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We introduce and study the problem of calibrating conditional risk, which involves estimating the expected loss of a prediction model conditional on input features. We analyze this problem in both classification and regression settings and…

Machine Learning · Computer Science 2026-04-23 Andrey Vasilyev , Yikai Wang , Xiaocheng Li , Guanting Chen

I provide a unifying perspective on forecast evaluation, characterizing accurate forecasts of all types, from simple point to complete probabilistic forecasts, in terms of two fundamental underlying properties, autocalibration and…

Methodology · Statistics 2020-05-06 Marc-Oliver Pohle

In the context of computer models, calibration is the process of estimating unknown simulator parameters from observational data. Calibration is variously referred to as model fitting, parameter estimation/inference, an inverse problem, and…

Methodology · Statistics 2023-10-16 Richard D. Wilkinson , Christopher W. Lanyon

Model diagnostics and forecast evaluation are two sides of the same coin. A common principle is that fitted or predicted distributions ought to be calibrated or reliable, ideally in the sense of auto-calibration, where the outcome is a…

Methodology · Statistics 2024-09-27 Tilmann Gneiting , Johannes Resin

We consider the problem of evaluating forecasts of binary events whose predictions are consumed by rational agents who take an action in response to a prediction, but whose utility is unknown to the forecaster. We show that optimizing…

Machine Learning · Computer Science 2023-07-04 Robert Kleinberg , Renato Paes Leme , Jon Schneider , Yifeng Teng

Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…

Machine Learning · Statistics 2026-03-02 Eugène Berta , Sacha Braun , David Holzmüller , Francis Bach , Michael I. Jordan

Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…

Machine Learning · Computer Science 2026-02-18 Aurora Grefsrud , Nello Blaser , Trygve Buanes

A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…

Data Analysis, Statistics and Probability · Physics 2020-12-09 Jochen Bröcker

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…

Machine Learning · Computer Science 2018-07-03 Volodymyr Kuleshov , Nathan Fenner , Stefano Ermon

Probabilistic predictions can be evaluated through comparisons with observed label frequencies, that is, through the lens of calibration. Recent scholarship on algorithmic fairness has started to look at a growing variety of…

Machine Learning · Computer Science 2023-05-16 Benedikt Höltgen , Robert C Williamson

Machine learning models typically focus on specific targets like creating classifiers, often based on known population feature distributions in a business context. However, models calculating individual features adapt over time to improve…

Machine Learning · Computer Science 2024-02-23 Emanuele Luzio , Moacir Antonelli Ponti , Christian Ramirez Arevalo , Luis Argerich

Binary classification is highly used in credit scoring in the estimation of probability of default. The validation of such predictive models is based both on rank ability, and also on calibration (i.e. how accurately the probabilities…

Econometrics · Economics 2017-10-25 Pedro G. Fonseca , Hugo D. Lopes

Accurate probabilistic predictions can be characterized by two properties -- calibration and sharpness. However, standard maximum likelihood training yields models that are poorly calibrated and thus inaccurate -- a 90% confidence interval…

Machine Learning · Computer Science 2025-05-14 Volodymyr Kuleshov , Shachi Deshpande

Post-hoc calibration methods are widely used to improve the reliability of probabilistic predictions from machine learning models. Despite their prevalence, a comprehensive theoretical understanding of these methods remains elusive,…

Machine Learning · Computer Science 2025-09-30 Kristina P. Sinaga , Arjun S. Nair

Modern image classifiers are very accurate, but the predictions come without uncertainty estimates. Conformal predictors provide uncertainty estimates by computing a set of classes containing the correct class with a user-specified…

Machine Learning · Computer Science 2023-06-06 Fatih Furkan Yilmaz , Reinhard Heckel

Conformal Prediction (CP) is a distribution-free uncertainty estimation framework that constructs prediction sets guaranteed to contain the true answer with a user-specified probability. Intuitively, the size of the prediction set encodes a…

Machine Learning · Computer Science 2025-02-18 Alvaro H. C. Correia , Fabio Valerio Massoli , Christos Louizos , Arash Behboodi

While the accuracy of modern deep learning models has significantly improved in recent years, the ability of these models to generate uncertainty estimates has not progressed to the same degree. Uncertainty methods are designed to provide…

Machine Learning · Statistics 2020-06-17 Adam M. Oberman , Chris Finlay , Alexander Iannantuono , Tiago Salvador

The mutual information between a set of stimuli and the elicited neural responses is compared to the corresponding decoded information. The decoding procedure is presented as an artificial distortion of the joint probabilities between…

Biological Physics · Physics 2007-05-23 Ines Samengo

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…

Machine Learning · Computer Science 2023-05-24 Lucas Clarté , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

Proper scoring rules are essential for evaluating probabilistic forecasts. We propose a simple algebraic rearrangement of the Yates covariance decomposition of the Brier score into three independently non-negative terms: a variance mismatch…

Methodology · Statistics 2026-03-09 Bruno Hebling Vieira