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Mathematics
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Probability, Stochastic Processes and Machine Learning
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Probability, Stochastic Processes and Machine Learning

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: closed (15 February 2025) | Viewed by 2205

Special Issue Editors

Dr. Qidi Peng

E-Mail Website
Guest Editor
Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, USA
Interests: multifractional process; statistical inferences; Malliavin calculus; stochastic differential equations; stochastic modeling; process simulation; unsupervised learning on processes; approximation theory; graph theory
Prof. Dr. Sunil Kumar

E-Mail Website
Guest Editor
Department of Electrical and Computer Engineering, San Diego State University, San Diego, CA 92182-1309, USA
Interests: cross-layer wireless network protocols; ad hoc networks; resource allocation; directional networks; cognitive networks
Special Issues, Collections and Topics in MDPI journals
Dr. Yu Bai

E-Mail Website
Guest Editor
College of Engineering and Computer Science, California State University, Fullerton, CA 90032, USA
Interests: artificial intelligence (AI); embedded hardware; neuromorphic computing; nano-scale computing system with novel silicon and post-silicon devices, and low-power digital and mixed-signal CMOS circuit design
Special Issues, Collections and Topics in MDPI journals
Dr. Chengcheng Zhang

E-Mail
Guest Editor Assistant
Department of Health Sciences, Towson University, Towson, MD 21252, USA
Interests: statistical inferences; health economics; econometrics; applied microeconomics

Special Issue Information

Dear Colleagues,

This Special Issue on "Probability, Stochastic Processes and Machine Learning" aims to discuss the advances at the intersection of probability theory, stochastic processes, machine learning, and their real-world applications. As machine learning has been successfully applied to an increasing number of fields, new challenges arise from applying traditional machine learning approaches to new data structures, such as images, stochastic processes, and high-dimensional signals. This issue aims to collect high-quality research works on the discussion of machine learning on high-dimensional datasets, or datasets which are indexed by time. Both methodologies and successful real-world applications will be appreciated.

Dr. Qidi Peng
Prof. Dr. Sunil Kumar
Dr. Yu Bai
Guest Editors

Dr. Chengcheng Zhang
Guest Editor Assistant

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • cluster analysis
  • signal processing
  • image recognition
  • natural language processing

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Published Papers (2 papers)

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Research

39 pages, 806 KiB  
Article
Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure
by Said Attaoui, Oum Elkheir Benouda, Salim Bouzebda and Ali Laksaci
Mathematics 2025, 13(5), 886; https://doi.org/10.3390/math13050886 - 6 Mar 2025
Viewed by 388
Abstract
In this paper, we develop kernel-based estimators for regression functions under a functional single-index model, applied to censored time series data. By capitalizing on the single-index structure, we reduce the dimensionality of the covariate-response relationship, thereby preserving the ability to capture intricate dependencies [...] Read more.
In this paper, we develop kernel-based estimators for regression functions under a functional single-index model, applied to censored time series data. By capitalizing on the single-index structure, we reduce the dimensionality of the covariate-response relationship, thereby preserving the ability to capture intricate dependencies while maintaining a relatively parsimonious form. Specifically, our framework utilizes nonparametric kernel estimation within a quasi-association setting to characterize the underlying relationships. Under mild regularity conditions, we demonstrate that these estimators attain both strong uniform consistency and asymptotic normality. Through extensive simulation experiments, we confirm their robust finite-sample performance. Moreover, an empirical examination using intraday Nikkei stock index returns illustrates that the proposed method significantly outperforms traditional nonparametric regression approaches. Full article
(This article belongs to the Special Issue Probability, Stochastic Processes and Machine Learning)
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18 pages, 4421 KiB  
Article
Assessing Scientific Text Similarity: A Novel Approach Utilizing Non-Negative Matrix Factorization and Bidirectional Encoder Representations from Transformer
by Zhixuan Jia, Wenfang Tian, Wang Li, Kai Song, Fuxin Wang and Congjing Ran
Mathematics 2024, 12(21), 3328; https://doi.org/10.3390/math12213328 - 23 Oct 2024
Viewed by 1126
Abstract
The patent serves as a vital component of scientific text, and over time, escalating competition has generated a substantial demand for patent analysis encompassing areas such as company strategy and legal services, necessitating fast, accurate, and easily applicable similarity estimators. At present, conducting [...] Read more.
The patent serves as a vital component of scientific text, and over time, escalating competition has generated a substantial demand for patent analysis encompassing areas such as company strategy and legal services, necessitating fast, accurate, and easily applicable similarity estimators. At present, conducting natural language processing(NLP) on patent content, including titles, abstracts, etc., can serve as an effective method for estimating similarity. However, the traditional NLP approach has some disadvantages, such as the requirement for a huge amount of labeled data and poor explanation of deep-learning-based model internals, exacerbated by the high compression of patent content. On the other hand, most knowledge-based deep learning models require a vast amount of additional analysis results as training variables in similarity estimation, which are limited due to human participation in the analysis part. Thus, in this research, addressing these challenges, we introduce a novel estimator to enhance the transparency of similarity estimation. This approach integrates a patent’s content with international patent classification (IPC), leveraging bidirectional encoder representations from transformers (BERT), and non-negative matrix factorization (NMF). By integrating these techniques, we aim to improve knowledge discovery transparency in NLP across various IPC dimensions and incorporate more background knowledge into context similarity estimation. The experimental results demonstrate that our model is reliable, explainable, highly accurate, and practically usable. Full article
(This article belongs to the Special Issue Probability, Stochastic Processes and Machine Learning)
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