Precision Matrix Research Articles

Arrhythmia detection by the graph convolution network and a proposed structure for communication between cardiac leads

One of the most common causes of death worldwide is heart disease, including arrhythmia. Today, sciences such as artificial intelligence and medical statistics are looking for methods and models for correct and automatic diagnosis of cardiac arrhythmia. In pursuit of increasing the accuracy of automated methods, many studies have been conducted. However, in none of the previous articles, the relationship and structure between the heart leads have not been included in the model. It seems that the structure of ECG data can help develop the accuracy of arrhythmia detection. Therefore, in this study, a new structure of Electrocardiogram (ECG) data was introduced, and the Graph Convolution Network (GCN), which has the possibility of learning the structure, was used to develop the accuracy of cardiac arrhythmia diagnosis. Considering the relationship between the heart leads and clusters based on different ECG poles, a new structure was introduced. In this structure, the Mutual Information(MI) index was used to evaluate the relationship between the leads, and weight was given based on the poles of the leads. Weighted Mutual Information (WMI) matrices (new structure) were formed by R software. Finally, the 15-layer GCN network was adjusted by this structure and the arrhythmia of people was detected and classified by it. To evaluate the performance of the proposed new network, sensitivity, precision, specificity, accuracy, and confusion matrix indices were used. Also, the accuracy of GCN networks was compared by three different structures, including WMI, MI, and Identity. Chapman’s 12-lead ECG Dataset was used in this study. The results showed that the values of sensitivity, precision, specificity, and accuracy of the GCN-WMI network with 15 intermediate layers were equal to 98.74%, 99.08%, 99.97% & 99.82%, respectively. This new proposed network was more accurate than the Graph Convolution Network-Mutual Information (GCN-MI) with an accuracy equal to 99.71% and GCN-Id with an accuracy equal to 92.68%. Therefore, utilizing this network, the types of arrhythmia were recognized and classified. Also, the new network proposed by the Graph Convolution Network-Weighted Mutual Information (GCN-WMI) was more accurate than those conducted in other studies on the same data set (Chapman). Based on the obtained results, the structure proposed in this study increased the accuracy of cardiac arrhythmia diagnosis and classification on the Chapman data set. Achieving such accuracy for arrhythmia diagnosis is a great achievement in clinical sciences.

CARE: Large Precision Matrix Estimation for Compositional Data

High-dimensional compositional data are prevalent in many applications. The simplex constraint poses intrinsic challenges to inferring the conditional dependence relationships among the components forming a composition, as encoded by a large precision matrix. We introduce a precise specification of the compositional precision matrix and relate it to its basis counterpart, which is shown to be asymptotically identifiable under suitable sparsity assumptions. By exploiting this connection, we propose a composition adaptive regularized estimation (CARE) method for estimating the sparse basis precision matrix. We derive rates of convergence for the estimator and provide theoretical guarantees on support recovery and data-driven parameter tuning. Our theory reveals an intriguing tradeoff between identification and estimation, thereby highlighting the blessing of dimensionality in compositional data analysis. In particular, in sufficiently high dimensions, the CARE estimator achieves minimax optimality and performs as well as if the basis were observed. We further discuss how our framework can be extended to handle data containing zeros, including sampling zeros and structural zeros. The advantages of CARE over existing methods are illustrated by simulation studies and an application to inferring microbial ecological networks in the human gut. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Decorrelated empirical likelihood for generalized linear models with high-dimensional longitudinal data

This paper focuses on decorrelated empirical likelihood-based inference for longitudinal data with ultrahigh-dimensional covariates. The primary issues we aim to address involve parameter estimation and hypothesis testing for a low-dimensional parameter of interest. Under the framework of the generalized linear model, we initially consider the within-subject correlation by linearizing the precision matrix with certain known matrices, which retains optimality even if the working correlated structure is misspecified. Coupled with the decorrelated matrix, we then eliminate the influence of nuisance parameters on the estimation procedure. The proposed approach not only yields more efficient estimators compared to generalized decorrelated estimating equations but also shares the same asymptotic variance as quadratic decorrelated inference function based methods. Furthermore, we define the decorrelated empirical log-likelihood ratio test statistic to assess the significance of regression coefficients. Finally, to evaluate the performance of the proposed procedure, we conduct simulation studies and apply it to a real data example.

Machine Learning Approaches of Lung Cancer Image Processing for Detecting and Identifying Various Stages of Analysis

The current paper is aimed at examining the use of machine learning approaches for lung cancer detection and classification using medical imaging data. In order to create the model, we collected a comprehensive dataset of 2400 images of lung cancer at different stages and healthy pictures. These data were preprocessed, and several approaches to the feature extraction were considered, namely Histogram of Oriented Gradients , and Local Binary Patterns . In addition, we attempted to use deep learning representations to determine their usefulness in this case. Moreover, these features were used for four ML models, namely Convolutional Neural Network , ResNet-18, , and VGG-19, to determine the most suitable one. To evaluate the general performance of these models, all the characteristic points were taken into account, such as the precision, recall, F1 score, accuracy, and confusion matrices. The results of the primary analysis indicate that the accuracy of our proposed model was the highest, 96.86%. The other places were taken by other deep learning architectures, which also demonstrate high level performance. In general, we may conclude that the findings show it is possible to use ML algorithms to improve the quality of clinical decisions and make the process of lung cancer detection and classification more accurate. At the same time, we were able to provide a comprehensive evaluation of all these results and the thorough analysis of the general performance of each model. This may serve as the basis for the subsequent improvements and changes that would allow enhancing the general quality of diagnostics and training more advanced models.

Minimax detection boundary and sharp optimal test for Gaussian graphical models

Abstract In this article, we derive the minimax detection boundary for testing a sub-block of variables in a precision matrix under the Gaussian distribution. Compared to the results on the minimum rate of signals for testing precision matrices in literature, our result gives the exact minimum signal strength in a precision matrix that can be detected. We propose a thresholding test that is able to achieve the minimax detection boundary under certain cases by adaptively choosing the threshold level. The asymptotic distribution of the thresholding statistic for precision matrices is derived. Power analysis is conducted to show the proposed test is powerful against sparse and weak signals, which cannot be detected by the existing Lmax and L2 tests. Simulation studies show the proposed test has an accurate size around the nominal level and is more powerful than the existing tests for detecting sparse and weak signals in precision matrices. Real data analysis on brain imaging data is carried out to illustrate the utility of the proposed test in practice, which reveals functional connectivity between brain regions for Alzheimer’s disease patients and normal healthy people.

Covariance Matrix Estimation for High-Throughput Biomedical Data with Interconnected Communities

Estimating a covariance matrix is central to high-dimensional data analysis. Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging, among others, consistently reveal strong modularity in the dependence patterns. In these analyses, intercorrelated high-dimensional biomedical features often form communities or modules that can be interconnected with others. While the interconnected community structure has been extensively studied in biomedical research (e.g., gene co-expression networks), its potential to assist in the estimation of covariance matrices remains largely unexplored. To address this gap, we propose a procedure that leverages the commonly observed interconnected community structure in high-dimensional biomedical data to estimate large covariance and precision matrices. We derive the uniformly minimum variance unbiased estimators for covariance and precision matrices in closed forms and provide theoretical results on their asymptotic properties. Our proposed method enhances the accuracy of covariance- and precision-matrix estimation and demonstrates superior performance compared to the competing methods in both simulations and real data analyses.

Algorithm XXX: Sparse Precision Matrix Estimation With SQUIC

We present SQUIC , a fast and scalable package for sparse precision matrix estimation. The algorithm employs a second-order method to solve the \(\ell_{1}\) -regularized maximum likelihood problem, utilizing highly optimized linear algebra subroutines. In comparative tests using synthetic datasets, we demonstrate that SQUIC not only scales to datasets of up to a million random variables but also consistently delivers run times that are significantly faster than other well-established sparse precision matrix estimation packages. Furthermore, we showcase the application of the introduced package in classifying microarray gene expressions. We demonstrate that by utilizing a matrix form of the tuning parameter (also known as the regularization parameter), SQUIC can effectively incorporate prior information into the estimation procedure, resulting in improved application results with minimal computational overhead.

Are minimum variance portfolios in multi-factor models long in low-beta assets?

Within the one-factor capital asset pricing model (CAPM), the minimum-variance portfolio (MVP) is known to have long positions in those assets of the underlying investment universe whose betas are less than a well-defined long-short threshold beta. We study the structure of MVPs in more general multi-factor asset pricing models and clarify the low-beta puzzle for multi-factor models: For multi-factor models we derive a similar criterion in terms of the betas with explicit closed-form formulas. But the structural relationship is now more involved and the long-short threshold turns out to be asset-specific. The results rely on recursive inverse-free formulas for the precision matrix, which hold for multi-factor models and allow quick computation of that inverse matrix without the need to invert matrices going beyond diagonal ones. We illustrate our findings by analyzing S &P 500 asset returns. Our empirical results of the S &P 500 constituents between 2019 and 2022 confirm the theoretical findings and shows that the minimum variance portfolio is long in low-beta assets when applying estimates of the established asset-specific thresholds.

Partial Tail-Correlation Coefficient Applied to Extremal-Network Learning

We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on the framework of multivariate regular variation and transformed-linear algebra operations. We show how this coefficient allows identifying pairs of variables that have partially uncorrelated tails given some other variables in a random vector. Unlike other recently introduced conditional independence frameworks for extremes, our approach requires minimal modeling assumptions and can thus be used in exploratory analyses to learn the structure of extremal graphical models. Similarly to traditional Gaussian graphical models where edges correspond to the nonzero entries of the precision matrix, we can exploit classical inference methods for high-dimensional data, such as the graphical Lasso with Laplacian spectral constraints, to efficiently learn the extremal network structure via the PTCC. We apply our new method to study extreme risk networks in two different datasets (extreme river discharges and historical global currency exchange data) and show that we can extract interesting extremal structures with meaningful domain-specific interpretations.

Distributed Sparse Precision Matrix Estimation via Alternating Block-Based Gradient Descent

Precision matrices can efficiently exhibit the correlation between variables and they have received much attention in recent years. When one encounters large datasets stored in different locations and when data sharing is not allowed, the implementation of high-dimensional precision matrix estimation can be numerically challenging or even infeasible. In this work, we studied distributed sparse precision matrix estimation via an alternating block-based gradient descent method. We obtained a global model by aggregating each machine’s information via a communication-efficient surrogate penalized likelihood. The procedure chooses the block coordinates using the local gradient, to guide the global gradient updates, which can efficiently accelerate precision estimation and lessen communication loads on sensors. The proposed method can efficiently achieve the correct selection of non-zero elements of a sparse precision matrix. Under mild conditions, we show that the proposed estimator achieved a near-oracle convergence rate, as if the estimation had been conducted with a consolidated dataset on a single computer. The promising performance of the method was supported by both simulated and real data examples.

Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms

Abstract Ecological analyses typically involve many interacting variables. Ecologists often specify lagged interactions in community dynamics (i.e. vector‐autoregressive models) or simultaneous interactions (e.g. structural equation models), but there is less familiarity with dynamic structural equation models (DSEM) that can include any simultaneous or lagged effect in multivariate time‐series analysis. We propose a novel approach to parameter estimation for DSEM, which involves constructing a Gaussian Markov random field (GMRF) representing simultaneous and lagged path coefficients, and then fitting this as a generalized linear mixed model to missing and/or non‐normal data. We provide a new R‐package dsem, which extends the ‘arrow interface’ from path analysis to represent user‐specified lags when constructing the GMRF. We also outline how the resulting nonseparable precision matrix can generalize existing separable models, for example, for time‐series and species interactions in a vector‐autoregressive model. We first demonstrate dsem by simulating a two‐species vector‐autoregressive model based on wolf–moose interactions on Isle Royale. We show that DSEM has improved precision when data are missing relative to a conventional dynamic linear model. We then demonstrate DSEM via two contrasting case studies. The first identifies a trophic cascade where decreased sunflower starfish has increased urchin and decreased kelp densities, while sea otters have a simultaneous positive effect on kelp in the California Current from 1999 to 2018. The second estimates how declining sea ice has decreased cold‐water habitats, driving a decreased density for fall copepod predation and inhibiting early‐life survival for Alaska pollock from 1963 to 2023. We conclude that DSEM can be fitted efficiently as a GLMM involving missing data, while allowing users to specify both simultaneous and lagged effects in a time‐series structural model. DSEM then allows conceptual models (developed with stakeholder input or from ecological expertise) to be fitted to incomplete time series and provides a simple interface for granular control over the number of estimated time‐series parameters. Finally, computational methods are sufficiently simple that DSEM can be embedded as component within larger (e.g. integrated population) models. We therefore recommend greater exploration and performance testing for DSEM relative to familiar time‐series forecasting methods.

Time Period Categorization in Fiction: A Comparative Analysis of Machine Learning Techniques

This study investigates the automatic categorization of time period metadata in fiction, a critical but often overlooked aspect of cataloging. Using a comparative analysis approach, the performance of three machine learning techniques, namely Latent Dirichlet Allocation (LDA), Sentence-BERT (SBERT), and Term Frequency-Inverse Document Frequency (TF-IDF) were assessed, by examining their precision, recall, F1 scores, and confusion matrix results. LDA identifies underlying topics within the text, TF-IDF measures word importance, and SBERT measures sentence semantic similarity. Based on F1-score analysis and confusion matrix outcomes, TF-IDF and LDA effectively categorize text data by time period, while SBERT performed poorly across all time period categories.

Comprehensive Classification of Fetal Health Using Cardiotocogram Data Based on Machine Learning

In the realm of obstetrics, the evaluation of fetal health remains a paramount yet challenging endeavor. Traditional approaches, such as electronic fetal monitoring (EFM), despite their widespread adoption, continue to grapple with uncertainties regarding their impact on neonatal outcomes and the reduction of emergency cesarean deliveries. This ambiguity is compounded by a prevailing confusion within the obstetric community about interpreting fetal heart rate patterns, often leading to inconsistent and subjective assessments. Addressing these complexities, our study presents an innovative machine learning-based techniques for the comprehensive classification of fetal health using cardiotocogram (CTG) data, offering a more objective and nuanced alternative to conventional methods. The core of our proposed solution is a novel model employing a sophisticated ensemble of machine learning classifiers, including Multi-Support Vector Machine (Multi-SVM), Decision Tree, Random Forest with Hyperparameter Tuning, XGBoost, and Neural Networks. This model is unique in its application, processing datasets in four different forms: raw datasets, datasets processed with MinMaxScaler, datasets subjected to feature selection using SelectKBest, and a combination of MinMaxScaler processing and SelectKBest feature selection. Such meticulous preprocessing, encompassing normalization and feature selection, is pivotal in ensuring equitable contribution from each feature, thereby optimizing the model's learning process and predictive accuracy. The effectiveness of our model is rigorously evaluated using a dataset comprising 2126 individual records from CTG exams, classified by specialist obstetricians into three types: Normal, Suspect, and Pathological. These records are exhaustively analyzed using various metrics, including Accuracy, Precision, Recall, F1-Score, ROC AUC, and Confusion Matrix. Among the classifiers, XGBoost emerged as the most proficient, consistently outperforming others across multiple metrics. This indicates its superior ability to accurately identify and categorize the different states of fetal health. Our findings thus underscore the significant promise of machine learning in revolutionizing fetal health monitoring, offering a more reliable, objective, and comprehensive method for assessing fetal well-being, with profound implications for prenatal care and clinical decision-making.

Modeling multivariate positive‐valued time series using R‐INLA

AbstractIn this article, we describe fast Bayesian statistical analysis of vector positive‐valued time series, with application to interesting financial data streams. We discuss a flexible level correlated model (LCM) framework for building hierarchical models for vector positive‐valued time series. The LCM allows us to combine marginal gamma distributions for the positive‐valued component responses, while accounting for association among the components at a latent level. We introduce vector autoregression evolution of the latent states, deriving its precision matrix and enabling its estimation using integrated nested Laplace approximation (INLA) for fast approximate Bayesian modeling via the R‐INLA package, building custom functions to handle this setup. We use the proposed method to model interdependencies between intraday volatility measures from several stock indexes.

Development of novel multiple-axis flexure hinges based on hook function curve and a generalized model for multiple-axis flexure hinges

A novel asymmetric multiple-axis hook-function-curve (HFC) flexure hinge (HFCFH) with higher motion precision is proposed. For obtaining high-accuracy compliance and motion precision models of multiple-axis flexure hinges, a brief and generalized analytical model is presented by using the finite beam based matrix modeling (FBMM) method. It can be used to quickly obtain the compliance and precision models by just changing the notch contour functions. The comparative results prove the high accuracy and efficiency of the analytical model. For a much fairer comparison of motion precision between flexure hinges, a new precision model is proposed, in which a non-dimension and more intuitive precision matrix is defined. By using the precision model, the comparison of motion precision between multiple-axis HFCFHs and other multiple-axis flexure hinges indicates that asymmetric flexure hinges have higher motion precision, and multiple-axis HFCFHs also have higher motion precision in asymmetric flexure hinges. Based on the design concept of hybrid flexure hinges, eight types of hybrid multiple-axis flexure hinges with much higher performance are designed, enriching the types of multiple-axis flexure hinges and providing more reference for the selection of hinges in spatial compliant mechanisms.

Application of fused graphical lasso to statistical inference for multiple sparse precision matrices.

In this paper, the fused graphical lasso (FGL) method is used to estimate multiple precision matrices from multiple populations simultaneously. The lasso penalty in the FGL model is a restraint on sparsity of precision matrices, and a moderate penalty on the two precision matrices from distinct groups restrains the similar structure across multiple groups. In high-dimensional settings, an oracle inequality is provided for FGL estimators, which is necessary to establish the central limit law. We not only focus on point estimation of a precision matrix, but also work on hypothesis testing for a linear combination of the entries of multiple precision matrices. We apply a de-biasing technology, which is used to obtain a new consistent estimator with known distribution for implementing the statistical inference, and extend the statistical inference problem to multiple populations. The corresponding de-biasing FGL estimator and its asymptotic theory are provided. A simulation study and an application of the diffuse large B-cell lymphoma data show that the proposed test works well in high-dimensional situation.

Alternative modified Cholesky decomposition of the precision matrix of longitudinal data

The correlation matrix might be of scientific interest for longitudinal data. However, few studies have focused on both robust estimation of the correlation matrix against model misspecification and robustness to outliers in the data, when the precision matrix possesses a typical structure. In this paper, we propose an alternative modified Cholesky decomposition (AMCD) for the precision matrix of longitudinal data, which results in robust estimation of the correlation matrix against model misspecification of the innovation variances. A joint mean-covariance model with multivariate normal distribution and AMCD is established, the quasi-Fisher scoring algorithm is developed, and the maximum likelihood estimators are proven to be consistent and asymptotically normally distributed. Furthermore, a double-robust joint modeling approach with multivariate Laplace distribution and AMCD is established, and the quasi-Newton algorithm for maximum likelihood estimation is developed. The simulation studies and real data analysis demonstrate the effectiveness of the proposed AMCD method.

Application of quantum technology Variational Quantum Classifier in agriculture for classification of wheat varieties

This study proposes the use of Variational Quantum Classifier for automated classification of wheat varieties. A model trained on a large data set will be able to identify unique patterns and relationships between seed characteristics and cultivar membership. This will allow farmers and researchers to more accurately identify wheat varieties, which in turn can improve growing and crop management processes. This approach is justified not only by the need to optimize agricultural production, but also in the context of the use of advanced technologies to achieve precision and efficiency in the agricultural sector. As a result of this research, it is expected that the quality and sustainability of wheat production will improve, which is important for food security and sustainable agricultural development. The goal of the problem is to classify wheat varieties based on seed characteristics. VQC is trained on the training dataset and then evaluated on the test dataset. To evaluate the performance of the model, various metrics are used, such as accuracy, precision, recall, F1-score and Confusion Matrix.

Enhanced Recognition of Handwritten Marathi Compound Characters using CNN-SVM Hybrid Approach

This study presents a hybrid recognition system for multi-class compound Marathi characters, which addresses the problem of handwritten Marathi character recognition. The methodology efficiently bridges the gap between feature extraction and classification by integrating a Convolutional Neural Network (CNN) and Support Vector Machine (SVM). The first step is gathering and preprocessing a wide range of handwritten Marathi compound characters that are written in different styles. Using conventional supervised learning methods, the CNN is trained on this dataset, paying special attention to data augmentation and validation in order to reduce overfitting. High-level features taken from the final fully connected layer of the CNN are fed into an SVM classifier in the next step. By using these features in its training, the SVM improves prediction accuracy. For multi-class classification, the one-vs-all method is used. The hybrid CNN-SVM algorithm demonstrates its effectiveness in the crucial phases of feature extraction and classification by identifying handwritten compound Marathi characters with remarkable accuracy. Evaluation metrics, such as accuracy, precision, recall, F1-score, and confusion matrix analysis, are employed in the process of evaluating the effectiveness of the model. This assessment is carried out on a different testing dataset, offering a thorough examination of the model's functionality. The proposed algorithm demonstrates its superior performance and potential for improved character recognition by achieving training accuracy of 98.60% and validation accuracy of 97.69%. The development of handwriting recognition systems has benefited greatly from this research, especially when it comes to intricate scripts like Marathi. The suggested hybrid algorithm shows encouraging outcomes and has a great deal of potential for use in document processing, natural language comprehension, and character recognition in languages that use the Marathi script. Subsequent efforts will centre on refining the model and investigating ensemble methods to increase the robustness and accuracy of recognition.

Multi-response Regression for Block-missing Multi-modal Data without Imputation.

Multi-modal data are prevalent in many scientific fields. In this study, we consider the parameter estimation and variable selection for a multi-response regression using block-missing multi-modal data. Our method allows the dimensions of both the responses and the predictors to be large, and the responses to be incomplete and correlated, a common practical problem in high-dimensional settings. Our proposed method uses two steps to make a prediction from a multi-response linear regression model with block-missing multi-modal predictors. In the first step, without imputing missing data, we use all available data to estimate the covariance matrix of the predictors and the cross-covariance matrix between the predictors and the responses. In the second step, we use these matrices and a penalized method to simultaneously estimate the precision matrix of the response vector, given the predictors, and the sparse regression parameter matrix. Lastly, we demonstrate the effectiveness of the proposed method using theoretical studies, simulated examples, and an analysis of a multi-modal imaging data set from the Alzheimer's Disease Neuroimaging Initiative.