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People are commonly interested in predicting a statistical property of a random event such as mean and variance. Proper scoring rules assess the quality of predictions and require that the expected score gets uniquely maximized at the…

Machine Learning · Computer Science 2025-06-24 Lingfang Hu , Ian A. Kash

Can one estimate the number of remaining faults in a software system? A credible estimation technique would be immensely useful to project managers as well as customers. It would also be of theoretical interest, as a general law of software…

Software Engineering · Computer Science 2013-08-14 Carlo A. Furia , Bertrand Meyer , Manuel Oriol , Andrey Tikhomirov , Yi Wei

Probabilistic forecasting relies on past observations to provide a probability distribution for a future outcome, which is often evaluated against the realization using a scoring rule. Here, we perform probabilistic forecasting with…

Machine Learning · Statistics 2024-03-06 Lorenzo Pacchiardi , Rilwan Adewoyin , Peter Dueben , Ritabrata Dutta

This study introduces novel superior scoring rules called Penalized Brier Score (PBS) and Penalized Logarithmic Loss (PLL) to improve model evaluation for probabilistic classification. Traditional scoring rules like Brier Score and…

Machine Learning · Computer Science 2025-05-05 Rouhollah Ahmadian , Mehdi Ghatee , Johan Wahlström

We provide methods to validate and compare sensor outputs, or inference algorithms applied to sensor data, by adapting statistical scoring rules. The reported output should either be in the form of a prediction interval or of a parameter…

Data Analysis, Statistics and Probability · Physics 2015-07-07 A. D. Martin , T. C. A. Molteno , M. Parry

Scoring rules are aimed at evaluation of the quality of predictions, but can also be used for estimation of parameters in statistical models. We propose estimating parameters of multivariate spatial models by maximising the average…

Methodology · Statistics 2024-08-23 Helga Kristin Olafsdottir , Holger Rootzén , David Bolin

Operational earthquake forecasting for risk management and communication during seismic sequences depends on our ability to select an optimal forecasting model. To do this, we need to compare the performance of competing models with each…

Applications · Statistics 2022-04-20 Francesco Serafini , Mark Naylor , Finn Lindgren , Maximilian Werner , Ian Main

Graded labels are ubiquitous in real-world learning-to-rank applications, especially in human rated relevance data. Traditional learning-to-rank techniques aim to optimize the ranked order of documents. They typically, however, ignore…

Information Retrieval · Computer Science 2023-06-21 Le Yan , Zhen Qin , Gil Shamir , Dong Lin , Xuanhui Wang , Mike Bendersky

Performative predictions are forecasts which influence the outcomes they aim to predict, undermining the existence of correct forecasts and standard methods of elicitation and estimation. We show that conditioning forecasts on covariates…

Statistics Theory · Mathematics 2025-10-27 Philip Boeken , Onno Zoeter , Joris M. Mooij

Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting…

Other Statistics · Statistics 2023-03-28 László Csató

State-of-the-art results in typical classification tasks are mostly achieved by unexplainable machine learning methods, like deep neural networks, for instance. Contrarily, in this paper, we investigate the application of rule learning…

Machine Learning · Computer Science 2024-03-11 Albert Nössig , Tobias Hell , Georg Moser

This paper forges a strong connection between two seemingly unrelated forecasting problems: incentive-compatible forecast elicitation and forecast aggregation. Proper scoring rules are the well-known solution to the former problem. To each…

Computer Science and Game Theory · Computer Science 2023-08-22 Eric Neyman , Tim Roughgarden

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various…

Machine Learning · Computer Science 2023-01-31 Viktor Bengs , Eyke Hüllermeier , Willem Waegeman

A falling rule list is a probabilistic decision list for binary classification, consisting of a series of if-then rules with antecedents in the if clauses and probabilities of the desired outcome ("1") in the then clauses. Just as in a…

Machine Learning · Computer Science 2018-03-21 Chaofan Chen , Cynthia Rudin

We discuss weighted scoring rules for forecast evaluation and their connection to hypothesis testing. First, a general construction principle for strictly locally proper weighted scoring rules based on conditional densities and scoring…

Methodology · Statistics 2017-01-12 Hajo Holzmann , Bernhard Klar

Virtually all machine learning tasks are characterized using some form of loss function, and "good performance" is typically stated in terms of a sufficiently small average loss, taken over the random draw of test data. While optimizing for…

Machine Learning · Statistics 2023-12-01 Matthew J. Holland , Kazuki Tanabe

Strategic classification studies learning in settings where self-interested users can strategically modify their features to obtain favorable predictive outcomes. A key working assumption, however, is that "favorable" always means…

Machine Learning · Computer Science 2022-06-22 Sagi Levanon , Nir Rosenfeld

In credit markets, screening algorithms aim to discriminate between good-type and bad-type borrowers. However, when doing so, they can also discriminate between individuals sharing a protected attribute (e.g. gender, age, racial origin) and…

Machine Learning · Statistics 2024-02-09 Christophe Hurlin , Christophe Pérignon , Sébastien Saurin

Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…

Methodology · Statistics 2019-01-08 Federica Giummolè , Valentina Mameli , Erlis Ruli , Laura Ventura

I introduce a model of predictive scoring. A receiver wants to predict a sender's quality. An intermediary observes multiple features of the sender and aggregates them into a score. Based on the score, the receiver makes a decision. The…

Theoretical Economics · Economics 2024-05-17 Ian Ball