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Forecasts for uncertain future events should be probabilistic. Probabilistic forecasts are commonly issued as prediction intervals, which provide a measure of uncertainty in the unknown outcome whilst being easier to understand and…

Methodology · Statistics 2025-08-26 Sam Allen , Julia Burnello , Johanna Ziegel

As machine learning models are increasingly deployed in high-stakes environments, ensuring both probabilistic reliability and prediction stability has become critical. This paper examines the interplay between classification calibration and…

Machine Learning · Computer Science 2026-03-17 Mustafa Cavus

This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…

Methodology · Statistics 2022-12-02 Joel L. Horowitz , Sokbae Lee

Binary classification is a task that involves the classification of data into one of two distinct classes. It is widely utilized in various fields. However, conventional classifiers tend to make overconfident predictions for data that…

Machine Learning · Computer Science 2025-03-13 Shoma Yokura , Akihisa Ichiki

The goal of confidence-set learning in the binary classification setting is to construct two sets, each with a specific probability guarantee to cover a class. An observation outside the overlap of the two sets is deemed to be from one of…

Machine Learning · Statistics 2018-10-01 Wenbo Wang , Xingye Qiao

Conformal predictive systems allow forecasters to issue predictive distributions for real-valued future outcomes that have out-of-sample calibration guarantees. On a more abstract level, conformal prediction makes use of in-sample…

Methodology · Statistics 2025-03-07 Sam Allen , Georgios Gavrilopoulos , Alexander Henzi , Gian-Reto Kleger , Johanna Ziegel

We prove calibration guarantees for the popular histogram binning (also called uniform-mass binning) method of Zadrozny and Elkan [2001]. Histogram binning has displayed strong practical performance, but theoretical guarantees have only…

Methodology · Statistics 2021-07-21 Chirag Gupta , Aaditya K. Ramdas

Machine learning classification tasks often benefit from predicting a set of possible labels with confidence scores to capture uncertainty. However, existing methods struggle with the high-dimensional nature of the data and the lack of…

Machine Learning · Computer Science 2024-07-08 Rui Luo , Zhixin Zhou

In this PhD thesis, we propose a novel framework for uncertainty quantification in machine learning, which is based on proper scores. Uncertainty quantification is an important cornerstone for trustworthy and reliable machine learning…

Machine Learning · Computer Science 2025-08-26 Sebastian G. Gruber

Existing conformal prediction algorithms estimate prediction intervals at target confidence levels to characterize the performance of a regression model on new test samples. However, considering an autonomous system consisting of multiple…

Machine Learning · Computer Science 2023-09-25 Yunye Gong , Yi Yao , Xiao Lin , Ajay Divakaran , Melinda Gervasio

Measurement of uncertainty of predictions from machine learning methods is important across scientific domains and applications. We present, to our knowledge, the first such technique that quantifies the uncertainty of predictions from a…

Machine Learning · Statistics 2022-04-04 Alex Hagen , Karl Pazdernik , Nicole LaHaye , Marjolein Oostrom

The regression function is one of the key objects of binary classification, since it not only determines a Bayes optimal classifier, hence, defines an optimal decision boundary, but also encodes the conditional distribution of the output…

Machine Learning · Statistics 2025-06-03 Ambrus Tamás , Balázs Csanád Csáji

Unbiased confidence estimates of neural networks are crucial especially for safety-critical applications. Many methods have been developed to calibrate biased confidence estimates. Though there is a variety of methods for classification,…

Computer Vision and Pattern Recognition · Computer Science 2020-12-15 Fabian Küppers , Jan Kronenberger , Amirhossein Shantia , Anselm Haselhoff

Calibrating neural networks is of utmost importance when employing them in safety-critical applications where the downstream decision making depends on the predicted probabilities. Measuring calibration error amounts to comparing two…

Machine Learning · Computer Science 2021-12-30 Kartik Gupta , Amir Rahimi , Thalaiyasingam Ajanthan , Thomas Mensink , Cristian Sminchisescu , Richard Hartley

With rapid adoption of deep learning in critical applications, the question of when and how much to trust these models often arises, which drives the need to quantify the inherent uncertainties. While identifying all sources that account…

Machine Learning · Statistics 2019-11-22 Jayaraman J. Thiagarajan , Bindya Venkatesh , Prasanna Sattigeri , Peer-Timo Bremer

Binary classification based on predicted probabilities (scores) is a fundamental task in supervised machine learning. While thresholding scores is Bayes-optimal in the unconstrained setting, using a single threshold generally violates…

Machine Learning · Computer Science 2026-02-10 Etam Benger , Katrina Ligett

This paper explores the calibration of a classifier output score in binary classification problems. A calibrator is a function that maps the arbitrary classifier score, of a testing observation, onto $[0,1]$ to provide an estimate for the…

Machine Learning · Computer Science 2022-04-29 Waleed A. Yousef , Issa Traore , William Briguglio

Model calibration is essential for ensuring that the predictions of deep neural networks accurately reflect true probabilities in real-world classification tasks. However, deep networks often produce over-confident or under-confident…

Machine Learning · Computer Science 2025-04-01 Jinxu Lin , Linwei Tao , Minjing Dong , Chang Xu

We are concerned with obtaining well-calibrated output distributions from regression models. Such distributions allow us to quantify the uncertainty that the model has regarding the predicted target value. We introduce the novel concept of…

Machine Learning · Statistics 2019-05-16 Hao Song , Tom Diethe , Meelis Kull , Peter Flach

We develop a new approach for quantifying uncertainty in finite populations, by using design distributions to calibrate sensitivity parameters in finite population identified sets. This yields uncertainty intervals that can be interpreted…

Econometrics · Economics 2026-05-12 Brendan Kline , Matthew A. Masten
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