Probability and Statistics Theory in Symmetry and Application from Machine Learning to Biomedical Data

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 15 July 2024 | Viewed by 1198

Special Issue Editors


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Guest Editor
Department of Information Sciences and Mathematics, Dong-A University, Busan 49315, Republic of Korea
Interests: limit theorems; random walks; Hawkes process; probability theory; stochastic process applications and data analytic and machine learning

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Guest Editor
Department of Translational Biomedical Sciences, College of Medicine, Dong-A University, Busan 49201, Republic of Korea
Interests: brain; diseases; image classification; medical image processing; neurophysiology; positron emission tomography; biomedical MRI; cognition; computerised tomography; feature extraction; image segmentation; neural nets; unsupervised learning
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Management and Information Systems, Dong-A University, Busan 49315, Republic of Korea
Interests: data mining; machine learning; deep learning; statistical analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Probability and statistics in symmetry have become important topics of study in recent years, possessing wide applications in various fields including medicine, biology, economics, engineering, and physics. Specifically, stochastic processes have come to play fundamental roles in the mathematical model of phenomena in wide areas, such as symmetric random walks, random walks in a random environment, Hawkes processes, etc. The study of these phenomena and applications has led to the development of new stochastic processes. Some important probability laws are heavy-tailed distributions, which can be modeled with discretizations of random variables or measured by parameters of either new or old statistical models. The growing data resources have led to the introduction of a variety of distributions and their properties.

The adoption of machine learning and deep learning analytics in the bio-medical field with symmetry properties is progressing at a rapid pace, with some applications already finding use in pre-clinical and clinical settings. In addition, various types of bio-medical data continue to be used, and CNN, RNN, and transform technologies used for analysis continue to undergo further development. There are many types of bio-medical data, such as image data, pathological tissue data, waveform data, natural language data, genetic data, voice data, etc.

The purpose of this Special Issue is to provide a collection of articles that reflect the importance of statistics and probability in symmetry and its applications in several areas, and also to assemble the current research on the latest machine learning and deep learning techniques of various bio-medical data with symmetry properties. Additionally, we would welcome hypotheses for a fusion analysis technique of various bio-medical data.

Dr. Youngsoo Seol
Prof. Dr. Do-Young Kang
Dr. Sangjin Kim
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • limit theorems
  • probability and statistics
  • stochastic processes and its applications

Published Papers (1 paper)

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Research

23 pages, 338 KiB  
Article
Conditional Strong Law of Large Numbers under G-Expectations
by Jiaqi Zhang, Yanyan Tang and Jie Xiong
Symmetry 2024, 16(3), 272; https://doi.org/10.3390/sym16030272 - 25 Feb 2024
Viewed by 688
Abstract
In this paper, we investigate two types of the conditional strong law of large numbers with a new notion of conditionally independent random variables under G-expectation which are related to the symmetry G-function. Our limit theorem demonstrates that the cluster points [...] Read more.
In this paper, we investigate two types of the conditional strong law of large numbers with a new notion of conditionally independent random variables under G-expectation which are related to the symmetry G-function. Our limit theorem demonstrates that the cluster points of empirical averages fall within the bounds of the lower and upper conditional expectations with lower probability one. Moreover, for conditionally independent random variables with identical conditional distributions, we show the existence of two cluster points of empirical averages that correspond to the essential minimum and essential maximum expectations, respectively, with G-capacity one. Full article
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