observations of the model response. The Bayesian approach is powerful for solving such problems; one formulates a prior distribution for the parameter state that is…

Computation · Statistics 2022-06-08 Max Ehre , Rafael Flock , Martin Fußeder , Iason Papaioannou , Daniel Straub

Bayesian model comparison implements Occam's razor through its sensitivity to the prior. However, prior-dependence makes it important to assess the influence of plausible alternative priors. Such prior sensitivity analyses for the Bayesian…

Methodology · Statistics 2026-01-22 Zixiao Hu , Jason D. McEwen

In many high-risk machine learning applications it is essential for a model to indicate when it is uncertain about a prediction. While large language models (LLMs) can reach and even surpass human-level accuracy on a variety of benchmarks,…

Computation and Language · Computer Science 2024-06-06 Evan Becker , Stefano Soatto

In this reproducibility study, we revisit the LLAMBO framework of Daxberger et al. (2024), a prompting-based Bayesian optimization (BO) method that uses large language models as discriminative surrogates and acquisition optimizers via…

Computation and Language · Computer Science 2025-11-25 Adam Rychert , Gasper Spagnolo , Evgenii Posashkov

We consider a PAC-Bayes type learning rule for binary classification, balancing the training error of a randomized ''posterior'' predictor with its KL divergence to a pre-specified ''prior''. This can be seen as an extension of a modified…

Machine Learning · Statistics 2026-03-25 Xiaohan Zhu , Mesrob I. Ohannessian , Nathan Srebro

The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…

Methodology · Statistics 2019-03-26 Victor Chen , Matthew M. Dunlop , Omiros Papaspiliopoulos , Andrew M. Stuart

It is common practice to combine deep neural networks into ensembles. These deep ensembles can benefit from the cancellation of errors effect: Errors by ensemble members may average out, leading to better generalization performance than…

Machine Learning · Computer Science 2025-01-07 Nick Hauptvogel , Christian Igel

We establish concentration rates for estimation of treatment effects in experiments that incorporate prior sources of information -- such as past pilots, related studies, or expert assessments -- whose external validity is uncertain. Each…

Econometrics · Economics 2026-03-24 Frederico Finan , Demian Pouzo

Large language models (LLMs) achieve strong reasoning performance by allocating substantial computation at inference time, often generating long and verbose reasoning traces. While recent work on efficient reasoning reduces this overhead…

Computation and Language · Computer Science 2026-04-28 Han Wang , Xiaodong Yu , Jialian Wu , Jiang Liu , Ximeng Sun , Mohit Bansal , Zicheng Liu

How can we precisely estimate a large language model's (LLM) accuracy on questions belonging to a specific topic within a larger question-answering dataset? The standard direct estimator, which averages the model's accuracy on the questions…

Machine Learning · Computer Science 2024-10-08 Riccardo Fogliato , Pratik Patil , Nil-Jana Akpinar , Mathew Monfort

Automated Essay Scoring (AES) systems now reach near human agreement on some public benchmarks, yet real-world adoption, especially in high-stakes examinations, remains limited. A principal obstacle is that most models output a single score…

Computation and Language · Computer Science 2025-09-22 Ahmed Karim , Qiao Wang , Zheng Yuan

The specification of prior distributions is fundamental in Bayesian inference, yet it remains a significant bottleneck. The prior elicitation process is often a manual, subjective, and unscalable task. We propose a novel framework which…

Machine Learning · Computer Science 2025-08-07 Yongchao Huang

One of the most popular methodologies for estimating the average treatment effect at the threshold in a regression discontinuity design is local linear regression (LLR), which places larger weight on units closer to the threshold. We…

Methodology · Statistics 2019-02-01 Zach Branson , Maxime Rischard , Luke Bornn , Luke Miratrix

Large language models (LLMs) are increasingly used for conversational clinical decision support, yet they conflate next token prediction with probabilistic decision making. We argue that this conflation reflects an architectural limitation:…

In this paper, we develop a generalized Bayesian inference framework for a collection of signal-plus-noise matrix models arising in high-dimensional statistics and many applications. The framework is built upon an asymptotically unbiased…

Statistics Theory · Mathematics 2022-04-01 Fangzheng Xie , Dingbo Wu