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Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model…

Methodology · Statistics 2023-03-20 Rina Foygel Barber , Emmanuel J. Candes , Aaditya Ramdas , Ryan J. Tibshirani

Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…

Methodology · Statistics 2025-03-04 Ning Xu , Christopher M. Foster , Jonathan H. Manton

Many popular algorithmic fairness measures depend on the joint distribution of predictions, outcomes, and a sensitive feature like race or gender. These measures are sensitive to distribution shift: a predictor which is trained to satisfy…

Machine Learning · Statistics 2022-02-11 Alan Mishler , Niccolò Dalmasso

A scoring rule is a function of a probabilistic forecast and a corresponding outcome that is used to evaluate forecast performance. A wide range of scoring rules have been defined over time and there is some debate as to which are the most…

Applications · Statistics 2019-08-27 Edward Wheatcroft

The artificial intelligence revolution is fueling a paradigm shift in weather forecasting: forecasts are generated with machine learning models trained on large datasets rather than with physics-based numerical models that solve partial…

Atmospheric and Oceanic Physics · Physics 2026-02-03 Zied Ben Bouallègue

Forecasting is usually framed as a problem of model choice. This paper starts earlier, asking how much predictive information is available at each horizon. Under logarithmic loss, the answer is exact: the mutual information between the…

Applications · Statistics 2026-03-31 Peter Maurice Catt

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are…

Machine Learning · Computer Science 2024-10-22 Yijie Zhang

Neural weather models have shown immense potential as inexpensive and accurate alternatives to physics-based models. However, most models trained to perform weather forecasting do not quantify the uncertainty associated with their…

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in…

Machine Learning · Computer Science 2021-11-17 Emily Black , Klas Leino , Matt Fredrikson

Many dependability techniques expect certain behaviors from the underlying subsystems and fail in chaotic ways if these expectations are not met. Under expected circumstances, however, software tends to work quite well. This paper suggests…

Operating Systems · Computer Science 2007-05-23 George Candea

We investigate the performance and sampling variability of estimated forecast combinations, with particular attention given to the combination of forecast distributions. Unknown parameters in the forecast combination are optimized according…

Methodology · Statistics 2022-06-07 Ryan Zischke , Gael M. Martin , David T. Frazier , D. S. Poskitt

This paper defines theoretical lower bounds of uncertainty of observations of macroeconomic variables that depend on statistical moments and correlations of random values and volumes of market trades. Any econometric assessments of…

General Economics · Economics 2024-10-08 Victor Olkhov

The discrepancy between realized volatility and the market's view of volatility has been known to predict individual equity options at the monthly horizon. It is not clear how this predictability depends on a forecast's ability to predict…

Statistical Finance · Quantitative Finance 2025-06-10 Austin Pollok

The common practice for displaying error bars on distributions of numbers of events is confusing and can lead to incorrect conclusions. A proposal is made for a different style of presentation that more directly indicates the level of…

Data Analysis, Statistics and Probability · Physics 2012-01-31 Ritu Aggarwal , Allen Caldwell

We propose a learning framework for calibrating predictive models to make loss-controlling prediction for exchangeable data, which extends our recently proposed conformal loss-controlling prediction for more general cases. By comparison,…

Machine Learning · Computer Science 2024-01-24 Di Wang , Junzhi Shi , Pingping Wang , Shuo Zhuang , Hongyue Li

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

Time series models often deal with extreme events and anomalies, both prevalent in real-world datasets. Such models often need to provide careful probabilistic forecasting, which is vital in risk management for extreme events such as…

Machine Learning · Statistics 2022-08-23 Ashkan Farhangi , Jiang Bian , Arthur Huang , Haoyi Xiong , Jun Wang , Zhishan Guo

Performance estimation aims at estimating the loss that a predictive model will incur on unseen data. These procedures are part of the pipeline in every machine learning project and are used for assessing the overall generalisation ability…

Machine Learning · Computer Science 2021-08-31 Vitor Cerqueira , Luis Torgo , Igor Mozetic

Improving algorithms via predictions is a very active research topic in recent years. This paper initiates the systematic study of mechanism design in this model. In a number of well-studied mechanism design settings, we make use of…

Computer Science and Game Theory · Computer Science 2023-01-13 Chenyang Xu , Pinyan Lu

Systematically biased forecasts are typically interpreted as evidence of forecasters' irrationality and/or asymmetric loss. In this paper we propose an alternative explanation: when forecasts inform policy decisions, and the resulting…

Theoretical Economics · Economics 2026-04-24 Robert P. Lieli , Augusto Nieto-Barthaburu