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Mathematics
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Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making
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Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 30 October 2024 | Viewed by 10344

Special Issue Editors

Prof. Dr. Zijiang Yang

E-Mail Website
Guest Editor
School of Information Technology, York University, 4700 Keele Street, Toronto, ON M3J1P3, Canada
Interests: machine learning algorithms; data mining; big data analytics and optimization
Prof. Dr. Xin Gao

E-Mail Website
Guest Editor
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J1P3, Canada
Interests: complex data; data fusion; multitask learning; model selection; statistical learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Prediction and decision making are hot topics in today’s economy and society. Technological advancement has enabled new approaches—notably machine learning—to be applied for finding the best decision-making strategies, together with statistical modeling. However, there are factors imposed by the nature of industry that constitute major challenges for building high-performance prediction or decision-making models in real-world applications. How to analyze complex and high-dimensional data is another great challenge faced by practitioners in building prediction models. The data can be collected from heterogenous sources, imposing open questions regarding how to integrate different types and sources of data to make decisions or predictions. All these challenges can be tackled from either theoretical or applied points of view. This Special Issue welcomes theoretical and applied research papers that explore machine learning and statistical methods in prediction and decision making. Papers related to this theme are especially encouraged, including papers on mathematics, machine learning, computer science, and statistics that investigate their roles in decision making and prediction.

Prof. Dr. Zijiang Yang
Prof. Dr. Xin Gao
Guest Editors

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

  • statistical modeling
  • machine learning
  • data mining
  • complex data
  • big data analytics
  • optimization

Published Papers (7 papers)

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Research

21 pages, 386 KiB  
Article
Optimization Models for the Vehicle Routing Problem under Disruptions
by Kai Huang and Michael Xu
Mathematics 2023, 11(16), 3521; https://0-doi-org.brum.beds.ac.uk/10.3390/math11163521 - 15 Aug 2023
Viewed by 1119
Abstract
In this paper, we study the role of disruptions in the multi-period vehicle routing problem (VRP), which naturally arises in humanitarian logistics and military applications. We assume that at any time during the delivery phase, each vehicle could have chance to be disrupted. [...] Read more.
In this paper, we study the role of disruptions in the multi-period vehicle routing problem (VRP), which naturally arises in humanitarian logistics and military applications. We assume that at any time during the delivery phase, each vehicle could have chance to be disrupted. When a disruption happens, vehicles will be unable to continue their journeys and supplies will be unable to be delivered. We model the occurrence of disruption as a given probability and consider the multi-period expected delivery. Our objective is to either minimize the total travel cost or maximize the demand fulfillment, depending on the supply quantity. This problem is denoted as the multi-period vehicle routing problem with disruption (VRPMD). VRPMD does not deal with disruptions in real-time and is more focused on the long-term performance of a single routing plan. We first prove that the proposed VRPMD problems are NP-hard. We then present some analytical properties related to the optimal solutions to these problems. We show that Dror and Trudeau’s property does not apply in our problem setting. Nevertheless, a generalization of Dror and Trudeau’s property holds. Finally, we present efficient heuristic algorithms to solve these problems and show the effectiveness of the proposed models and algorithms through numerical studies. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)
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16 pages, 346 KiB  
Article
Estimation of Mediation Effect on Zero-Inflated Microbiome Mediators
by Dongyang Yang and Wei Xu
Mathematics 2023, 11(13), 2830; https://0-doi-org.brum.beds.ac.uk/10.3390/math11132830 - 24 Jun 2023
Viewed by 966
Abstract
The mediation analysis methodology of the cause-and-effect relationship through mediators has been increasingly popular over the past decades. The human microbiome can contribute to the pathogenesis of many complex diseases by mediating disease-leading causal pathways. However, standard mediation analysis is not adequate for [...] Read more.
The mediation analysis methodology of the cause-and-effect relationship through mediators has been increasingly popular over the past decades. The human microbiome can contribute to the pathogenesis of many complex diseases by mediating disease-leading causal pathways. However, standard mediation analysis is not adequate for microbiome data due to the excessive number of zero values and the over-dispersion in the sequencing reads, which arise for both biological and sampling reasons. To address these unique challenges brought by the zero-inflated mediator, we developed a novel mediation analysis algorithm under the potential-outcome framework to fill this gap. The proposed semiparametric model estimates the mediation effect of the microbiome by decomposing indirect effects into two components according to the zero-inflated distributions. The bootstrap algorithm is utilized to calculate the empirical confidence intervals of the causal effects. We conducted extensive simulation studies to investigate the performance of the proposed weighting-based approach and some model-based alternatives, and our proposed model showed robust performance. The proposed algorithm was implemented in a real human microbiome study of identifying whether some taxa mediate the relationship between LACTIN-V treatment and immune response. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)
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19 pages, 484 KiB  
Article
Graphical Local Genetic Algorithm for High-Dimensional Log-Linear Models
by Lyndsay Roach and Xin Gao
Mathematics 2023, 11(11), 2514; https://0-doi-org.brum.beds.ac.uk/10.3390/math11112514 - 30 May 2023
Cited by 2 | Viewed by 1773
Abstract
Graphical log-linear models are effective for representing complex structures that emerge from high-dimensional data. It is challenging to fit an appropriate model in the high-dimensional setting and many existing methods rely on a convenient class of models, called decomposable models, which lend well [...] Read more.
Graphical log-linear models are effective for representing complex structures that emerge from high-dimensional data. It is challenging to fit an appropriate model in the high-dimensional setting and many existing methods rely on a convenient class of models, called decomposable models, which lend well to a stepwise approach. However, these methods restrict the pool of candidate models from which they can search, and these methods are difficult to scale. It can be shown that a non-decomposable model can be approximated by the decomposable model which is its minimal triangulation, thus extending the convenient computational properties of decomposable models to any model. In this paper, we propose a local genetic algorithm with a crossover-hill-climbing operator, adapted for log-linear graphical models. We show that the graphical local genetic algorithm can be used successfully to fit non-decomposable models for both a low number of variables and a high number of variables. We use the posterior probability as a measure of fitness and parallel computing to decrease the computation time. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)
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26 pages, 436 KiB  
Article
Modified BIC Criterion for Model Selection in Linear Mixed Models
by Hang Lai and Xin Gao
Mathematics 2023, 11(9), 2130; https://0-doi-org.brum.beds.ac.uk/10.3390/math11092130 - 02 May 2023
Viewed by 1538
Abstract
Linear mixed-effects models are widely used in applications to analyze clustered, hierarchical, and longitudinal data. Model selection in linear mixed models is more challenging than that of linear models as the parameter vector in a linear mixed model includes both fixed effects and [...] Read more.
Linear mixed-effects models are widely used in applications to analyze clustered, hierarchical, and longitudinal data. Model selection in linear mixed models is more challenging than that of linear models as the parameter vector in a linear mixed model includes both fixed effects and variance component parameters. When selecting the variance components of the random effects, the variance of the random effects must be non-negative and the parameters may lie on the boundary of the parameter space. Therefore, classical model selection methods cannot be directly used to handle this situation. In this article, we propose a modified BIC for model selection with linear mixed-effects models that can solve the case when the variance components are on the boundary of the parameter space. Through the simulation results, we found that the modified BIC performed better than the regular BIC in most cases for linear mixed models. The modified BIC was also applied to a real dataset to choose the most-appropriate model. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)
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18 pages, 1450 KiB  
Article
Explicit Gaussian Variational Approximation for the Poisson Lognormal Mixed Model
by Xiaoping Shi, Xiang-Sheng Wang and Augustine Wong
Mathematics 2022, 10(23), 4542; https://0-doi-org.brum.beds.ac.uk/10.3390/math10234542 - 01 Dec 2022
Viewed by 1023
Abstract
In recent years, the Poisson lognormal mixed model has been frequently used in modeling count data because it can accommodate both the over-dispersion of the data and the existence of within-subject correlation. Since the likelihood function of this model is expressed in terms [...] Read more.
In recent years, the Poisson lognormal mixed model has been frequently used in modeling count data because it can accommodate both the over-dispersion of the data and the existence of within-subject correlation. Since the likelihood function of this model is expressed in terms of an intractable integral, estimating the parameters and obtaining inference for the parameters are challenging problems. Some approximation procedures have been proposed in the literature; however, they are computationally intensive. Moreover, the existing studies of approximate parameter inference using the Gaussian variational approximation method are usually restricted to models with only one predictor. In this paper, we consider the Poisson lognormal mixed model with more than one predictor. By extending the Gaussian variational approximation method, we derive explicit forms for the estimators of the parameters and examine their properties, including the asymptotic distributions of the estimators of the parameters. Accurate inference for the parameters is also obtained. A real-life example demonstrates the applicability of the proposed method, and simulation studies illustrate the accuracy of the proposed method. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)
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20 pages, 4764 KiB  
Article
Tongue Segmentation and Color Classification Using Deep Convolutional Neural Networks
by Bo Yan, Sheng Zhang, Zijiang Yang, Hongyi Su and Hong Zheng
Mathematics 2022, 10(22), 4286; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224286 - 16 Nov 2022
Cited by 3 | Viewed by 2268
Abstract
Tongue color classification serves as important assistance for traditional Chinese medicine (TCM) doctors to make a precise diagnosis. This paper proposes a novel two-step framework based on deep learning to improve the performance of tongue color classification. First, a semantic-based CNN called SegTongue [...] Read more.
Tongue color classification serves as important assistance for traditional Chinese medicine (TCM) doctors to make a precise diagnosis. This paper proposes a novel two-step framework based on deep learning to improve the performance of tongue color classification. First, a semantic-based CNN called SegTongue is applied to segment the tongues from the background. Based on DeepLabv3+, multiple atrous spatial pyramid pooling (ASPP) modules are added, and the number of iterations of fusions of low-level and high-level information is increased. After segmentation, various classical feature extraction networks are trained using softmax and center loss. The experiment results are evaluated using different measures, including overall accuracy, Kappa coefficient, individual sensitivity, etc. The results demonstrate that the proposed framework with SVM achieves up to 97.60% accuracy in the tongue image datasets. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)
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18 pages, 328 KiB  
Article
The Intrinsic Structure of High-Dimensional Data According to the Uniqueness of Constant Mean Curvature Hypersurfaces
by Junhong Dong, Qiong Li and Ximin Liu
Mathematics 2022, 10(20), 3894; https://0-doi-org.brum.beds.ac.uk/10.3390/math10203894 - 20 Oct 2022
Viewed by 987
Abstract
In this paper, we study the intrinsic structures of high-dimensional data sets for analyzing their geometrical properties, where the core message of the high-dimensional data is hiding on some nonlinear manifolds. Using the manifold learning technique with a particular focus on the mean [...] Read more.
In this paper, we study the intrinsic structures of high-dimensional data sets for analyzing their geometrical properties, where the core message of the high-dimensional data is hiding on some nonlinear manifolds. Using the manifold learning technique with a particular focus on the mean curvature, we develop new methods to investigate the uniqueness of constant mean curvature spacelike hypersurfaces in the Lorentzian warped product manifolds. Furthermore, we extend the uniqueness of stochastically complete hypersurfaces using the weak maximum principle. For the more general cases, we propose some non-existence results and a priori estimates for the constant higher-order mean curvature spacelike hypersurface. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Methods to Prediction and Optimal Decision-Making)
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