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Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…

Methodology · Statistics 2025-05-23 Sam Allen , Jonathan Koh , Johan Segers , Johanna Ziegel

While deep learning models often achieve high predictive accuracy, their predictions typically do not come with any provable guarantees on risk or reliability, which are critical for deployment in high-stakes applications. The framework of…

Machine Learning · Computer Science 2025-10-13 Christopher Yeh , Nicolas Christianson , Adam Wierman , Yisong Yue

We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible…

Risk Management · Quantitative Finance 2013-01-22 Thomas Breuer , Imre Csiszar

We analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the…

Machine Learning · Statistics 2014-10-28 Chang Xu , Tongliang Liu , Dacheng Tao , Chao Xu

The increasing penetration of embedded renewables makes forecasting net-load, consumption less embedded generation, a significant and growing challenge. Here a framework for producing probabilistic forecasts of net-load is proposed with…

Applications · Statistics 2022-10-06 Jethro Browell , Matteo Fasiolo

In recent years research on credit risk modelling has mainly focused on default probabilities. Recovery rates are usually modelled independently, quite often they are even assumed constant. Then, however, the structural connection between…

Risk Management · Quantitative Finance 2015-03-06 Alexander F. R. Koivusalo , Rudi Schäfer

To ensure that real-world infrastructure is safe and durable, systems are designed to not fail for any but the most rarely occurring parameter values. By only happening deep in the tails of the parameter distribution, failure probabilities…

Methodology · Statistics 2025-05-27 Promit Chakroborty , Michael D. Shields

Long-tailed classification is challenging due to its heavy imbalance in class probabilities. While existing methods often focus on overall accuracy or accuracy for tail classes, they overlook a critical aspect: certain types of errors can…

Machine Learning · Computer Science 2025-01-27 Bolian Li , Ruqi Zhang

Quantifying the data uncertainty in learning tasks is often done by learning a prediction interval or prediction set of the label given the input. Two commonly desired properties for learned prediction sets are \emph{valid coverage} and…

Machine Learning · Computer Science 2022-05-31 Yu Bai , Song Mei , Huan Wang , Yingbo Zhou , Caiming Xiong

Value-at-Risk (VaR) estimation at high confidence levels is inherently a rare-event problem and is particularly sensitive to tail behavior and model misspecification. This paper studies the performance of two simulation-based VaR estimation…

Risk Management · Quantitative Finance 2026-01-16 Aditri

We investigate high-dimensional sparse regression when both the noise and the design matrix exhibit heavy-tailed behavior. Standard algorithms typically fail in this regime, as heavy-tailed covariates distort the empirical risk geometry. We…

Methodology · Statistics 2026-01-12 Kaiyuan Zhou , Xiaoyu Zhang , Wenyang Zhang , Di Wang

In risk analysis, a global fit that appropriately captures the body and the tail of the distribution of losses is essential. Modelling the whole range of the losses using a standard distribution is usually very hard and often impossible due…

Methodology · Statistics 2017-09-19 Tom Reynkens , Roel Verbelen , Jan Beirlant , Katrien Antonio

An interesting phenomenon arises: Empirical Risk Minimization (ERM) sometimes outperforms methods specifically designed for out-of-distribution tasks. This motivates an investigation into the reasons behind such behavior beyond algorithmic…

Machine Learning · Computer Science 2026-01-21 Hong Zheng , Fei Teng

Fairness-aware learning is a novel framework for classification tasks. Like regular empirical risk minimization (ERM), it aims to learn a classifier with a low error rate, and at the same time, for the predictions of the classifier to be…

Machine Learning · Statistics 2015-06-26 Kazuto Fukuchi , Jun Sakuma

In order to circumvent statistical and computational hardness results in sequential decision-making, recent work has considered smoothed online learning, where the distribution of data at each time is assumed to have bounded likeliehood…

Machine Learning · Statistics 2024-02-26 Adam Block , Alexander Rakhlin , Abhishek Shetty

Empirical risk minimization stands behind most optimization in supervised machine learning. Under this scheme, labeled data is used to approximate an expected cost (risk), and a learning algorithm updates model-defining parameters in search…

Machine Learning · Statistics 2023-05-25 James Schmidt

In this article, by using composite asymmetric least squares (CALS) and empirical likelihood, we propose a two-step procedure to estimate the conditional value at risk (VaR) and conditional expected shortfall (ES) for the GARCH series.…

Statistics Theory · Mathematics 2018-07-05 Sheng Wu , Yi Zhang , Jun Zhao , Liming Shen

We introduce a new actuarial tail-shape index, the $\theta$-index, based on a probability equal level relationship between Value at Risk and Expected Shortfall. The index is defined at each tail probability level as the parameter value for…

Risk Management · Quantitative Finance 2026-01-29 Georgios I. Papayiannis , Georgios Psarrakos

Expectile, as the minimizer of an asymmetric quadratic loss function, is a coherent risk measure and is helpful to use more information about the distribution of the considered risk. In this paper, we propose a new risk measure by replacing…

Methodology · Statistics 2023-10-31 Qian Xiong , Zuoxiang Peng

Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to 'mine' variables of interest…

Econometrics · Economics 2020-12-22 Mochen Yang , Edward McFowland , Gordon Burtch , Gediminas Adomavicius
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