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arXiv 2025年

作者： Jürgens, Mira Mortier, Thomas Hüllermeier, Eyke Bengs, Viktor Waegeman, Willem Department of Data Analysis and Mathematical Modeling Ghent University Belgium Department of Environment Ghent University Belgium Department of Informatics Munich Center for Machine Learning LMU Munich Germany

The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of constructing these credal sets is via ensembling or specialized supervised learning methods, where the epistemic uncertainty can be quantified through measures such as the set size or the disagreement among members. In principle, these sets should contain the true data-generating distribution. As a necessary condition for this validity, we adopt the strongest notion of calibration as a proxy. Concretely, we propose a novel statistical test to determine whether there is a convex combination of the set’s predictions that is calibrated in distribution. In contrast to previous methods, our framework allows the convex combination to be instance dependent, recognizing that different ensemble members may be better calibrated in different regions of the input space. Moreover, we learn this combination via proper scoring rules, which inherently optimize for calibration. Building on differentiable, kernel-based estimators of calibration errors, we introduce a nonparametric testing procedure and demonstrate the benefits of capturing instance-level variability on of synthetic and real-world experiments. © 2025, CC BY.

关键词： Self-supervised learning

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Statistical inference for smoothed quantile regression with streaming data

引用

Journal of Econometrics 2025年 249卷

作者： Xie, Jinhan Yan, Xiaodong Jiang, Bei Kong, Linglong Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming650091 China Department of Mathematical and Statistical Sciences University of Alberta Edmonton AlbertaT6G 2G1 Canada School of Mathematics and Statistics Xi'an Jiaotong University China

In this paper, we tackle the problem of conducting valid statistical inference for quantile regression with streaming data. The main difficulties are that the quantile regression loss function is non-smooth and it is often infeasible to store the entire dataset in memory, rendering traditional methodologies ineffective. We introduce a fully online updating method for statistical inference in smoothed quantile regression with streaming data to overcome these issues. Our main contributions are twofold. First, for low-dimensional data, we present an incremental updating algorithm to obtain the smoothed quantile regression estimator with the streaming data set. The proposed estimator allows us to construct asymptotically exact statistical inference procedures. Second, within the realm of high-dimensional data, we develop an online debiased lasso procedure to accommodate the special sparse structure of streaming data. The proposed online debiased approach is updated with only the current data and summary statistics of historical data and corrects an approximation error term from online updating with streaming data. Furthermore, theoretical results such as estimation consistency and asymptotic normality are established to justify its validity in both settings. Our findings are supported by simulation studies and illustrated through applications to Seoul's bike-sharing demand data and index fund data. © 2024

关键词： Logistic regression

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Online federated learning framework for classification

arXiv

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arXiv 2025年

作者： Guo, Wenxing Xie, Jinhan Lu, Jianya Jiang, Bei Dai, Hongsheng Kong, Linglong School of Mathematics Statistics and Actuarial Science University of Essex ColchesterCO4 3SQ United Kingdom Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming650091 China Department of Mathematical and Statistical Sciences University of Alberta EdmontonABT6G 2G1 Canada School of Mathematics Statistics and Physics Newcastle University Newcastle upon TyneNE1 7RU United Kingdom

In this paper, we develop a novel online federated learning framework for classification, designed to handle streaming data from multiple clients while ensuring data privacy and computational efficiency. Our method leverages the generalized distance-weighted discriminant technique, making it robust to both homogeneous and heterogeneous data distributions across clients. In particular, we develop a new optimization algorithm based on the Majorization-Minimization principle, integrated with a renewable estimation procedure, enabling efficient model updates without full retraining. We provide a theoretical guarantee for the convergence of our estimator, proving its consistency and asymptotic normality under standard regularity conditions. In addition, we establish that our method achieves Bayesian risk consistency, ensuring its reliability for classification tasks in federated environments. We further incorporate differential privacy mechanisms to enhance data security, protecting client information while maintaining model performance. Extensive numerical experiments on both simulated and real-world datasets demonstrate that our approach delivers high classification accuracy, significant computational efficiency gains, and substantial savings in data storage requirements compared to existing methods. © 2025, CC BY.

关键词： Federated learning

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Investigating the sensitivity of nanofluid flow around a cylindrical disk: A study of Walter's B nanofluid using response surface methodology and artificial neural networks

Journal of Engineering Research (Kuwait)

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Journal of Engineering Research (Kuwait) 2025年

作者： Shafiq, Anum Çolak, Andaç Batur Sindhu, Tabassum Naz Abushal, Tahani A. School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing 210044 China Department of Information Systems and Technologies Niğde Ömer Halisdemir University Niğde 51240 United States Department of Statistics Quaid-I-Azam University Islamabad 44000 Pakistan Department of Mathematical Sciences Umm Al-Qura University Makkah 24382 Saudi Arabia

Modern technology development heavily relies on nanotechnology, which has gained significant attention from researchers in recent years, particularly in finding ways to enhance heat transfer rates. One approach to addressing this issue is to use nanoparticles in host fluids to greatly improve their thermal properties. This study employed response surface methods to investigate the Walter's B nanofluid, incorporating thermophoresis, Brownian diffusion, activation energy, and thermal radiation, using the Buongiorno model to examine nanofluid properties. To reduce the formed system of flow equations into a dimensionless differential form system, appropriate variables were used. In addition, we build a dataset for the proposed multilayer perceptron neural network using the Runge-Kutta fourth-order shooting method. The study analyzed effects of flow variables on the velocity field, temperature field, and species volumetric concentration fields, and probable error correlation coefficients were calculated to evaluate the statistical significance of the parameters. Additionally, a sensitivity analysis was conducted, which showed that with a high thermophoresis number, the Nusselt number is more sensitive. © 2024 The Authors

关键词： Artificial neural networks Brownian motion Response surface methodology (RSM) Sensitivity analysis Thermophoresis Walter's B nanofluid

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Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods? 41

Is Epistemic Uncertainty Faithfully Represented by Evidentia...

引用

41st International Conference on Machine Learning, ICML 2024

作者： Jürgens, Mira Meinert, Nis Bengs, Viktor Hüllermeier, Eyke Waegeman, Willem Department of Data Analysis and Mathematical Modeling Ghent University Belgium Neustrelitz Germany Germany

Trustworthy ML systems should not only return accurate predictions, but also a reliable representation of their uncertainty. Bayesian methods are commonly used to quantify both aleatoric and epistemic uncertainty, but alternative approaches, such as evidential deep learning methods, have become popular in recent years. The latter group of methods in essence extends empirical risk minimization (ERM) for predicting second-order probability distributions over outcomes, from which measures of epistemic (and aleatoric) uncertainty can be extracted. This paper presents novel theoretical insights of evidential deep learning, highlighting the difficulties in optimizing second-order loss functions and interpreting the resulting epistemic uncertainty measures. With a systematic setup that covers a wide range of approaches for classification, regression and counts, it provides novel insights into issues of identifiability and convergence in second-order loss minimization, and the relative (rather than absolute) nature of epistemic uncertainty measures. Copyright 2024 by the author(s)

关键词： Contrastive Learning

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Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation 36

Pitfalls of Epistemic Uncertainty Quantification through Los...

引用

36th Conference on Neural Information Processing Systems, NeurIPS 2022

作者： Bengs, Viktor Hüllermeier, Eyke Waegeman, Willem Germany Munich Center for Machine Learning Germany Department of Data Analysis and Mathematical Modeling Ghent University Belgium

ISBN: (纸本)9781713871088

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way. © 2022 Neural information processing systems foundation. All rights reserved.

关键词： Probability distributions

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Machine Learning Models and Technology for Classification of Forest on Satellite data 20

Machine Learning Models and Technology for Classification of...

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20th International Conference on Smart Technologies, EUROCON 2023

作者： Salii, Yevhenii Kuzin, Volodymyr Hohol, Anton Kussul, Nataliia Yailymova, Hanna National Technical University of Ukraine 'Igor Sikorsky Kyiv Polytechnic Institute' Department of Mathematical Modeling and Data Analysis Kyiv Ukraine National University of 'Kyiv-Mohyla Academy' Department of Informatics Kyiv Ukraine National Technical University of Ukraine 'Igor Sikorsky Kyiv Polytechnic Institute' Department of Space Information Technologies and Systems Space Research Institute NASU-SSAU Department of Mathematical Modeling and Data Analysis Kyiv Ukraine

ISBN: (纸本)9781665463973

The paper deals with the problem of semantic segmentation of satellite imagery to deliver forest type map with high resolution. To solve the problem, we propose 4 machine learning models. Two of them are based on Random Forest (RF) and other two - on Convolutional Neural Network (CNN) - U-Net. As an input we use 2 images of Sentinel-2 (one for summer and one for winter, 4 spectral bands from each). As an output (labels) we use the Copernicus Forest Type dataset for 2018 year. Our models showed promising results on validation data. Of all models the one based on U-Net ended up being the most efficient in forest classification with overall accuracy 91.7%. At the same time the best RF model scored with 86.5%. After comparing the results, in order to check our model transferability we created and compared forest map of northern part of Kyiv region of 2018 and 2022. The experiment confirmed the robustness of the model and it's scalability. The developed models have been implemented in the cloud platform specialized on satellite data - CREODIAS. The developed map can provide valuable data for foresters, biologists, or other researchers to make decisions about forest management and conservation, as well as to ensure that Europe's forests are managed in an ecologically sustainable way. © 2023 IEEE.

关键词： Machine learning

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Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?

arXiv

引用

arXiv 2024年

作者： Jürgens, Mira Meinert, Nis Bengs, Viktor Hüllermeier, Eyke Waegeman, Willem Department of Data Analysis and Mathematical Modeling Ghent University Belgium Neustrelitz Germany Germany

关键词： Contrastive Learning

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Geospatial analysis of Leased Lands in Ukraine

Geospatial Analysis of Leased Lands in Ukraine

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2021 IEEE International Conference on Information and Telecommunication Technologies and Radio Electronics, UkrMiCo 2021

作者： Shelestov, Andrii Yailymov, Bohdan Parkhomchuk, Oleksandr Department of Mathematical Modeling and Data Analysis National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute» Kyiv Ukraine Department of Space Information Systems and Services Space Research Institute NAS Ukraine SSA Ukraine Kyiv Ukraine

ISBN: (纸本)9781665426527

With the opening of the land market, the analysis of leased land in Ukraine becomes more and more important. On the base of remote sensing data we can use additional capabilities and tools to analyze and predict the state of the land. Thanks to the public cadastral map, we can check our results on the base of up-to date official information. In this article we have analyzed the large leased fields in the Kyiv region. In particular, operations had performed on geospatial objects with georeference, as on sets of pixels. The main purpose of this work is to use a crop classification map and geographic information systems in order to find large areas, and check the information about the tenant using the service of state geocadastre. © 2021 UkrMiCo 2021 - 2021 IEEE International Conference on Information and Telecommunication Technologies and Radio Electronics, Proceedings. All rights reserved.

关键词： Remote sensing

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ON SECOND-ORDER SCORING RULES FOR EPISTEMIC UNCERTAINTY QUANTIFICATION

arXiv

引用

arXiv 2023年

作者： Bengs, Viktor Hüllermeier, Eyke Waegeman, Willem Munich Center for Machine Learning Germany Department of Data Analysis and Mathematical Modeling Ghent University Belgium

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 methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring *** Codes 68T37 (Primary) 68T30 (Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Probability distributions

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