Expectation Maximization Research Articles

Automated phase-type distribution fitting via expectation maximization

Automated phase-type distribution fitting via expectation maximization

Mora: abundance aware metagenomic read re-assignment for disentangling similar strains

BackgroundTaxonomic classification of reads obtained by metagenomic sequencing is often a first step for understanding a microbial community, but correctly assigning sequencing reads to the strain or sub-species level has remained a challenging computational problem.ResultsWe introduce Mora, a MetagenOmic read Re-Assignment algorithm capable of assigning short and long metagenomic reads with high precision, even at the strain level. Mora is able to accurately re-assign reads by first estimating abundances through an expectation-maximization algorithm and then utilizing abundance information to re-assign query reads. The key idea behind Mora is to maximize read re-assignment qualities while simultaneously minimizing the difference from estimated abundance levels, allowing Mora to avoid over assigning reads to the same genomes. On simulated diverse reads, this allows Mora to achieve F1 scores comparable to other algorithms while having less runtime. However, Mora significantly outshines other algorithms on very similar reads. We show that the high penalty of over assigning reads to a common reference genome allows Mora to accurately infer correct strains for real data in the form of E. coli reads.ConclusionsMora is a fast and accurate read re-assignment algorithm that is modularized, allowing it to be incorporated into general metagenomics and genomics workflows. It is freely available at https://github.com/AfZheng126/MORA.

Uncertainty Computation at Finite Distance in Nonlinear Mixed Effects Models-a New Method Based on Metropolis-Hastings Algorithm.

The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration.

Block-wise imputation EM algorithm in multi-source scenario: ADNI case

Alzheimer’s disease is the most common form of dementia and the early detection is essential to prevent its proliferation. Real data available has been of paramount importance in order to achieve progress in the automatic detection despite presenting two major challenges: Multi-source observations containing Magnetic resonance (MRI), Positron emission tomography (PET) and Cerebrospinal fluid data (CSF); and also missing values within all these sources. Most machine learning techniques perform this predictive task by using a single data modality. Nevertheless, the integration of all these sources of evidence could possibly bring a higher performance at different stages of disease progression. The Expectation Maximization (EM) algorithm has been successfully employed to handle missing values, but it is not designed for typical Machine Learning scenarios where an imputation model is created over training data and subsequently applied on a testing set. In this work, we propose EMreg-KNN, a novel supervised and multi-source imputation algorithm. Based on the EM algorithm, EMreg-KNN builds a regression ensemble model for the imputation of future data thus allowing the further utilization of any vector-based Machine Learning method to automatically assess the Alzheimer’s disease diagnosis. Using the ADNI database, the proposed method achieves significant improvements on F1, AUC and Accuracy measures over classical imputation methods for this database using four classification algorithms. Considering these classifiers in four different classification scenarios, our algorithm is experimentally superior in terms of the F measure, in nearly 82% of the cases under evaluation.

Phantom and clinical evaluation of the Bayesian penalised likelihood reconstruction algorithm Q.Clear without PSF correction in amyloid PET images

PurposeBayesian penalised likelihood (BPL) reconstruction, which incorporates point-spread-function (PSF) correction, provides higher signal-to-noise ratios and more accurate quantitation than conventional ordered subset expectation maximization (OSEM) reconstruction. However, applying PSF correction to brain PET imaging is controversial due to Gibbs artefacts that manifest as unpredicted cortical uptake enhancement. The present study aimed to validate whether BPL without PSF would be useful for amyloid PET imaging.MethodsImages were acquired from Hoffman 3D brain and cylindrical phantoms for phantom study and 71 patients administered with [18F]flutemetamol in clinical study using a Discovery MI. All images were reconstructed using OSEM, BPL with PSF correction, and BPL without PSF correction. Count profile, %contrast, recovery coefficients (RCs), and image noise were calculated from the images acquired from the phantoms. Amyloid β deposition in patients was visually assessed by two physicians and quantified based on the standardised uptake value ratio (SUVR).ResultsThe overestimated radioactivity in profile curves was eliminated using BPL without PSF correction. The %contrast and image noise decreased with increasing β values in phantom images. Image quality and RCs were better using BPL with, than without PSF correction or OSEM. An optimal β value of 600 was determined for BPL without PSF correction. Visual evaluation almost agreed perfectly (κ = 0.91–0.97), without depending on reconstruction methods. Composite SUVRs did not significantly differ between reconstruction methods.ConclusionGibbs artefacts disappeared from phantom images using the BPL without PSF correction. Visual and quantitative evaluation of [18F]flutemetamol imaging was independent of the reconstruction method. The BPL without PSF correction could be the standard reconstruction method for amyloid PET imaging, despite being qualitatively inferior to BPL with PSF correction for [18F]flutemetamol amyloid PET imaging.

Semiparametric Probit Regression Model with General Interval-Censored Failure Time Data

Interval-censored data frequently arise in various biomedical areas involving periodical follow-ups where the failure or event time of interest cannot be observed exactly but is only known to fall into a time interval. This article considers a semiparametric probit regression model, a valuable alternative to other commonly used semiparametric models in survival analysis, to investigate potential risk factors for the interval-censored failure time of interest. We develop an expectation-maximization (EM) algorithm to conduct the pseudo maximum likelihood estimation (MLE) using the working independence strategy for general or mixed-case interval-censored data. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal with the empirical process techniques. In addition, we propose a novel penalized EM algorithm for simultaneously achieving variable selection and parameter estimation in the case of high-dimensional covariates. The proposed variable selection method can be readily implemented with some existing software and considerably reduces the estimation error of the proposed pseudo-MLE approach. Simulation studies demonstrate the satisfactory performance of the proposed methods. An application to a set of interval-censored data on prostate cancer further confirms the utility of the methodology. Supplementary materials for this article are available online.

A semiparametric Gaussian mixture model for chest CT-based 3D blood vessel reconstruction.

Computed tomography (CT) has been a powerful diagnostic tool since its emergence in the 1970s. Using CT data, 3D structures of human internal organs and tissues, such as blood vessels, can be reconstructed using professional software. This 3D reconstruction is crucial for surgical operations and can serve as a vivid medical teaching example. However, traditional 3D reconstruction heavily relies on manual operations, which are time-consuming, subjective, and require substantial experience. To address this problem, we develop a novel semiparametric Gaussian mixture model tailored for the 3D reconstruction of blood vessels. This model extends the classical Gaussian mixture model by enabling nonparametric variations in the component-wise parameters of interest according to voxel positions. We develop a kernel-based expectation-maximization algorithm for estimating the model parameters, accompanied by a supporting asymptotic theory. Furthermore, we propose a novel regression method for optimal bandwidth selection. Compared to the conventional cross-validation-based (CV) method, the regression method outperforms the CV method in terms of computational and statistical efficiency. In application, this methodology facilitates the fully automated reconstruction of 3D blood vessel structures with remarkable accuracy.

Robust acoustic reflector localization using a modified EM algorithm

In robotics, echolocation has been used to detect acoustic reflectors, e.g., walls, as it aids the robotic platform to navigate in darkness and also helps detect transparent surfaces. However, the transfer function or response of an acoustic system, e.g., loudspeakers/emitters, contributes to non-ideal behavior within the acoustic systems that can contribute to a phase lag due to propagation delay. This non-ideal response can hinder the performance of a time-of-arrival (TOA) estimator intended for acoustic reflector localization especially when the estimation of multiple reflections is required. In this paper, we, therefore, propose a robust expectation-maximization (EM) algorithm that takes into account the response of acoustic systems to enhance the TOA estimation accuracy when estimating multiple reflections when the robot is placed in a corner of a room. A non-ideal transfer function is built with two parameters, which are estimated recursively within the estimator. To test the proposed method, a hardware proof-of-concept setup was built with two different designs. The experimental results show that the proposed method could detect an acoustic reflector up to a distance of 1.6 m with 60%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$60\\%$$\\end{document} accuracy under the signal-to-noise ratio (SNR) of 0 dB. Compared to the state-of-the-art EM algorithm, our proposed method provides improved performance when estimating TOA by 10%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10\\%$$\\end{document} under a low SNR value.

A bridge damage monitoring and assessment strategy based on Gaussian mixture modelling

For the bridges equipped with health monitoring systems, it is essential to precisely assess the health status of the bridge from the data with noise and outliers. An improved Gaussian mixture model clustering algorithm is used to process the obtained bridge strain sensor monitoring data and generate the characteristic data of clustering in order to improve the accuracy of data analysis of bridge health monitoring system. The cluster and feature data are obtained by Expectation Maximization process, and the isolated clusters are filtered out by the threshold parameters of weight and the Euclidean distance between clusters center. Based on the feature data, a scoring strategy is established to assess the bridge health and sensor status. The proposed strategy is used to analyze the monitoring data of a bridge in western China, and the analysis results show the availability of this strategy. Compared with the directly collected data, the processed bridge health scoring curve variation is smooth, which can reduce the influence of noise and abnormal data. The sensor status scoring curve can track changes in collected data and respond to different transformation scenarios. This shows that the proposed strategy can evaluate the state of this bridge and the sensors. provided a reference for bridge maintenance decision during the operational period.

Multivariate Approach for Texture Segmentation using Probabilistic Statistical Model

The analysis of the regions of the image is of the prerogatives in the fields of medical and global systems meant for location identification. This analysis is strongly associated with partitions of regions of interest such as segmentation. For an effective strategy of analyzing the regions of interest, texture of the image plays a major concern. The texture is generally characterized using signal processing methods namely Discrete Cosine Transformation coefficients and their specific insights leading to feature vector selection. Further, to identify regions, a statistical model needs to be identified for the feature matrix vector and thus make use of Gaussian mixture model with extensions. The Expectation Maximization approach is used, and performance is assessed by experimenting with random images from the Brodatz data store domain. Performance measurements for texture segmentation that can be attributed are Global Cons. Error (GC), Prob. Rand. Index (PR) and Variation of data (VA). These are determined alongside the confusion matrix. To assess the improvement, a comparison was made with other existing models and showed better. The algorithms will be exceptionally helpful for clinical analysis and in radio navigation map systems.

Kalman filter with impulse noised outliers: a robust sequential algorithm to filter data with a large number of outliers.

Impulse noised outliers are data points that differ significantly from other observations. They are generally removed from the data set through local regression or the Kalman filter algorithm. However, these methods, or their generalizations, are not well suited when the number of outliers is of the same order as the number of low-noise data (often called nominal measurement). In this article, we propose a new model for impulsed noise outliers. It is based on a hierarchical model and a simple linear Gaussian process as with the Kalman Filter. We present a fast forward-backward algorithm to filter and smooth sequential data and which also detects these outliers. We compare the robustness and efficiency of this algorithm with classical methods. Finally, we apply this method on a real data set from a Walk Over Weighing system admitting around 60 % of outliers. For this application, we further develop an (explicit) EM algorithm to calibrate some algorithm parameters.

Stability of radiomic features from positron emission tomography images: a phantom study comparing advanced reconstruction algorithms and ordered subset expectation maximization.

In this study, we compared the repeatability and reproducibility of radiomic features obtained from positron emission tomography (PET) images according to the reconstruction algorithm used-advanced reconstruction algorithms, such as HYPER iterative (IT), HYPER deep learning reconstruction (DLR), and HYPER deep progressive reconstruction (DPR), or traditional Ordered Subset Expectation Maximization (OSEM)-to understand the potential variations and implications of using advanced reconstruction techniques in PET-based radiomics. We used a heterogeneous phantom with acrylic spherical beads (4- or 8-mm diameter) filled with 18F. PET images were acquired and reconstructed using OSEM, IT, DLR, and DPR. Original and wavelet radiomic features were calculated using SlicerRadiomics. Radiomic feature repeatability was assessed using the Coefficient of Variance (COV) and intraclass correlation coefficient (ICC), and inter-acquisition time reproducibility was assessed using the concordance correlation coefficient (CCC). For the 4- and 8-mm diameter beads phantom, the proportion of radiomic features with a COV < 10% was equivocal or higher for the advanced reconstruction algorithm than for OSEM. ICC indicated that advanced methods generally outperformed OSEM in repeatability, except for the original features of the 8-mm beads phantom. In the inter-acquisition time reproducibility analysis, the combinations of 3 and 5min exhibited the highest reproducibility in both phantoms, with IT and DPR showing the highest proportion of radiomic features with CCC > 0.8. Advanced reconstruction methods provided enhanced stability of radiomic features compared with OSEM, suggesting their potential for optimal image reconstruction in PET-based radiomics, offering potential benefits in clinical diagnostics and prognostics.

RPEM: Randomized Monte Carlo parametric expectation maximization algorithm.

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis-Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi-Random Parametric Expectation Maximization (QRPEM) for a realistic two-compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log-normal cases.

Classifying Liver Fibrosis through the Utilization of Transfer Learning and FCNET Classifiers

Abdominal Radiology is used for monitoring patients with liver diseases and to measure severity of liver fibrosis by using Ultrasound (US) images which is obtained by scanning. Scanning uses high frequency sound waves to take images of the affected human organs. Since liver is situated deep into the body the signal get weaker each time it passes through other organs which makes it difficult for diagnosis to overcome this difficult transfer learning technique is proposed in this system. The first step is to remove unwanted disturbances from the US images which is accomplished by pre-processing steps. To ensure the quality of the input images they undergo resizing of resolution, adjusting variations in brightness and contrast. The goal of pre-processing technique is to enhance the quality, uniformity, and relevance of the input images, making them suitable for feature extraction and subsequent classification of liver fibrosis stages. The next step is to apply the Expectation Maximum (EM) algorithm based on Region of Interest (ROI), which is a clustering technique used for image segmentation. The EM algorithm iteratively assigns pixels to different clusters based on their intensities and probabilistic models, aiming to identify distinct regions. The feature extraction process is carried out by Fully Connected Convolutional Neural Network (FCNET) models which enable extracting high level representations from original images and transfer learning classification is used for classification of fibrosis stages with improved accuracy.

Stochastic model for enhanced PET image reconstruction

In this paper, we present a detailed stochastic model of crystal-to-crystal response for PET scanners, which is crucial for addressing their physical constraints. We present both a closed-form solution and several accurate approximations to manage the complexity of the exact mathematical expressions. Through experimental and analytical validation, we demonstrate that the disparities between the best approximations and actual crystal-to-crystal response are negligible. These responses are utilized to develop a compensation model termed a white image. This model is expressed in a single closed-form equation, simplifying its integration into established reconstruction methods. We modify the maximum likelihood expectation maximization (MLEM) algorithm and integrate our white image model into it. Unlike the conventional approach that relies on the system matrix, the modified MLEM algorithm operates on ray-driven projections and back-projections. The system matrix, being large and requiring complex methods and simulations for evaluation, contrasts with the white image, which is smaller and enables efficient computation. Our compensation model provides comprehensive information about the PET system. We validate our approach with both synthetic and real data. For real-world data acquisition, we utilize the Raytest ClearPET camera for small animals and the NEMA NU 4-2008 phantom. The proposed modification outperforms competing uncompensated reconstruction methods, delivering superior Peak Signal-to-Noise Ratio (PSNR) and reduced execution time. This research deepens our understanding of real PET measurement systems, providing improved input for subsequent reconstruction algorithms and ultimately producing high-quality images.

HOW MUCH EUROPEAN YOU ARE? CULTURAL CHANGES OF EUROPEAN COUNTRIES IN THE LAST 20 YEARS WITH SURVEY DATA

This study deviates from traditional approaches by focusing on data analysis instead of historical information to comprehend the dynamics shaping societal culture. Analyzing the cultural changes in European countries over the past two decades, the study utilizes the largest dataset to date, the Integrated Values Survey. Data from four distinct time periods spanning from 2000 to 2022 have been scrutinized. Expectation Maximization method is employed to address missing data in the dataset, and factor analysis-CLARA clustering algorithm is applied for each time period. The primary objective of this academic endeavor is to understand the dynamics of cultural evolution from a data-centric perspective. This analytical approach provides a robust foundation for comprehending cultural changes and predicting potential future developments.

Estimation in shape mixtures of skew-normal linear regression models via ECM coupled with Gibbs sampling

Abstract In this paper, we study linear regression models in which the error term has shape mixtures of skew-normal distribution. This type of distribution belongs to the skew-normal (SN) distribution class that can be used for heavy tails and asymmetry data. For the first time, for the classical (non-Bayesian) estimation of the parameters of the SN family, we apply the Markov chains Monte Carlo ECM (MCMC-ECM) algorithm where the samples are generated by Gibbs sampling, denoted by Gibbs-ECM, and also, we extend two other types of the EM algorithm for the above model. Finally, the proposed method is evaluated through a simulation and compared with the Numerical Math-ECM algorithm and Monte Carlo ECM (MC-ECM) using a real data set.

A discrete approximation method for modeling interval-censored multistate data.

Many longitudinal studies are designed to monitor participants for major events related to the progression of diseases. Data arising from such longitudinal studies are usually subject to interval censoring since the events are only known to occur between two monitoring visits. In this work, we propose a new method to handle interval-censored multistate data within a proportional hazards model framework where the hazard rate of events is modeled by a nonparametric function of time and the covariates affect the hazard rate proportionally. The main idea of this method is to simplify the likelihood functions of a discrete-time multistate model through an approximation and the application of data augmentation techniques, where the assumed presence of censored information facilitates a simpler parameterization. Then the expectation-maximization algorithm is used to estimate the parameters in the model. The performance of the proposed method is evaluated by numerical studies. Finally, the method is employed to analyze a dataset on tracking the advancement of coronary allograft vasculopathy following heart transplantation.

Enhancing water quality prediction for fluctuating missing data scenarios: A dynamic Bayesian network-based processing system to monitor cyanobacteria proliferation

Tackling the impact of missing data in water management is crucial to ensure the reliability of scientific research that informs decision-making processes in public health. The goal of this study is to ascertain the root causes associated with cyanobacteria proliferation under major missing data scenarios. For this purpose, a dynamic missing data management methodology is proposed using Bayesian Machine Learning for accurate surface water quality prediction of a river from Limia basin (Spain). The methodology used entails a sequence of analytical steps, starting with data pre-processing, followed by the selection of a reliable dynamic Bayesian missing value prediction system, leading finally to a supervised analysis of the behavioral patterns exhibited by cyanobacteria. For that, a total of 2,118,844 data points were used, with 205,316 (9.69 %) missing values identified. The machine learning testing showed the iterative structural expectation maximization (SEM) as the best performing algorithm, above the dynamic imputation (DI) and entropy-based dynamic imputation methods (EBDI), enhancing in some cases the accuracy of imputations by approximately 50 % in R2, RMSE, NRMSE, and logarithmic loss values. These findings can impact how data on water quality is being processed and studied, thus, opening the door for more reliable water management strategies that better inform public health decisions.

Efficient Computation of the Quantum Rate-Distortion Function

The quantum rate-distortion function plays a fundamental role in quantum information theory, however there is currently no practical algorithm which can efficiently compute this function to high accuracy for moderate channel dimensions. In this paper, we show how symmetry reduction can significantly simplify common instances of the entanglement-assisted quantum rate-distortion problems. This allows us to better understand the properties of the quantum channels which obtain the optimal rate-distortion trade-off, while also allowing for more efficient computation of the quantum rate-distortion function regardless of the numerical algorithm being used. Additionally, we propose an inexact variant of the mirror descent algorithm to compute the quantum rate-distortion function with provable sublinear convergence rates. We show how this mirror descent algorithm is related to Blahut-Arimoto and expectation-maximization methods previously used to solve similar problems in information theory. Using these techniques, we present the first numerical experiments to compute a multi-qubit quantum rate-distortion function, and show that our proposed algorithm solves faster and to higher accuracy when compared to existing methods.