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In the face of uncertainty, the need for probabilistic assessments has long been recognized in the literature on forecasting. In classification, however, comparative evaluation of classifiers often focuses on predictions specifying a single…

Methodology · Statistics 2023-05-31 Johannes Resin

Prediction markets are well-studied in the case where predictions are probabilities or expectations of future random variables. In 2008, Lambert, et al. proposed a generalization, which we call "scoring rule markets" (SRMs), in which…

Computer Science and Game Theory · Computer Science 2017-09-29 Rafael Frongillo , Bo Waggoner

The classical paradigm of scoring rules is to discriminate between two different forecasts by comparing them with observations. The probability distribution of the observed record is assumed to be perfect as a verification benchmark. In…

Methodology · Statistics 2021-08-06 Julie Bessac , Philippe Naveau

Two indicators are classically used to evaluate the quality of rule-based classification systems: predictive accuracy, i.e. the system's ability to successfully reproduce learning data and coverage, i.e. the proportion of possible cases for…

Artificial Intelligence · Computer Science 2020-04-07 Nassim Dehouche

Multivariate probabilistic time series forecasts are commonly evaluated via proper scoring rules, i.e., functions that are minimal in expectation for the ground-truth distribution. However, this property is not sufficient to guarantee good…

Machine Learning · Computer Science 2023-06-07 Étienne Marcotte , Valentina Zantedeschi , Alexandre Drouin , Nicolas Chapados

Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual terms in these averages are based on observations and forecasts from different distributions. We show that some of the most…

Statistics Theory · Mathematics 2022-03-29 David Bolin , Jonas Wallin

All proper scoring rules incentivize an expert to predict \emph{accurately} (report their true estimate), but not all proper scoring rules equally incentivize \emph{precision}. Rather than treating the expert's belief as exogenously given,…

Computer Science and Game Theory · Computer Science 2021-06-01 Eric Neyman , Georgy Noarov , S. Matthew Weinberg

When eliciting forecasts from a group of experts, it is important to reward predictions so that market participants are incentivized to tell the truth. Existing mechanisms partially accomplish this but remain susceptible to groups of…

Theoretical Economics · Economics 2024-11-26 Jack Edwards

Accurately forecasting the probability distribution of phenomena of interest is a classic and ever more widespread goal in statistics and decision theory. In comparison to point forecasts, probabilistic forecasts aim to provide a more…

Statistics Theory · Mathematics 2025-05-05 Erez Buchweitz , João Vitor Romano , Ryan J. Tibshirani

Risk scoring systems are widely used in high-stakes domains to assist decision-making. However, existing approaches often focus on optimizing predictive accuracy or likelihood-based criteria, which may not align with the main goal of…

Machine Learning · Computer Science 2026-04-07 Wenhao Chi , Ş. İlker Birbil

Inherent risk scoring is an important function in anti-money laundering, used for determining the riskiness of an individual during onboarding $\textit{before}$ fraudulent transactions occur. It is, however, often fraught with two…

Machine Learning · Computer Science 2018-12-02 W. Ronny Huang , Miguel A. Perez

Algorithmic decision systems are increasingly used in areas such as hiring, school admission, or loan approval. Typically, these systems rely on labeled data for training a classification model. However, in many scenarios, ground-truth…

Machine Learning · Computer Science 2021-07-19 Jakob Schoeffer , Niklas Kuehl , Isabel Valera

We advocate the use of conformal prediction (CP) to enhance rule-based multi-label classification (MLC). In particular, we highlight the mutual benefit of CP and rule learning: Rules have the ability to provide natural (non-)conformity…

Machine Learning · Computer Science 2020-12-09 Eyke Hüllermeier , Johannes Fürnkranz , Eneldo Loza Mencia

Recently, several authors have advocated the use of rule learning algorithms to model multi-label data, as rules are interpretable and can be comprehended, analyzed, or qualitatively evaluated by domain experts. Many rule learning…

Machine Learning · Computer Science 2020-12-09 Michael Rapp , Eneldo Loza Mencía , Johannes Fürnkranz

Forecasts of multivariate probability distributions are required for a variety of applications. Scoring rules enable the evaluation of forecast accuracy, and comparison between forecasting methods. We propose a theoretical framework for…

Statistics Theory · Mathematics 2026-01-30 Xiaochun Meng , James W. Taylor , Souhaib Ben Taieb , Siran Li

Scoring rules promote rational and honest decision-making, which is important for model evaluation and becoming increasingly important for automated procedures such as `AutoML'. In this paper we survey common squared and logarithmic scoring…

Statistics Theory · Mathematics 2025-06-03 Raphael Sonabend , John Zobolas , Riccardo Be Bin , Philipp Kopper , Lukas Burk , Andreas Bender

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

Machine Learning · Computer Science 2022-09-02 Zac Cranko , Robert C. Williamson , Richard Nock

Many forecasts consist not of point predictions but concern the evolution of quantities. For example, a central bank might predict the interest rates during the next quarter, an epidemiologist might predict trajectories of infection rates,…

Methodology · Statistics 2021-11-12 Patric Bonnier , Harald Oberhauser

Scoring rules are widely used to rank athletes in sports and candidates in elections. Each position in each individual ranking is worth a certain number of points; the total sum of points determines the aggregate ranking. The question is…

Computer Science and Game Theory · Computer Science 2022-09-09 Aleksei Y. Kondratev , Egor Ianovski , Alexander S. Nesterov

Methods for split conformal prediction leverage calibration samples to transform any prediction rule into a set-prediction rule that complies with a target coverage probability. Existing methods provide remarkably strong performance…

Machine Learning · Statistics 2025-10-15 Santiago Mazuelas