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Access to multiple predictive models trained for the same task, whether in regression or classification, is increasingly common in many applications. Aggregating their predictive uncertainties to produce reliable and efficient uncertainty…

Machine Learning · Statistics 2026-03-06 Nabil Alami , Jad Zakharia , Souhaib Ben Taieb

Conformal prediction is a framework for uncertainty quantification that constructs prediction sets for previously unseen data, guaranteeing coverage of the true label with a specified probability. However, the efficiency of these prediction…

Machine Learning · Computer Science 2026-01-06 Erfan Hajihashemi , Yanning Shen

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

Time series anomaly detection is critical for modern digital infrastructures, yet existing methods lack systematic cross-domain evaluation. We present a comprehensive forecasting-based framework unifying classical methods (Holt-Winters,…

Machine Learning · Computer Science 2025-10-14 Mohammad Karami , Mostafa Jalali , Fatemeh Ghassemi

The rise of parallel computing hardware has made it increasingly important to understand which nonlinear state space models can be efficiently parallelized. Recent advances like DEER (arXiv:2309.12252) and DeepPCR (arXiv:2309.16318) recast…

Optimization and Control · Mathematics 2026-02-10 Xavier Gonzalez , Leo Kozachkov , David M. Zoltowski , Kenneth L. Clarkson , Scott W. Linderman

Accurate forecasts are vital for supporting the decisions of modern companies. Forecasters typically select the most appropriate statistical model for each time series. However, statistical models usually presume some data generation…

Calibration is a pivotal aspect in predictive modeling, as it ensures that the predictions closely correspond with what we observe empirically. The contemporary calibration framework, however, is predominantly focused on prediction models…

Methodology · Statistics 2023-09-18 Bavo De Cock Campo

This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…

Machine Learning · Computer Science 2024-06-12 Andres Altieri , Marco Romanelli , Georg Pichler , Florence Alberge , Pablo Piantanida

When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly…

Time series forecasting plays a vital role in various real-world applications and has attracted significant attention in recent decades. While recent methods have achieved remarkable accuracy by incorporating advanced inductive biases and…

Machine Learning · Computer Science 2025-12-16 Zhiding Liu , Mingyue Cheng , Guanhao Zhao , Jiqian Yang , Qi Liu , Enhong Chen

Within the field of complicated multivariate time series forecasting (TSF), popular techniques frequently rely on intricate deep learning architectures, ranging from transformer-based designs to recurrent neural networks. However, recent…

Machine Learning · Computer Science 2023-12-25 Aiyinsi Zuo , Haixi Zhang , Zirui Li , Ce Zheng

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

Chaotic Dynamics · Physics 2025-10-06 Chenyu Dong , Davide Faranda , Adriano Gualandi , Valerio Lucarini , Gianmarco Mengaldo

Hierarchical forecasting is a key problem in many practical multivariate forecasting applications - the goal is to simultaneously predict a large number of correlated time series that are arranged in a pre-specified aggregation hierarchy.…

Machine Learning · Computer Science 2021-10-13 Biswajit Paria , Rajat Sen , Amr Ahmed , Abhimanyu Das

Machine learning classification tasks often benefit from predicting a set of possible labels with confidence scores to capture uncertainty. However, existing methods struggle with the high-dimensional nature of the data and the lack of…

Machine Learning · Computer Science 2024-07-08 Rui Luo , Zhixin Zhou

In recent years, specific evaluation metrics for time series anomaly detection algorithms have been developed to handle the limitations of the classical precision and recall. However, such metrics are heuristically built as an aggregate of…

Machine Learning · Computer Science 2022-10-13 Alexis Huet , Jose Manuel Navarro , Dario Rossi

Large pretrained foundation models demonstrate exceptional performance and, in some high-stakes applications, even surpass human experts. However, most of these models are currently evaluated primarily on prediction accuracy, overlooking…

Machine Learning · Computer Science 2024-11-08 Tang Li , Mengmeng Ma , Xi Peng

Conformal Prediction (CP) is a popular method for uncertainty quantification with machine learning models. While conformal prediction provides probabilistic guarantees regarding the coverage of the true label, these guarantees are agnostic…

Machine Learning · Computer Science 2025-10-21 Aditya T. Vadlamani , Anutam Srinivasan , Pranav Maneriker , Ali Payani , Srinivasan Parthasarathy

Accurate evaluation of forecasting models is essential for ensuring reliable predictions. Current practices for evaluating and comparing forecasting models focus on summarising performance into a single score, using metrics such as SMAPE.…

Machine Learning · Statistics 2024-06-25 Vitor Cerqueira , Luis Roque , Carlos Soares

Financial forecasting increasingly uses large neural network models, but their opacity raises challenges for trust and regulatory compliance. We present several approaches to explainable and reliable AI in finance. \emph{First}, we describe…

Machine Learning · Computer Science 2025-10-31 Albi Isufaj , Pablo Mollá , Helmut Prendinger

This paper introduces a novel decision-making framework that promotes consistency among decisions made by diverse models while utilizing external knowledge. Leveraging the Integer Linear Programming (ILP) framework, we map predictions from…

Artificial Intelligence · Computer Science 2024-02-07 Hossein Rajaby Faghihi , Parisa Kordjamshidi