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In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…

Machine Learning · Computer Science 2024-08-08 Agathe Fernandes Machado , Arthur Charpentier , Emmanuel Flachaire , Ewen Gallic , François Hu

We investigate the problem of determining the predictive confidence (or, conversely, uncertainty) of a neural classifier through the lens of low-resource languages. By training models on sub-sampled datasets in three different languages, we…

Computation and Language · Computer Science 2022-10-28 Dennis Ulmer , Jes Frellsen , Christian Hardmeier

We study the problem of actively learning a classifier with a low calibration error. One of the most popular Acquisition Functions (AFs) in pool-based Active Learning (AL) is querying by the model's uncertainty. However, we recognize that…

Machine Learning · Computer Science 2025-10-06 Ha Manh Bui , Iliana Maifeld-Carucci , Anqi Liu

Quantitative characterizations and estimations of uncertainty are of fundamental importance in optimization and decision-making processes. Herein, we propose intuitive scores, which we call certainty and doubt, that can be used in both a…

Nonparametric estimation using uniform-width binning is a standard approach for evaluating the calibration performance of machine learning models. However, existing theoretical analyses of the bias induced by binning are limited to binary…

Machine Learning · Computer Science 2025-07-14 Masahiro Fujisawa , Futoshi Futami

Predictions of uncertainty-aware models are diverse, ranging from single point estimates (often averaged over prediction samples) to predictive distributions, to set-valued or credal-set representations. We propose a novel unified…

Machine Learning · Computer Science 2025-02-18 Shireen Kudukkil Manchingal , Muhammad Mubashar , Kaizheng Wang , Fabio Cuzzolin

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last…

Machine Learning · Computer Science 2020-01-06 Mohammad Hossein Shaker , Eyke Hüllermeier

Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a…

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…

Machine Learning · Computer Science 2023-06-27 Lisa Wimmer , Yusuf Sale , Paul Hofman , Bern Bischl , Eyke Hüllermeier

When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for…

Machine Learning · Computer Science 2019-03-18 Richard Harang , Ethan M. Rudd

A common approach to aggregate classification estimates in an ensemble of decision trees is to either use voting or to average the probabilities for each class. The latter takes uncertainty into account, but not the reliability of the…

Machine Learning · Computer Science 2022-08-17 Florian Busch , Moritz Kulessa , Eneldo Loza Mencía , Hendrik Blockeel

We study three notions of uncertainty quantification -- calibration, confidence intervals and prediction sets -- for binary classification in the distribution-free setting, that is without making any distributional assumptions on the data.…

Machine Learning · Statistics 2022-02-17 Chirag Gupta , Aleksandr Podkopaev , Aaditya Ramdas

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

Machine Learning · Computer Science 2025-05-29 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…

In causal inference, sensitivity models assess how unmeasured confounders could alter causal analyses, but the sensitivity parameter -- which quantifies the degree of unmeasured confounding -- is often difficult to interpret. For this…

Methodology · Statistics 2025-09-04 Alec McClean , Zach Branson , Edward H. Kennedy

Uncertainty quantification by ensemble learning is explored in terms of an application from computational optical form measurements. The application requires to solve a large-scale, nonlinear inverse problem. Ensemble learning is used to…

Machine Learning · Computer Science 2021-03-03 Lara Hoffmann , Ines Fortmeier , Clemens Elster

Nested dichotomies are used as a method of transforming a multiclass classification problem into a series of binary problems. A tree structure is induced that recursively splits the set of classes into subsets, and a binary classification…

Machine Learning · Computer Science 2018-10-04 Tim Leathart , Eibe Frank , Bernhard Pfahringer , Geoffrey Holmes

Probabilistic models must be well calibrated to support reliable decision-making. While calibration in single-output regression is well studied, defining and achieving multivariate calibration in multi-output regression remains considerably…

Machine Learning · Statistics 2025-10-28 Naomi Desobry , Elnura Zhalieva , Souhaib Ben Taieb

We provide another look at the statistical calibration problem in computer models. This viewpoint is inspired by two overarching practical considerations of computer models: (i) many computer models are inadequate for perfectly modeling…

Methodology · Statistics 2018-09-26 Xiaowu Dai , Peter Chien

In classification applications, we often want probabilistic predictions to reflect confidence or uncertainty. Dropout, a commonly used training technique, has recently been linked to Bayesian inference, yielding an efficient way to quantify…

Machine Learning · Computer Science 2019-06-25 Zhilu Zhang , Adrian V. Dalca , Mert R. Sabuncu
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