Precision Matrix Research Articles

Generalized Fused Lasso for Treatment Pooling in Network Meta-Analysis.

This work develops a generalized fused lasso (GFL) approach to fitting contrast-based network meta-analysis (NMA) models. The GFL method penalizes all pairwise differences between treatment effects, resulting in the pooling of treatments that are not sufficiently different. This approach offers an intriguing avenue for potentially mitigating biases in treatment rankings and reducing sparsity in networks. To fit contrast-based NMA models within the GFL framework, we formulate the models as generalized least squares problems, where the precision matrix depends on the standard error in the data, the estimated between-study heterogeneity and the correlation between contrasts in multi-arm studies. By utilizing a Cholesky decomposition of the precision matrix, we linearly transform the data vector and design matrix to frame NMA within the GFL framework. We demonstrate how to construct the GFL penalty such that every pairwise difference is penalized similarly. The model is straightforward to implement in R via the "genlasso" package, and runs instantaneously, contrary to other regularization approaches that are Bayesian. A two-step GFL-NMA approach is recommended to obtain measures of uncertainty associated with the (pooled) relative treatment effects. Two simulation studies confirm the GFL approach's ability to pool treatments that have the same (or similar) effects while also revealing when incorrect pooling may occur, and its potential benefits against alternative methods. The novel GFL-NMA method is successfully applied to a real-world dataset on diabetes where the standard NMA model was not favored compared to the best-fitting GFL-NMA model with AICc selection of the tuning parameter ( .

Multi-task Learning for Gaussian Graphical Regressions with High Dimensional Covariates

Gaussian graphical regression is a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which permits the response variables and covariates to outnumber the sample size. However, traditional approaches of fitting the model via separate node-wise lasso regressions overlook the network-induced structure among these regressions, leading to high error rates, particularly when the number of nodes is large. To address this issue, we propose a multi-task learning estimator for fitting Gaussian graphical regression models, which incorporates a cross-task group sparsity penalty and a within-task element-wise sparsity penalty to govern the sparsity of active covariates and their effects on the graph, respectively. We also develop an efficient augmented Lagrangian algorithm for computation, which solves subproblems with a semi-smooth Newton method. We further prove that our multi-task learning estimator has considerably lower error rates than the separate node-wise regression estimates, as the cross-task penalty enables borrowing information across tasks. We examine the utility of our method through simulations and an application to a gene co-expression network study with brain cancer patients.

Asphalt pavement raveling recognition based on deep learning algorithms

Abstract Pavement raveling can lead to the development of issues such as potholes. Monitoring and providing real-time early warnings for road surface developments is crucial for timely maintenance planning and effectively controlling the occurrence and progression of surface issues. To achieve intelligent identification of raveling distress on asphalt pavement surfaces, we utilized a portable laser-based pavement surface scanning device to collect raveling images, followed by histogram equalization to eliminate noise caused by environmental factors. Additionally, data enhancement strategies such as rotation and mirroring were used to enrich training data and expand the sample size. A Convolutional Neural Network (CNN) was employed to perform multi-layer convolution and pooling operations on the images to quickly extract features of distress. Finally, five pre-trained transfer learning models—ResNet-18, DenseNet, VGG16, Inception, and EfficientNet—were introduced to identify the asphalt surface disease data and the normal surface data. The results showed that the accuracy and loss of the training sets of several models exhibited a positive trend, with the EfficientNet model demonstrating stable and superior performance under the same training conditions. The precision matrix, confusion matrix, precision, recall, and F1 score were used as evaluation indexes to assess the effectiveness of the models for identifying pavement raveling. The EfficientNet and Inception models had the best accuracy and comprehensive performance, with accuracy rates of 0.96 and 0.95, respectively. The precision, recall, and F1 score are 0.95, 0.96, and 0.96 for the EfficientNet model respectively. A total of 146 images correctly predicted raveling disease and only 4 normal images were incorrectly predicted as diseased. For example, the EfficientNet model’s identification accuracy for pockmark disease on the PC platform was 0.963, verifying the model’s feasibility in practical applications. The principal contribution of this paper lies in the efficient and precise identification of asphalt pavement raveling, which adversely affects vehicular traveling comfortability. This provides theoretical and technical support for the intelligent identification of asphalt pavement defects and enhancing road asset maintenance management in the pavement engineering industry.

Concentration of a Sparse Bayesian Model With Horseshoe Prior in Estimating High‐Dimensional Precision Matrix

ABSTRACTPrecision matrices are crucial in many fields such as social networks, neuroscience and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off‐diagonal position of the precision matrix indicates conditional independence between nodes. In high‐dimensional settings where the dimension of the precision matrix exceeds the sample size and the matrix is sparse, methods like graphical Lasso, graphical SCAD and CLIME are popular for estimating GGMs. While frequentist methods are well‐studied, Bayesian approaches for (unstructured) sparse precision matrices are less explored. The graphical horseshoe estimate, applying the global‐local horseshoe prior, shows superior empirical performance, but theoretical work for sparse precision matrix estimations using shrinkage priors is limited. This paper addresses these gaps by providing concentration results for the tempered posterior with the fully specified horseshoe prior in high‐dimensional settings. Moreover, we also provide novel theoretical results for model misspecification, offering a general oracle inequality for the posterior. A concise set of simulations is performed to validate our theoretical findings.

Ridge-type covariance and precision matrix estimators of the multivariate normal distribution

AbstractWe consider ridge-type estimation of the multivariate normal distribution’s covariance matrix and its inverse, the precision matrix. While several ridge-type covariance and precision matrix estimators have been presented in the literature, their respective inverses are often not considered as precision and covariance matrix estimators even though their estimands are one-to-one related through the matrix inverse. We study which estimator is to be preferred in what case. Hereto we compare the ridge-type covariance matrix estimators and their properties to that of the inverse of the ridge-type precision matrix estimators, and vice versa. The comparison, in which we take all ridge-type estimators along, is limited to a specific case that is illustrative of the difference between the covariance and precision matrix estimators. The comparison addresses the estimators’ estimating equation, analytic expression, analytic properties like positive definiteness and penalization limit, mean squared error, consistency, Bayesian formulation, and their loss and potential for marginal and partial correlation screening.

Machine learning based tuberculosis (ML-TB) health predictor model: early TB health disease prediction with ML models for prevention in developing countries

Background Tuberculosis (TB) remains one of the top infectious killers in the world and a prominent fatal disease in developing countries. This study proposes a prototypical solution to early prevention of TB based on its primary symptoms, signs, and risk factors, implemented by means of machine learning (ML) predictive algorithms. Further novelty of the study lies in the uniqueness of patient dataset collected from three top-ranked hospitals of Sindh, Pakistan, via a self-administered survey patient-records that comprises a set of questions asked by the doctors treating TB patients in real-time. A total of 1,200 survey patient-records were evenly distributed among all three hospitals, viz. ICT Kotri, LUMHS Jamshoro, and Civil Hospital Hyderabad. Methods To develop the required prototypes, the research made use of five distinct benchmark ML algorithms: decision tree (DT), Gaussian naive Bayes (GNB), logistic regression classifier (LRC), adaptive boosting (AdaBoost), and neural network (NN), whose performance was evaluated by considering various performance metrics, i.e., accuracy, precision, recall, F1 score, and confusion matrix. Results The experimental results, graphically visualized and systematically discoursed, demonstrate that early detection of TB classifiers, including DT, GNB, LRC, AdaBoost, and NN, attained accuracy rates of 92.11%, 89.04%, 90.35%, 93.42%, and 92.98%, respectively. These results indicate effective diagnosis of TB disease by each implemented ML algorithm.

Hybrid machine learning approach for accurate prediction of the drilling rock index

The drilling rate index (DRI) of rocks is important for optimizing drilling operations, as it informs the choice of appropriate methods and equipment, ultimately improving the efficiency of rock excavation projects. This study presents a hybrid machine learning approach to predict the DRI of rocks accurately. By integrating grey wolf optimization with support vector machine (GWO-SVM), random forest (GWO-RF), and extreme gradient boosting (GWO-XGBoost) models, the aim was to enhance predictive accuracy. Among these, the GWO-XGBoost model exhibited superior predictive performance, achieving a coefficient of determination (R²) of 0.999, mean absolute error (MAE) of 0.00043, root mean square error (RMSE) of 1.98017, and severity index (SI) of 0.0350 during training. Testing results confirmed its accuracy with R² of 0.999, MAE of 0.00038, RMSE of 1.80790, and SI of 0.0312. Furthermore, the GWO-XGBoost model outperformed the other models in terms of precision, recall, f1-score, and multi-class confusion matrix results for each DRI class. The GWO-RF model also demonstrated high accuracy, ranking second, while the GWO-SVM model showed comparatively lower performance. This research aims to advance rock excavation practices by providing a highly accurate and reliable tool for DRI prediction. The results highlight the significant potential of the GWO-XGBoost model in improving DRI predictions, offering valuable intuitions and practical applications in the field.

A parallel recursive framework for modelling time series

Abstract Time series modelling is of significance to several scientific fields. Several approaches based on statistics, machine learning or combinations have been utilized. In order to model and forecast time series a novel parallel framework based on recursive pseudoinverse matrices is proposed. This framework enables the design of arbitrary statistical and machine learning models, adaptively, from a set of potential basis functions. This unification enables compact definition of existing and new models as well as easy implementation for new massively parallel architectures. The choice of appropriate basis functions is analysed and the fitting accuracy, termination criteria and model update operations are presented. A block variant for multivariate time series is also proposed. Parallel GPU implementation and performance optimization of the framework are provided, based on mixed precision arithmetic and matrix operations. The use of different basis functions is showcased with respect to various model univariate and multivariate time series for applications such as regression, frequency estimation and automatic trend detection. Discussions on limitations and future directions of research are also provided.

On network deconvolution for undirected graphs.

Network deconvolution (ND) is a method to reconstruct a direct-effect network describing direct (or conditional) effects (or associations) between any two nodes from a given network depicting total (or marginal) effects (or associations). Its key idea is that, in a directed graph, a total effect can be decomposed into the sum of a direct and an indirect effects, with the latter further decomposed as the sum of various products of direct effects. This yields a simple closed-form solution for the direct-effect network, facilitating its important applications to distinguish direct and indirect effects. Despite its application to undirected graphs, it is not well known why the method works, leaving it with skepticism. We first clarify the implicit linear model assumption underlying ND, then derive a surprisingly simple result on the equivalence between ND and use of precision matrices, offering insightful justification and interpretation for the application of ND to undirected graphs. We also establish a formal result to characterize the effect of scaling a total-effect graph. Finally, leveraging large-scale genome-wide association study data, we show a novel application of ND to contrast marginal versus conditional genetic correlations between body height and risk of coronary artery disease; the results align with an inferred causal directed graph using ND. We conclude that ND is a promising approach with its easy and wide applicability to both directed and undirected graphs.

Efficient Modeling of Spatial Extremes over Large Geographical Domains

Various natural phenomena exhibit spatial extremal dependence at short spatial distances. However, existing models proposed in the spatial extremes literature often assume that extremal dependence persists across the entire domain. This is a strong limitation when modeling extremes over large geographical domains, and yet it has been mostly overlooked in the literature. We here develop a more realistic Bayesian framework based on a novel Gaussian scale mixture model, with the Gaussian process component defined by a stochastic partial differential equation yielding a sparse precision matrix, and the random scale component modeled as a low-rank Pareto-tailed or Weibull-tailed spatial process determined by compactly-supported basis functions. We show that our proposed model is approximately tail-stationary and that it can capture a wide range of extremal dependence structures. Its inherently sparse structure allows fast Bayesian computations in high spatial dimensions based on a customized Markov chain Monte Carlo algorithm prioritizing calibration in the tail. We fit our model to analyze heavy monsoon rainfall data in Bangladesh. Our study shows that our model outperforms natural competitors and that it fits precipitation extremes well. We finally use the fitted model to draw inference on long-term return levels for marginal precipitation and spatial aggregates.

Variance Matrix Priors for Dirichlet Process Mixture Models With Gaussian Kernels

SummaryBayesian mixture modelling is widely used for density estimation and clustering. The Dirichlet process mixture model (DPMM) is the most popular Bayesian non‐parametric mixture modelling approach. In this manuscript, we study the choice of prior for the variance or precision matrix when Gaussian kernels are adopted. Typically, in the relevant literature, the assessment of mixture models is done by considering observations in a space of only a handful of dimensions. Instead, we are concerned with more realistic problems of higher dimensionality, in a space of up to 20 dimensions. We observe that the choice of prior is increasingly important as the dimensionality of the problem increases. After identifying certain undesirable properties of standard priors in problems of higher dimensionality, we review and implement possible alternative priors. The most promising priors are identified, as well as other factors that affect the convergence of MCMC samplers. Our results show that the choice of prior is critical for deriving reliable posterior inferences. This manuscript offers a thorough overview and comparative investigation into possible priors, with detailed guidelines for their implementation. Although our work focuses on the use of the DPMM in clustering, it is also applicable to density estimation.

Multilevel approximation of Gaussian random fields: Covariance compression, estimation, and spatial prediction

The distribution of centered Gaussian random fields (GRFs) indexed by compacta such as smooth, bounded Euclidean domains or smooth, compact and orientable manifolds is determined by their covariance operators. We consider centered GRFs given as variational solutions to coloring operator equations driven by spatial white noise, with an elliptic self-adjoint pseudodifferential coloring operator from the Hörmander class. This includes the Matérn class of GRFs as a special case. Using biorthogonal multiresolution analyses on the manifold, we prove that the precision and covariance operators, respectively, may be identified with bi-infinite matrices and finite sections may be diagonally preconditioned rendering the condition number independent of the dimension p of this section. We prove that a tapering strategy by thresholding applied on finite sections of the bi-infinite precision and covariance matrices results in optimally numerically sparse approximations. That is, asymptotically only linearly many nonzero matrix entries are sufficient to approximate the original section of the bi-infinite covariance or precision matrix using this tapering strategy to arbitrary precision. The locations of these nonzero matrix entries can be determined a priori. The tapered covariance or precision matrices may also be optimally diagonally preconditioned. Analysis of the relative size of the entries of the tapered covariance matrices motivates novel, multilevel Monte Carlo (MLMC) oracles for covariance estimation, in sample complexity that scales log-linearly with respect to the number p of parameters. In addition, we propose and analyze novel compressive algorithms for simulating and kriging of GRFs. The complexity (work and memory vs. accuracy) of these three algorithms scales near-optimally in terms of the number of parameters p of the sample-wise approximation of the GRF in Sobolev scales.

Inference on the eigenvalues of the normalized precision matrix

Recent developments in the spectral theory of Bayesian Networks has led to a need for a developed theory of estimation and inference on the eigenvalues of the normalized precision matrix, Ω. In this paper, working under conditions where n→∞ and p remains fixed, we provide multivariate normal asymptotic distributions of the sample eigenvalues of Ω under general conditions and under normal populations, a formula for second-order bias correction of these sample eigenvalues, and a Stein-type shrinkage estimator of the eigenvalues. Numerical simulations are performed which demonstrate under what generative conditions each estimation technique is most effective. When the largest eigenvalue of Ω is small the simulations show that the second order bias-corrected eigenvalue was considerably less biased than the sample eigenvalue, whereas the smallest eigenvalue was estimated with less bias using either the sample eigenvalue or the proposed shrinkage method.

Network Congestion Tracking and Detection in Banking Industry Using Machine Learning Models

The escalating threat of congestion in wireless networks on a global scale prompts the need for effective detection and management techniques. This study investigates the tracking and detection of congestion in wireless networks, particularly within the banking industry, where digital transactions are rapidly increasing. It addresses the challenge of congestion management through machine learning (ML) models, aiming to enhance network performance and service quality. This research evaluates various ML algorithms, including Support Vector Machines, Decision Trees, and Random Forests, to identify the most effective approach for congestion detection. This research utilizes a dataset sourced from MainOne Limited, which covered August 18th, 20th, 22nd, 23rd, and 24th, 2023, and included banking operation hours from 7 AM to 4 PM each day. Preprocessing of data is conducted to optimize model training. Following training, various performance metrics including accuracy, precision, recall, F1 score, response time, and confusion matrix are assessed. Results demonstrate that Random Forest outperforms other models in accuracy, precision, recall, F1 score, and response time, with an accuracy of 98.90%. This research discusses the importance of continuous innovation in banking network analytics to tackle evolving congestion challenges. Future recommendations include leveraging advanced ML techniques like deep learning and reinforcement learning and exploring ensemble learning methods to enhance congestion detection models further.

Statistical Inference for Hüsler–Reiss Graphical Models Through Matrix Completions

The severity of multivariate extreme events is driven by the dependence between the largest marginal observations. The Hüsler–Reiss distribution is a versatile model for this extremal dependence, and it is usually parameterized by a variogram matrix. In order to represent conditional independence relations and obtain sparse parameterizations, we introduce the novel Hüsler–Reiss precision matrix. Similarly to the Gaussian case, this matrix appears naturally in density representations of the Hüsler–Reiss Pareto distribution and encodes the extremal graphical structure through its zero pattern. For a given, arbitrary graph we prove the existence and uniqueness of the completion of a partially specified Hüsler–Reiss variogram matrix so that its precision matrix has zeros on non-edges in the graph. Using suitable estimators for the parameters on the edges, our theory provides the first consistent estimator of graph structured Hüsler–Reiss distributions. If the graph is unknown, our method can be combined with recent structure learning algorithms to jointly infer the graph and the corresponding parameter matrix. Based on our methodology, we propose new tools for statistical inference of sparse Hüsler–Reiss models and illustrate them on large flight delay data in the United States, as well as Danube river flow data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Research on work-stress recognition for deep ground miners based on depth-separable convolutional neural network

In deep mine production operations, the challenging operating environment intensifies the workload and pressure on coal miners. Long-term exposure to high-intensity operating pressure can seriously impact the physical and mental health of miners, leading to unsafe behaviors and accidents. To identify the pressure of miners' operations, this paper examines various driving scenarios, such as the deep-well tunneling machine cutting the wall and opening the alley, the shoveling machine shoveling ore, and the pickup truck driver transporting. The paper randomly collects facial images of miners during each operation using an explosion-proof CCD camera to obtain the facial expression characteristic data of miners. The Ferface2013 facial expression dataset was used to establish the dataset. The depth separable convolutional neural network MiniXception was used for training and to output the classification results of the pressure degree of deep shaft miners. A MiniXception-based miners' operating pressure recognition model was established. The training time, precision, recall, F1 score, and classification accuracy confusion matrix were selected. The study evaluated the effectiveness of the recognition model by measuring its training time, precision, recall, F1 score, and classification accuracy confusion matrix. The results indicate that the model has a correct recognition rate of 88% for the pressure state, 91% for the pleasure state, and 74% for the normal state. The overall accuracy of the model is 0.843. Therefore, the MiniXception recognition model is suitable for recognizing the pressure of miners' operations in deep mines. This can meet practical needs and is useful for preventing major accidents in mines, managing on-site safety, and managing safety in non-hazardous areas. It has important theoretical and practical significance.

Manifold Gaussian Variational Bayes on the Precision Matrix.

We propose an optimization algorithm for variational inference (VI) in complex models. Our approach relies on natural gradient updates where the variational space is a Riemann manifold. We develop an efficient algorithm for gaussian variational inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Our manifold gaussian variational Bayes on the precision matrix (MGVBP) solution provides simple update rules, is straightforward to implement, and the use of the precision matrix parameterization has a significant computational advantage. Due to its black-box nature, MGVBP stands as a ready-to-use solution for VI in complex models. Over five data sets, we empirically validate our feasible approach on different statistical and econometric models, discussing its performance with respect to baseline methods.

Comparative Analysis of YOLOv8 and YOLOv10 in Vehicle Detection: Performance Metrics and Model Efficacy

Accurate vehicle detection is crucial for the advancement of intelligent transportation systems, including autonomous driving and traffic monitoring. This paper presents a comparative analysis of two advanced deep learning models—YOLOv8 and YOLOv10—focusing on their efficacy in vehicle detection across multiple classes such as bicycles, buses, cars, motorcycles, and trucks. Using a range of performance metrics, including precision, recall, F1 score, and detailed confusion matrices, we evaluate the performance characteristics of each model.The findings reveal that YOLOv10 generally outperformed YOLOv8, particularly in detecting smaller and more complex vehicles like bicycles and trucks, which can be attributed to its architectural enhancements. Conversely, YOLOv8 showed a slight advantage in car detection, underscoring subtle differences in feature processing between the models. The performance for detecting buses and motorcycles was comparable, indicating robust features in both YOLO versions. This research contributes to the field by delineating the strengths and limitations of these models and providing insights into their practical applications in real-world scenarios. It enhances understanding of how different YOLO architectures can be optimized for specific vehicle detection tasks, thus supporting the development of more efficient and precise detection systems.

Deep SqueezeNet learning model for diagnosis and prediction of maize leaf diseases

The maize leaf diseases create severe yield reductions and critical problems. The maize leaf disease should be discovered early, perfectly identified, and precisely diagnosed to make greater yield. This work studies three main leaf diseases: common rust, blight, and grey leaf spot. This approach involves pre-processing, including sampling and labelling, while ensuring class balance and preventing overfitting via the SMOTE algorithm. The maize leaf dataset with augmentation was used to classify these diseases using several deep-learning pre-trained networks, including VGG16, Resnet34, Resnet50, and SqueezeNet. The model was evaluated using a maize leaf dataset that included various leaf classes, mini-batch sizes, and input sizes. Performance measures, recall, precision, accuracy, F1-score, and confusion matrix were computed for each network. The SqueezeNet learning model produces an accuracy of 97% in classifying four different classes of plant leaf datasets. Comparatively, the SqueezeNet learning model has improved accuracy by 2–5% and reduced the mean square error by 4–11% over VGG16, Resnet34, and Resnet50 deep learning models.

CBAM VGG16: An efficient driver distraction classification using CBAM embedded VGG16 architecture

Driver monitoring systems (DMS) are crucial in autonomous driving systems (ADS) when users are concerned about driver/vehicle safety. In DMS, the significant influencing factor of driver/vehicle safety is the classification of driver distractions or activities. The driver’s distractions or activities convey meaningful information to the ADS, enhancing the driver/ vehicle safety in real-time vehicle driving. The classification of driver distraction or activity is challenging due to the unpredictable nature of human driving. This paper proposes a convolutional block attention module embedded in Visual Geometry Group (CBAM VGG16) deep learning architecture to improve the classification performance of driver distractions. The proposed CBAM VGG16 architecture is the hybrid network of the CBAM layer with conventional VGG16 network layers. Adding a CBAM layer into a traditional VGG16 architecture enhances the model’s feature extraction capacity and improves the driver distraction classification results. To validate the significant performance of our proposed CBAM VGG16 architecture, we tested our model on the American University in Cairo (AUC) distracted driver dataset version 2 (AUCD2) for cameras 1 and 2 images. Our experiment results show that the proposed CBAM VGG16 architecture achieved 98.65% classification accuracy for camera 1 and 97.85% for camera 2 AUCD2 datasets. The CBAM VGG16 architecture also compared the driver distraction classification performance with DenseNet121, Xception, MoblieNetV2, InceptionV3, and VGG16 architectures based on the proposed model’s accuracy, loss, precision, F1 score, recall, and confusion matrix. The drivers’ distraction classification results indicate that the proposed CBAM VGG16 has 3.7% classification improvements for AUCD2 camera 1 images and 5% for camera 2 images compared to the conventional VGG16 deep learning classification model. We also tested our proposed architecture with different hyperparameter values and estimated the optimal values for best driver distraction classification. The significance of data augmentation techniques for the data diversity performance of the CBAM VGG16 model is also validated in terms of overfitting scenarios. The Grad-CAM visualization of our proposed CBAM VGG16 architecture is also considered in our study, and the results show that VGG16 architecture without CBAM layers is less attentive to the essential parts of the driver distraction images. Furthermore, we tested the effective classification performance of our proposed CBAM VGG16 architecture with the number of model parameters, model size, various input image resolutions, cross-validation, Bayesian search optimization and different CBAM layers. The results indicate that CBAM layers in our proposed architecture enhance the classification performance of conventional VGG16 architecture and outperform the state-of-the-art deep learning architectures.