Expectation Maximization Research Articles

Optimization and application of renal depth measurement method in the cadmium-zinc-telluride‑based SPECT/CT renal dynamic imaging.

This study aims to evaluate the accuracy of four kidney depth measurement methods-nuclear medicine tomography, nuclear medicine lateral scanning, ultrasound, and Tonnesen's formula-based estimation-using CT measurements as the reference standard. Additionally, it investigates the feasibility of utilizing nuclear medicine tomography and lateral scanning for measuring kidney depth in 99mTc-DTPA renal dynamic imaging. Hollow kidney phantoms mimicking the shape and volume of adult kidneys were 3D printed and filled with 99mTcO4- solution. These phantoms were then subjected to lateral scanning and nuclear medicine tomography using CZT (cadmium-zinc-telluride) SPECT/CT to determine the optimal post-processing method. Forty patients who underwent renal dynamic imaging were recruited for the study. Renal depths were derived from ultrasound, lateral imaging, nuclear medicine tomography, formula-based estimation, and CT measurements. The renal depths obtained through these four methods were for correlation with CT-measured renal depths. Additionally, the absolute differences between renal depths obtained by each method and the CT standard were analyzed and compared across groups. Using kidney phantoms, nuclear medicine tomography images were processed with a Butterworth filter (cutoff frequency = 0.6), and renal outlines in lateral images was manually delineated. In the clinical validation phase, correlation coefficients indicated strong associations between renal depths measured by nuclear medicine tomography (left kidney: R = 0.885, P < 0.05; right kidney: R = 0.927, P < 0.05) and lateral scanning (left kidney: R = 0.933, P < 0.05; right kidney: R = 0.956, P < 0.05) compared to CT measurements. The difference in kidney depth between nuclear medicine tomography and CT measurements were the smallest and statistically significant (left kidney: 0.69 ± 0.51; right kidney: 0.58 ± 0.41, P < 0.05). Using ordered subset expectation maximization (OSEM) in conjunction with a Butterworth filter (fc = 0.6) as the post-processing method, nuclear medicine tomography enables more accurate renal depth measurements without increasing the radiation dose to patients.

Sieve Maximum Likelihood Estimation of Partially Linear Transformation Models With Interval-Censored Data.

Partially linear models provide a valuable tool for modeling failure time data with nonlinear covariate effects. Their applicability and importance in survival analysis have been widely acknowledged. To date, numerous inference methods for such models have been developed under traditional right censoring. However, the existing studies seldom target interval-censored data, which provide more coarse information and frequently occur in many scientific studies involving periodical follow-up. In this work, we propose a flexible class of partially linear transformation models to examine parametric and nonparametric covariate effects for interval-censored outcomes. We consider the sieve maximum likelihood estimation approach that approximates the cumulative baseline hazard function and nonparametric covariate effect with the monotone splines and -splines, respectively. We develop an easy-to-implement expectation-maximization algorithm coupled with three-stage data augmentation to facilitate maximization. We establish the consistency of the proposed estimators and the asymptotic distribution of parametric components based on the empirical process techniques. Numerical results from extensive simulation studies indicate that our proposed method performs satisfactorily in finite samples. An application to a study on hypobaric decompression sickness suggests that the variable TR360 exhibits a significant dynamic and nonlinear effect on the risk of developing hypobaric decompression sickness.

Data discretization impact on deep learning for missing value imputation of continuous data

In various fields of information examination, for example, AI, profoundly getting the hang of missing information is a typical issue. Missing qualities should be tended to since they can adversely affect the exactness and adequacy of prescient models. This research investigates how data discretization affects deep learning methods for filling the missing values in datasets with continuous features. They provide a unique method for imputing missing values using deep neural networks (DNNs) called extravagant expectation maximization-deep neural network (EEM-DNN). This approach discretizes continuous features into separate intervals initially. This is justified by treating the issue of missing value imputation as a classification work, with the missing values being considered a distinct class. A DNN, designed explicitly for imputation, is then trained using the discretized data. The expectation maximization concepts are incorporated into the network architecture, and as a result, the network iteratively improves its imputation predictions. They run comprehensive experiments on several datasets from different fields to gauge the efficacy of the suggested strategy. The effectiveness of EEM-DNN is compared to that of other imputation approaches, such as traditional imputation techniques and deep learning methods without data discretization. Our findings show that data discretization significantly enhances imputation accuracy. In terms of imputation accuracy and prediction performance on downstream tasks, the EEM-DNN method regularly performs better than alternative methods. It also examines if various discretization techniques affect the overall imputation process. They find that the trade-off between bias and variance in imputed data depends on the discretization method selected. This highlights the significance of choosing a suitable discretization approach depending on the unique properties of the dataset.

Fast standard error estimation for joint models of longitudinal and time-to-event data based on stochastic EM algorithms.

Maximum likelihood inference can often become computationally intensive when performing joint modeling of longitudinal and time-to-event data, due to the intractable integrals in the joint likelihood function. The computational challenges escalate further when modeling HIV-1 viral load data, owing to the nonlinear trajectories and the presence of left-censored data resulting from the assay's lower limit of quantification. In this paper, for a joint model comprising a nonlinear mixed-effect model and a Cox Proportional Hazards model, we develop a computationally efficient Stochastic EM (StEM) algorithm for parameter estimation. Furthermore, we propose a novel technique for fast standard error estimation, which directly estimates standard errors from the results of StEM iterations and is broadly applicable to various joint modeling settings, such as those containing generalized linear mixed-effect models, parametric survival models, or joint models with more than two submodels. We evaluate the performance of the proposed methods through simulation studies and apply them to HIV-1 viral load data from six AIDS Clinical Trials Group studies to characterize viral rebound trajectories following the interruption of antiretroviral therapy (ART), accounting for the informative duration of off-ART periods.

Regularized Bayesian algorithms for Q-matrix inference based on saturated cognitive diagnosis modelling.

Q-matrices are crucial components of cognitive diagnosis models (CDMs), which are used to provide diagnostic information and classify examinees according to their attribute profiles. The absence of an appropriate Q-matrix that correctly reflects item-attribute relationships often limits the widespread use of CDMs. Rather than relying on expert judgment for specification and post-hoc methods for validation, there has been a notable shift towards Q-matrix estimation by adopting Bayesian methods. Nevertheless, their dependency on Markov chain Monte Carlo (MCMC) estimation requires substantial computational burdens and their exploratory tendency is unscalable to large-scale settings. As a scalable and efficient alternative, this study introduces the partially confirmatory framework within a saturated CDM, where the Q-matrix can be partially defined by experts and partially inferred from data. To address the dual needs of accuracy and efficiency, the proposed framework accommodates two estimation algorithms-an MCMC algorithm and a Variational Bayesian Expectation Maximization (VBEM) algorithm. This dual-channel approach extends the model's applicability across a variety of settings. Based on simulated and real data, the proposed framework demonstrated its robustness in Q-matrix inference.

An investigation to improve a nonlinear mixed-effects approach for EC50 estimation based on multi-donor dose–response data

ABSTRACT Dose–response relationships are important in assessing the efficacy and potency of compounds, which can usually be characterized by a 4-parameter logistic (4-PL) model estimating EC50, slope factor, lower asymptote, and upper asymptote. EC50, the concentration of a compound that induces a response halfway between the baseline and maximum, is a key quantity to evaluate compound potency. For multi-donor dose–response data, it is often of interest to estimate the overall EC50 (i.e. the average EC50 of the population of donors) and its 95% confidence interval (CI). A few multi-donor EC50 estimation methods have been proposed in the literature. Jiang and Kopp-Schneider (2014) systematically compared the meta-analysis approach and the nonlinear mixed-effects approach and concluded that the meta-analysis approach is simple and robust to summarize EC50 estimates from multiple experiments, especially suited in the case of a small number of experiments, while the nonlinear mixed-effects approach has the issue of convergence failures probably due to overparameterization. In this article, we propose a modification of the nonlinear mixed-effects approach by using the stochastic approximation expectation-maximization (SAEM) algorithm to estimate model parameters and using multiple starting points to search for globally optimal values, which can substantially alleviate the issue of convergence failures even for small number of donors (e.g. n = 3), and achieve a smaller absolute median bias and better coverage probability of 95% confidence interval than the meta-analysis approach when the number of donors is not too small (e.g. n ≥ 7).

Estimation of Jacquard's genetic identity coefficients with bi-allelic variants by constrained least-squares.

The Jacquard genetic identity coefficients are of fundamental importance in relatedness research. We address the estimation of these coefficients as well as other relationship parameters that derive from them such as kinship and inbreeding coefficients using a concise matrix framework. Estimation of the Jacquard coefficients via likelihood methods and the expectation-maximization algorithm is computationally very demanding for large numbers of polymorphisms. We propose a constrained least squares approach to estimate the Jacquard coefficients. A simulation study shows constrained least squares achieves root-mean-squared errors that are comparable with those of the maximum likelihood approach, in particular when founder allele frequencies are unknown, while obtaining enormous computational savings.

Optimizing Parameters for Enhanced Iterative Image Reconstruction Using Extended Power Divergence

In this paper, we propose a method for optimizing the parameter values in iterative reconstruction algorithms that include adjustable parameters in order to optimize the reconstruction performance. Specifically, we focus on the power divergence-based expectation-maximization algorithm, which includes two power indices as adjustable parameters. Through numerical and physical experiments, we demonstrate that optimizing the evaluation function based on the extended power-divergence and weighted extended power-divergence measures yields high-quality image reconstruction. Notably, the optimal parameter values derived from the proposed method produce reconstruction results comparable to those obtained using the true image, even when using distance functions based on differences between forward projection data and measured projection data, as verified by numerical experiments. These results suggest that the proposed method effectively improves reconstruction quality without the need for machine-learning techniques in parameter selection. Our findings also indicate that this approach is useful for enhancing the performance of iterative reconstruction algorithms, especially in medical imaging, where high-accuracy reconstruction under noisy conditions is required.

Gamma Process Based Degradation Model with Fractional Gaussian Noise

In modern industrial and engineering systems, stochastic degradation models are widely used for reliability analysis and maintenance decision-making. However, due to imperfect sensors and environmental influences, it is difficult to directly observe the latent degradation states. Traditional degradation models typically assume that measurement errors have simple statistical properties, but this assumption often does not hold in practical applications. To address this issue, this paper constructs a degradation model based on the Gamma process (GP) and assumes that measurement noise can be characterized by the fractional Gaussian noise (FGN). Furthermore, this paper proposes a method combining Gibbs sampling with the stochastic expectation-maximization (SEM) algorithm to achieve efficient estimation of the model parameters and accurate inference of the latent degradation states. Simulation results indicate that the proposed model exhibits better generalizability compared to the GP model with Gaussian noise.

Filtering Useful App Reviews Using Naïve Bayes—Which Naïve Bayes?

App reviews provide crucial feedback for software maintenance and evolution, but manually extracting useful reviews from vast volumes is time-consuming and challenging. This study investigates the effectiveness of six Naïve Bayes variants for automatically filtering useful app reviews. We evaluated these variants on datasets from five popular apps, comparing their performance in terms of accuracy, precision, recall, F-measure, and processing time. Our results show that Expectation Maximization-Multinomial Naïve Bayes with Laplace smoothing performed best overall, achieving up to 89.2% accuracy and 0.89 F-measure. Complement Naïve Bayes with Laplace smoothing demonstrated particular effectiveness for imbalanced datasets. Generally, incorporating Laplace smoothing and Expectation Maximization improved performance, albeit with increased processing time. This study also examined the impact of data imbalance on classification performance. Our findings suggest that these advanced Naïve Bayes variants hold promise for filtering useful app reviews, especially when dealing with limited labeled data or imbalanced datasets. This research contributes to the body of evidence around app review mining and provides insights for enhancing software maintenance and evolution processes.

Consensus Guidelines for Delineation of Clinical Target Volumes for Intensity-Modulated Radiotherapy for Intact Cervical Cancer: An Update.

Accurate target delineation is essential when using intensity-modulated radiotherapy (IMRT) for intact cervical cancer. In 2011, the Radiation Therapy Oncology Group (RTOG) published a consensus guideline using magnetic resonance imaging (MRI). The current project expands on the previous atlas by including computed tomography (CT)-based contours, contours with MRI and positron- emission- tomography (PET) registrations, the addition of common and complex scenarios, and to incorporate information on simulation and treatment planning techniques. Twenty-eight experts in gynecologic radiation oncology contoured three cases, first on a non-contrast CT simulation scan, then with registered diagnostic scans. The cases included (1) FIGO IIIC1 with a bulky tumor and vaginal metastasis, (2) FIGO IIB with calcified uterine fibromas, and (3) FIGO IIIC2 with large lymph nodes. The contours on all six datasets (three CT simulations without diagnostic images and three with registered images) were analyzed for consistency of delineation using an expectation-maximization algorithm for simultaneous truth and performance level estimation (STAPLE) with kappa statistics as a measure of agreement. The contours were reviewed, discussed, and edited in a group meeting prior to finalizing. Contours showed considerable agreement between experts in each of the cases with kappa statistics of 0.67-0.72. For each case, diagnostic PET±MRI was associated with an increase in volume. The largest increase was the CTV primary for Case 2 with a 20% increase in volume and 54% increase in STAPLE estimate volume, which may be due to variance in registration priorities. For the third case, 92.9% increased their CTVs based on the addition of the diagnostic PET scan. The main areas of variance were in determining the superior extent of CTV coverage, coverage of the mesorectum, and simulation and planning protocols. This study shows the value as well as the challenges of using co-registered diagnostic imaging, with an average increase in volumes when incorporating MRI and PET.

Color image watermarking using vector SNCM-HMT

An image watermarking scheme is typically evaluated using three main conflicting characteristics: imperceptibility, robustness, and capacity. Developing a good image watermarking method is challenging because it requires a trade-off between these three basic characteristics. In this paper, we proposed a statistical color image watermarking based on robust discrete nonseparable Shearlet transform (DNST)-fast quaternion generic polar complex exponential transform (FQGPCET) magnitude and vector skew-normal-Cauchy mixtures (SNCM)-hidden Markov tree (HMT). The proposed watermarking system consists of two main parts: watermark inserting and watermark extraction. In watermark inserting, we first perform DNST on R, G, and B components of color host image, respectively. We then compute block FQGPCET of DNST domain color components, and embed watermark signal in DNST-FQGPCET magnitudes using multiplicative approach. In watermark extraction, we first analyze the robustness and statistical characteristics of local DNST-FQGPCET magnitudes of color image. We then observe that, vector SNCM-HMT model can capture accurately the marginal distribution and multiple strong dependencies of local DNST-FQGPCET magnitudes. Meanwhile, vector SNCM-HMT parameters can be computed effectively using variational expectation–maximization (VEM) parameter estimation. Motivated by our modeling results, we finally develop a new statistical color image watermark decoder based on vector SNCM-HMT and maximum likelihood (ML) decision rule. Experimental results on extensive test images demonstrate that the proposed statistical color image watermarking provides a performance better than that of most of the state-of-the-art statistical methods and some deep learning approaches recently proposed in the literature.

Research on the P‐S‐N Curve Fitting Method of Notched Specimens Considering Small Sample Properties

ABSTRACTAiming at the issue of fatigue test data for large‐scale mechanical components of building steel are very limited, a method for fitting P‐S‐N curves under small sample data of notched specimens is proposed to predict fatigue life. First, a fatigue life subsample augmented and its reliability assessment method are established, based on Bayesian hierarchical modeling and modified Monte Carlo method. Second, a clustering combination weighting method is proposed, to define weights of hidden variables of the binomial mixture Weibull distribution, and the expectation–maximization algorithm is used to determine probability density function of the distribution. Finally, the P‐S‐N curves under various failure probabilities are fitted with Weibull distributed life models, and the convergence and prediction accuracy of the different models are compared. The results show that the fatigue data of small samples can be predicted better by using mixed Weibull distribution, and the fitting P‐S‐N curve is more reliable and accurate.

The Fault Diagnosis Method for Photovoltaic Modules Based on Machine Learning

Based on the urban natural gas pipeline accident statistics and semi-quantitative risk evaluation index system, this paper applies Bayesian network to establish a network model between various types of risk factors and the risk of natural gas pipeline failure. The EM algorithm was used to learn from the statistical accident data to obtain the parameters of the model. Based on the principle of evidential reasoning in reverse, the probability of occurrence of all risk indicators can be obtained when the probability of occurrence of urban natural gas pipeline accidents is 100%, the index weight is obtained by normalizing the occurrence probability. On this basis, this paper develops an efficient urban natural gas pipeline integrity risk identification and management software. The software can realize the basic data management of urban natural gas pipeline system, pipeline relative risk value calculation, pipeline risk level calculation and other functions, and the results are visualized. Finally, the practicability and effectiveness of the model and software are verified by a case of natural gas pipeline evaluation in a block.

Parallel-way: Multi-modality-based brain tumor segmentation using parallel capsule network

ABSTRACT Brain tumors present a formidable diagnostic challenge due to their aberrant cell growth. Accurate determination of tumor location and size is paramount for effective diagnosis. Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET) are pivotal tools in clinical diagnosis, yet tumor segmentation within their images remains challenging, particularly at boundary pixels, owing to limited sensitivity. Recent endeavors have introduced fusion-based strategies to refine segmentation accuracy, yet these methods often prove inadequate. In response, we introduce the Parallel-Way framework to surmount these obstacles. Our approach integrates MRI and PET data for a holistic analysis. Initially, we enhance image quality by employing noise reduction, bias field correction, and adaptive thresholding, leveraging Improved Kalman Filter (IKF), Expectation Maximization (EM), and Improved Vibe Algorithm (IVib), respectively. Subsequently, we conduct multi-modality image fusion through the Dual-Tree Complex Wavelet Transform (DTWCT) to amalgamate data from both modalities. Following fusion, we extract pertinent features using the Advanced Capsule Network (ACN) and reduce feature dimensionality via Multi-objective Diverse Evolution-based selection. Tumor segmentation is then executed utilizing the Twin Vision Transformer with dual attention mechanism. Implemented our Parallel-Way framework which exhibits heightened model performance. Evaluation across multiple metrics, including accuracy, sensitivity, specificity, F1-Score, and AUC, underscores its superiority over existing methodologies.

Missing Data Imputation in Balanced Construction for Incomplete Block Designs

Observational data with massive sample sizes are often distributed on many local machines. From an experimental design perspective, investigators often desire to identify the effect of new treatments (even ML algorithms) on many blocks of experimental data. With time requirements or budget constraints, assigning all treatments to each block is not always feasible. This creates incomplete responses with respect to a randomized complete block design (RCBD). These incomplete responses are missing by design. However, whether they can be estimated with missing imputation methods is not well understood. Thus, it is challenging to correctly identify the treatment effects with missing data. To this end, this paper provides a method for imputation and analysis of the responses with missing data. The proposed method consists of three steps: Reconstruction, Imputation, and `Complete’-data Analysis (RICA). The incomplete responses are imputed with the expectation-maximization (EM) algorithm. The RCBD model is then fitted by the resulting dataset. The identifiability result suggests that the missing may be nonignorable for each block, but the whole data of an incomplete design are missing by design when the design is balanced. Theoretical results on relative efficiency also inform us when the missingness should be imputed for incomplete designs with the role of balanced variance. Applications on real-world data verify the efficacy of this method.

Modeling uncertainty with the truncated zeta distribution in mixture models for ordinal responses

In recent three decades, there has been a rapid increasing interest in the mixture models for ordinal responses, and the classical CUB model as a fundamental one has been extended to different preference and uncertainty models. In this article, based on a response style supported by Zipf’s law, we propose a novel mixture model for ordinal responses via replacing the uncertainty component of the CUB model with a truncated Zeta distribution. Parameters estimation with EM algorithm, inferential issues with respect to the approximation of a truncated Riemann Zeta function and estimators’ variance-covariance information matrix are investigated. The advantages of the proposed model over the CUB model have been illustrated with simulations of two sets of Monte Carlo experiments and practical applications of a health survey and a bicycle use. The intention of the article is to distinguish the respondents’ true preference from the response style of “the higher, the less”, so as to understand more reasonably the formation causes of ordinal responses.

Applying Bayesian Networks for Detecting Bank Fraudulent Transactions in Nigeria

Bank fraud is an increasingly prevalent issue, causing substantial financial losses for both financial institutions and customers. Also, with the increasing prevalence of bank fraud, especially facilitated by online banking and digital payments, there is a pressing need for potential expertise deployment and advanced fraud detection techniques in real-world banking systems. This study specified the Bayesian Network models for detecting fraudulent bank transactions. Bayesian Networks offer a probabilistic graphical modeling approach that can effectively capture complex relationships and dependencies within financial data. Thus, the research aimed at developing a custom Bayesian network model trained on a large dataset of bank transactions comprising over one million bank transactions to classify instances as fraudulent or non-fraudulent. Python 3.11.10 was used for the graphical representations. Down-sampling was employed to reduce the dataset from its initial size of 1 million observations to 17,650 observations, ensuring a balanced representation of both fraud and non-fraud instances. Various estimation techniques: Maximum Likelihood, Bayesian Networks, and Expectation Maximization were employed and evaluated to learn the model parameters. The model's performance was measured using metrics: accuracy, precision, recall, F1-score, and ROC-AUC. The Bayesian Networks estimator achieved an overall accuracy of 66.18%, precision of 67.73%, F1-score of 64.06%, ROC-AUC of 66.13%, Recall of 60.77%, Sensitivity of 60.77% and Specificity of 71.50%. Also, the Maximum Likelihood achieved an overall Accuracy of 66.77%, Precision of 69.22%, F1-score of 63.96%, ROC-AUC of 66.71%, Recall of 59.45%, Sensitivity of 59.45% and Specificity of 73.97%. Likewise, the Expectation Maximization achieved an overall Accuracy of 66.83%, Precision of 69.31%, F1-score of 64.00%, ROC-AUC of 66.77%, Recall of 59.45%, Sensitivity of 59.45% and Specificity of 74.09%. On the confusion matrix, the model correctly classified 1272 instances as Non-Fraudulent transactions (True Negative). Also, it was observed that the model incorrectly classified 507 instances as fraudulent transactions when they were Non-Fraudulent (False Positive). The model similarly incorrectly classified 687 instances as Non-Fraudulent transactions when they were Fraudulent (False Negative). Finally, it correctly classified 1064 instances as fraudulent transactions (True Positive). These results demonstrated the Bayesian Network's ability to identify fraudulent transactions while minimizing false alarms accurately. The findings highlight the potential of Bayesian Networks as a robust framework for fraud detection in the banking sector, contributing to enhanced security and reduced financial losses. The developed model can be introduced into existing banking systems to strengthen fraud prevention strategies.

Order-restricted statistical inference and optimal censoring scheme for Gompertz distribution based on joint type-II progressive censored data

This paper considers the order-restricted statistical inference for two populations based on the joint type-II progressive censoring scheme. The lifetime distributions of the two populations are supposed to follow the Gompertz distribution with the same shape parameter but different scale parameters. The maximum likelihood estimates of the unknown parameters are derived by employing the Newton-Raphson algorithm and the expectation-maximization algorithm, respectively. The Fisher information matrix is then employed to construct asymptotic confidence intervals. For Bayes estimation, we assume an ordered Beta-Gamma prior for the scale parameters and a Gamma prior for the common shape parameter. Bayes estimations and the highest posterior density credible intervals for unknown parameters under two different loss functions are obtained with the importance sampling technique. To evaluate the performance of order-restricted inference, extensive Monte Carlo simulations are performed and two air-conditioning systems datasets are used to illustrate the proposed inference methods. In addition, the results are compared with the case when there is no order restriction on the parameters. Finally, the optimal censoring scheme is obtained by four optimality criteria.

A semiparametric accelerated failure time-based mixture cure tree

The mixture cure rate model (MCM) is the most widely used model for the analysis of survival data with a cured subgroup. In this context, the most common strategy to model the cure probability is to assume a generalized linear model with a known link function, such as the logit link function. However, the logit model can only capture simple effects of covariates on the cure probability. In this article, we propose a new MCM where the cure probability is modeled using a decision tree-based classifier and the survival distribution of the uncured is modeled using an accelerated failure time structure. To estimate the model parameters, we develop an expectation maximization algorithm. Our simulation study shows that the proposed model performs better in capturing nonlinear classification boundaries when compared to the logit-based MCM and the spline-based MCM. This results in more accurate and precise estimates of the cured probabilities, which in-turn results in improved predictive accuracy of cure. We further show that capturing nonlinear classification boundary also improves the estimation results corresponding to the survival distribution of the uncured subjects. Finally, we apply our proposed model and the EM algorithm to analyze an existing bone marrow transplant data.