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The problem of error density estimation for a functional single index model with dependent errors is studied. A Bayesian method is utilized to simultaneously estimate the bandwidths in the kernel-form error density and regression function,…

Applications · Statistics 2018-10-23 Han Lin Shang

Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of…

Machine Learning · Computer Science 2022-09-15 Fabricio Olivetti de Franca , Gabriel Kronberger

In this paper we develop pivotal inference for the final (FPE) and relative final prediction error (RFPE) of linear forecasts in stationary processes. Our approach is based on a self-normalizing technique and avoids the estimation of the…

Statistics Theory · Mathematics 2026-04-16 Holger Dette , Sebastian Kühnert

Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…

Data Analysis, Statistics and Probability · Physics 2009-03-03 Marek W. Gutowski

Class-incremental learning (CIL) is a particularly challenging variant of continual learning, where the goal is to learn to discriminate between all classes presented in an incremental fashion. Existing approaches often suffer from…

Machine Learning · Computer Science 2024-03-12 Michał Zając , Tinne Tuytelaars , Gido M. van de Ven

Social goods, such as healthcare, smart city, and information networks, often produce ordered event data in continuous time. The generative processes of these event data can be very complex, requiring flexible models to capture their…

Machine Learning · Computer Science 2020-12-29 Shuang Li , Shuai Xiao , Shixiang Zhu , Nan Du , Yao Xie , Le Song

Confidence estimation, a task that aims to evaluate the trustworthiness of the model's prediction output during deployment, has received lots of research attention recently, due to its importance for the safe deployment of deep models.…

Computer Vision and Pattern Recognition · Computer Science 2022-10-14 Haoxuan Qu , Yanchao Li , Lin Geng Foo , Jason Kuen , Jiuxiang Gu , Jun Liu

Large Language Models (LLMs) have become increasingly pervasive, finding applications across many industries and disciplines. Ensuring the trustworthiness of LLM outputs is paramount, where Uncertainty Estimation (UE) plays a key role. In…

Computation and Language · Computer Science 2025-11-06 Kevin Wang , Subre Abdoul Moktar , Jia Li , Kangshuo Li , Feng Chen

By employing various empirical estimators for the Mutual Information (MI) measure, we calculate and compare the estimates and their confidence intervals for both normal and non-normal bivariate data samples. We find that certain nonlinear…

Information Theory · Computer Science 2024-10-10 Theo Grigorenko , Leo Grigorenko

A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…

Methodology · Statistics 2022-01-19 Geoffrey S Johnson

Confidence estimation (CE) indicates how reliable the answers of large language models are and impacts user trust and decision-making. Existing evaluations mainly concern the alignment between confidence and correctness, but ignore the…

Computation and Language · Computer Science 2026-05-29 Yuxi Xia , Dennis Ulmer , Terra Blevins , Yihong Liu , Hinrich Schütze , Benjamin Roth

Large Language Models (LLMs) have exhibited remarkable performance across various downstream tasks, but they may generate inaccurate or false information with a confident tone. One of the possible solutions is to empower the LLM confidence…

Computation and Language · Computer Science 2024-04-17 Haixia Han , Tingyun Li , Shisong Chen , Jie Shi , Chengyu Du , Yanghua Xiao , Jiaqing Liang , Xin Lin

Matching algorithms are commonly used to predict matches between items in a collection. For example, in 1:1 face verification, a matching algorithm predicts whether two face images depict the same person. Accurately assessing the…

Methodology · Statistics 2024-04-30 Riccardo Fogliato , Pratik Patil , Pietro Perona

Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model…

Machine Learning · Statistics 2025-08-05 Yan Sun , Pratik Chaudhari , Ian J. Barnett , Edgar Dobriban

Conformal prediction can yield statistically valid prediction intervals for any regression model, with no model modifications and small computational costs. To assess its practical value, we apply conformal methods to quantify uncertainty…

Atmospheric and Oceanic Physics · Physics 2026-03-31 Miriam Simm , Corinna Hoose , Tom Beucler

There are over 55 different ways to construct a confidence respectively credible interval (CI) for the binomial proportion. Methods to compare them are necessary to decide which should be used in practice. The interval score has been…

Methodology · Statistics 2022-07-08 Lisa J. Hofer , Leonhard Held

We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly…

Statistics Theory · Mathematics 2018-04-03 Timothy B. Armstrong , Michal Kolesár

Estimating uncertainties associated with the predictions of Machine Learning (ML) models is of crucial importance to assess their robustness and predictive power. In this submission, we introduce MAPIE (Model Agnostic Prediction Interval…

Machine Learning · Statistics 2022-07-26 Vianney Taquet , Vincent Blot , Thomas Morzadec , Louis Lacombe , Nicolas Brunel

High-stakes applications require AI-generated models to be interpretable. Current algorithms for the synthesis of potentially interpretable models rely on objectives or regularization terms that represent interpretability only coarsely…

Machine Learning · Computer Science 2021-04-28 Marco Virgolin , Andrea De Lorenzo , Francesca Randone , Eric Medvet , Mattias Wahde

In today's era, Neural Networks (NN) are applied in various scientific fields such as robotics, medicine, engineering, etc. However, the predictions of neural networks themselves contain a degree of uncertainty that must always be taken…

Machine Learning · Computer Science 2025-04-01 E. V. Aretos , D. G. Sotiropoulos