Bayesian Learning and Its Advanced Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D1: Probability and Statistics".

Deadline for manuscript submissions: 25 June 2025 | Viewed by 1081

Special Issue Editors


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Guest Editor
School of Mathematical and Physical Sciences, University of Sheffield, Sheffield, UK
Interests: Bayesian optimization; machine learning; multi-fidelity fusion; physics-enhanced machine learning; spatial–temporal field modeling for digital twins; machine learning techniques for engineering; electronic design automation

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Guest Editor
School of Computing, University of Utah, Salt Lake City, UT, USA
Interests: probabilistic machine learning; probabilistic graphical models; Bayesian deep learning; Bayesian nonparametrics; physics-informed machine learning; approximate inference; sparse learning; large-scale machine learning; kernel methods

Special Issue Information

Dear Colleagues,

This Special Issue focuses on the cutting-edge advancements and applications of Bayesian learning across various domains. Bayesian methods have gained significant traction in recent years due to their ability to quantify uncertainty, incorporate prior knowledge, and provide robust probabilistic frameworks for decision making. This Special Issue aims to showcase innovative research that pushes the boundaries of Bayesian learning, exploring its intersection with deep learning, physics-informed models, and large-scale data analysis. This Special Issue welcomes contributions that address theoretical developments, novel algorithms, and practical applications of Bayesian learning.

Topics of interest include, but are not limited to, the following:

  • Bayesian optimization;
  • Multi-fidelity fusion;
  • Physics-enhanced machine learning;
  • Spatial–temporal field modeling for digital twins;
  • Probabilistic graphical models;
  • Bayesian deep learning;
  • Approximate inference techniques;
  • Sparse learning methods.

We particularly encourage submissions that demonstrate the power of Bayesian approaches in solving complex real-world problems in engineering, electronic design automation, and other data-intensive fields.

This Special Issue seeks to bring together researchers and practitioners to share their latest findings, fostering cross-disciplinary collaborations and advancing the state of the art in Bayesian learning and its applications.

Dr. Wei W. Xing
Dr. Shandian Zhe
Guest Editors

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Keywords

  • Bayesian learning
  • variational inference
  • Markov chain Monte Carlo (MCMC)
  • Bayesian neural networks
  • probabilistic graphical models
  • Bayesian optimization
  • Bayesian nonparametrics
  • approximate Bayesian computation (ABC)
  • Bayesian model selection
  • Bayesian reinforcement learning
  • uncertainty quantification
  • multi-fidelity modeling
  • physics-informed machine learning
  • spatial–temporal modeling
  • digital twins
  • Bayesian methods for design and optimization

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Published Papers (2 papers)

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Research

20 pages, 3616 KiB  
Article
Bayesian Prototypical Pruning for Transformers in Human–Robot Collaboration
by Bohua Peng and Bin Chen
Mathematics 2025, 13(9), 1411; https://doi.org/10.3390/math13091411 - 25 Apr 2025
Abstract
Action representations are essential for developing mutual cognition toward efficient human–AI collaboration, particularly in human–robot collaborative (HRC) workspaces. As such, it has become an emerging research direction for robots to understand human intentions with video Transformers. Despite their remarkable success in capturing long-range [...] Read more.
Action representations are essential for developing mutual cognition toward efficient human–AI collaboration, particularly in human–robot collaborative (HRC) workspaces. As such, it has become an emerging research direction for robots to understand human intentions with video Transformers. Despite their remarkable success in capturing long-range dependencies, local redundancy in video frames can add up to the inference latency of Transformers due to overparameterization. Recently, token pruning has become a computationally efficient solution that selectively removes input tokens with minimal impact on task performance. However, existing sparse coding methods often have an exhaustive threshold searching process, leading to intensive hyperparameter search. In this paper, Bayesian Prototypical Pruning (ProtoPrune), a novel end-to-end Bayesian framework, is proposed for token pruning in video understanding. To improve robustness, ProtoPrune leverages prototypical contrastive learning for fine-grained action representations, bringing sub-action level supervision to the video token pruning task. With variational dropout, our method bypasses the exhaustive threshold searching process. Experiments show that the proposed method can achieve a pruning rate of 37.2% while retaining 92.9% of task performance using Uniformer and ActionCLIP, which significantly improves computational efficiency. Convergence analysis ensures the stability of our method. The proposed efficient video understanding method offers a theoretically grounded and hardware-friendly solution for deploying video Transformers in real-world HRC environments. Full article
(This article belongs to the Special Issue Bayesian Learning and Its Advanced Applications)
13 pages, 1953 KiB  
Article
Quantifying Uncertainty of Insurance Claims Based on Expert Judgments
by Budhi Handoko, Yeny Krista Franty and Fajar Indrayatna
Mathematics 2025, 13(2), 245; https://doi.org/10.3390/math13020245 - 13 Jan 2025
Viewed by 662
Abstract
In Bayesian statistics, prior specification has an important role in determining the quality of posterior estimates. We use expert judgments to quantify uncertain quantities and produce appropriate prior distribution. The aim of this study was to quantify the uncertainty of life insurance claims, [...] Read more.
In Bayesian statistics, prior specification has an important role in determining the quality of posterior estimates. We use expert judgments to quantify uncertain quantities and produce appropriate prior distribution. The aim of this study was to quantify the uncertainty of life insurance claims, especially on the policy owner’s age, as it is the main factor determining the insurance premium. A one-day workshop was conducted to elicit expert judgments from those who have experience in accepting claims. Four experts from different insurance companies were involved in the workshop. The elicitation protocol used in this study was The Sheffield Elicitation Framework (SHELF), which produces four different statistical distributions for each expert. A linear pooling method was used to aggregate the distributions to obtain the consensus distribution among experts. The consensus distribution suggested that the majority of policy owners will make a claim at the age of 54 years old. Full article
(This article belongs to the Special Issue Bayesian Learning and Its Advanced Applications)
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