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Mathematics
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Interpretable Models and Their Applications in Neural Computation and Statistical...
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Interpretable Models and Their Applications in Neural Computation and Statistical Learning

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 6703

Special Issue Editor

Prof. Dr. Jinwen Ma

E-Mail Website
Guest Editor
Department of Information Science, School of Mathematical Sciences and LMAM, Peking University, Beijing 100871, China
Interests: neural computation; statistical learning; pattern recognition; clustering analysis; computer vision; bioinformatics

Special Issue Information

Dear Colleagues,

Neural networks and machine learning models have recently developed very fast and achieved the best results for many practical applications in AI and related fields. Although the advanced neural network models can effectively solve many challenging problems with complicated and deep architectures, they are generally designed by experience and cannot be theoretically interpreted. This has strongly limited their application and developments. Therefore, model interpretability analysis, as well as interpretable model design in neural computation and statistical learning, has become important and necessary. It is clear that model interpretability can be discovered by mathematical analysis under a statistical or probability framework. On the other hand, the data should be assumed to be generated from a probability model. Moreover, model interpretability should focus on a certain kind of practical problem for data analysis and mining.

The aim of this Special Issue is to publish original research articles covering advances in model interpretability and interpretable models in neural computation and statistical learning. Potential topics include but are not limited to the following: interpretable deep learning models; Gaussian processes and their mixtures; curve clustering analysis and prediction; and automated model selection.

Prof. Dr. Jinwen Ma
Guest Editor

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

  • model interoperability
  • interpretable deep learning model
  • Gaussian process regression
  • mixture of gaussian process
  • automated model selection
  • Gaussian mixture learning

Published Papers (5 papers)

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Research

13 pages, 10728 KiB  
Article
Multi-Scale Feature Selective Matching Network for Object Detection
by Yuanhua Pei, Yongsheng Dong, Lintao Zheng and Jinwen Ma
Mathematics 2023, 11(12), 2655; https://doi.org/10.3390/math11122655 - 10 Jun 2023
Viewed by 1075
Abstract
Numerous deep learning-based object detection methods have achieved excellent performance. However, the performance on small-size object detection and positive and negative sample imbalance problems is not satisfactory. We propose a multi-scale feature selective matching network (MFSMNet) to improve the performance of small-size object [...] Read more.
Numerous deep learning-based object detection methods have achieved excellent performance. However, the performance on small-size object detection and positive and negative sample imbalance problems is not satisfactory. We propose a multi-scale feature selective matching network (MFSMNet) to improve the performance of small-size object detection and alleviate the positive and negative sample imbalance problems. First, we construct a multi-scale semantic enhancement module (MSEM) to compensate for the information loss of small-sized targets during down-sampling by obtaining richer semantic information from features at multiple scales. Then, we design the anchor selective matching (ASM) strategy to alleviate the training dominated by negative samples caused by the imbalance of positive and negative samples, which converts the offset values of the localization branch output in the detection head into localization scores and reduces negative samples by discarding low-quality anchors. Finally, a series of quantitative and qualitative experiments on the Microsoft COCO 2017 and PASCAL VOC 2007 + 2012 datasets show that our method is competitive compared to nine other representative methods. MFSMNet runs on a GeForce RTX 3090. Full article
(This article belongs to the Special Issue Interpretable Models and Their Applications in Neural Computation and Statistical Learning)
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25 pages, 4773 KiB  
Article
Automated Model Selection of the Two-Layer Mixtures of Gaussian Process Functional Regressions for Curve Clustering and Prediction
by Chengxin Gong and Jinwen Ma
Mathematics 2023, 11(12), 2592; https://doi.org/10.3390/math11122592 - 06 Jun 2023
Viewed by 817
Abstract
As a reasonable statistical learning model for curve clustering analysis, the two-layer mixtures of Gaussian process functional regressions (TMGPFR) model has been developed to fit the data of sample curves from a number of independent information sources or stochastic processes. Since the sample [...] Read more.
As a reasonable statistical learning model for curve clustering analysis, the two-layer mixtures of Gaussian process functional regressions (TMGPFR) model has been developed to fit the data of sample curves from a number of independent information sources or stochastic processes. Since the sample curves from a certain stochastic process naturally form a curve cluster, the model selection of TMGPFRs, i.e., the selection of the number of mixtures of Gaussian process functional regressions (MGPFRs) in the upper layer, corresponds to the discovery of the cluster number and structure of the curve data. In fact, this is rather challenging because the conventional model selection criteria, such as BIC and cross-validation, cannot lead to a stable result in practice even with a heavy burden of repetitive computation. In this paper, we improve the original TMGPFR model and propose a Bayesian Ying-Yang (BYY) annealing learning algorithm for the parameter learning of the improved model with automated model selection. The experimental results of both synthetic and realistic datasets demonstrate that our proposed algorithm can make correct model selection automatically during parameter learning of the model. Full article
(This article belongs to the Special Issue Interpretable Models and Their Applications in Neural Computation and Statistical Learning)
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19 pages, 978 KiB  
Article
An Improved Mixture Model of Gaussian Processes and Its Classification Expectation–Maximization Algorithm
by Yurong Xie, Di Wu and Zhe Qiang
Mathematics 2023, 11(10), 2251; https://doi.org/10.3390/math11102251 - 11 May 2023
Cited by 2 | Viewed by 1380
Abstract
The mixture of experts (ME) model is effective for multimodal data in statistics and machine learning. To treat non-stationary probabilistic regression, the mixture of Gaussian processes (MGP) model has been proposed, but it may not perform well in some cases due to the [...] Read more.
The mixture of experts (ME) model is effective for multimodal data in statistics and machine learning. To treat non-stationary probabilistic regression, the mixture of Gaussian processes (MGP) model has been proposed, but it may not perform well in some cases due to the limited ability of each Gaussian process (GP) expert. Although the mixture of Gaussian processes (MGP) and warped Gaussian process (WGP) models are dominant and effective for non-stationary probabilistic regression, they may not be able to handle general non-stationary probabilistic regression in practice. In this paper, we first propose the mixture of warped Gaussian processes (MWGP) model as well as its classification expectation–maximization (CEM) algorithm to address this problem. To overcome the local optimum of the CEM algorithm, we then propose the split and merge CEM (SMC EM) algorithm for MWGP. Experiments were done on synthetic and real-world datasets, which show that our proposed MWGP is more effective than the models used for comparison, and the SMCEM algorithm can solve the local optimum for MWGP. Full article
(This article belongs to the Special Issue Interpretable Models and Their Applications in Neural Computation and Statistical Learning)
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13 pages, 4642 KiB  
Article
CCTrans: Improving Medical Image Segmentation with Contoured Convolutional Transformer Network
by Jingling Wang, Haixian Zhang and Zhang Yi
Mathematics 2023, 11(9), 2082; https://doi.org/10.3390/math11092082 - 27 Apr 2023
Cited by 3 | Viewed by 1230
Abstract
Medical images contain complex information, and the automated analysis of medical images can greatly assist doctors in clinical decision making. Therefore, the automatic segmentation of medical images has become a hot research topic in recent years. In this study, a novel architecture called [...] Read more.
Medical images contain complex information, and the automated analysis of medical images can greatly assist doctors in clinical decision making. Therefore, the automatic segmentation of medical images has become a hot research topic in recent years. In this study, a novel architecture called a contoured convolutional transformer (CCTrans) network is proposed to solve the segmentation problem. A dual convolutional transformer block and a contoured detection module are designed, which integrate local and global contexts to establish reliable relational connections. Multi-scale features are effectively utilized to enhance semantic feature understanding. The dice similarity coefficient (DSC) is employed to evaluate experimental performance. Two public datasets with two different modalities are chosen as the experimental datasets. Our proposed method achieved an average DSC of 83.97% on a synapse dataset (abdominal multi-organ CT) and 92.15% on an ACDC dataset (cardiac MRI). Especially for the segmentation of small and complex organs, our proposed model achieves better segmentation results than other advanced approaches. Our experiments demonstrate the effectiveness and robustness of the novel method and its potential for real-world applications. The proposed CCTrans network offers a universal solution with which to achieve precise medical image segmentation. Full article
(This article belongs to the Special Issue Interpretable Models and Their Applications in Neural Computation and Statistical Learning)
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24 pages, 2986 KiB  
Article
Hidden Markov Mixture of Gaussian Process Functional Regression: Utilizing Multi-Scale Structure for Time Series Forecasting
by Tao Li and Jinwen Ma
Mathematics 2023, 11(5), 1259; https://doi.org/10.3390/math11051259 - 05 Mar 2023
Viewed by 1430
Abstract
The mixture of Gaussian process functional regressions (GPFRs) assumes that there is a batch of time series or sample curves that are generated by independent random processes with different temporal structures. However, in real situations, these structures are actually transferred in a random [...] Read more.
The mixture of Gaussian process functional regressions (GPFRs) assumes that there is a batch of time series or sample curves that are generated by independent random processes with different temporal structures. However, in real situations, these structures are actually transferred in a random manner from a long time scale. Therefore, the assumption of independent curves is not true in practice. In order to get rid of this limitation, we propose the hidden-Markov-based GPFR mixture model (HM-GPFR) by describing these curves with both fine- and coarse-level temporal structures. Specifically, the temporal structure is described by the Gaussian process model at the fine level and the hidden Markov process at the coarse level. The whole model can be regarded as a random process with state switching dynamics. To further enhance the robustness of the model, we also give a priori parameters to the model and develop a Bayesian-hidden-Markov-based GPFR mixture model (BHM-GPFR). The experimental results demonstrated that the proposed methods have both high prediction accuracy and good interpretability. Full article
(This article belongs to the Special Issue Interpretable Models and Their Applications in Neural Computation and Statistical Learning)
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