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The finite mixture model for the tails of distribution: Monte Carlo experiment and empirical applications

STATISTICAL ANALYSIS AND DATA MINING 2024年第2期17卷 e11671-e11671页

作者： Furno, Marilena Caracciolo, Francesco Univ Napoli Federico II Via Univ 100 I-80055 Portici Naples Italy

The finite mixture model estimates regression coefficients distinct in each of the different groups of the dataset endogenously determined by this estimator. In what follows the analysis is extended beyond the mean, estimating the model in the tails of the conditional distribution of the dependent variable within each group. While the clustering reduces the overall heterogeneity, since the model is estimated for groups of similar observations, the analysis in the tails uncovers within groups heterogeneity and/or skewness. By integrating the endogenously determined clustering with the quantile regression analysis within each group, enhances the finite mixture models and focuses on the tail behavior of the conditional distribution of the dependent variable. A Monte Carlo experiment and two empirical applications conclude the analysis. In the well-known birthweight dataset, the finite mixture model identifies and computes the regression coefficients of different groups, each one with its own characteristics, both at the mean and in the tails. In the family expenditure data, the analysis of within and between groups heterogeneity provides interesting economic insights on price elasticities. The analysis in classes proves to be more efficient than the model estimated without clustering. By extending the finite mixture approach to the tails provides a more accurate investigation of the data, introducing a robust tool to unveil sources of within groups heterogeneity and asymmetry otherwise left undetected. It improves efficiency and explanatory power with respect to the standard OLS-based FMM.

关键词： expectation-maximization algorithm finite mixture model quantiles

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A Gaussian mixture model method for eigenvalue-based spectrum sensing with uncalibrated multiple antennas

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SIGNAL PROCESSING 2022年 192卷 108404-108404页

作者： Majumder, Saikat Natl Inst Technol Raipur Dept Elect & Commun Engn GE Rd Raipur 492010 Chhattisgarh India

In this article, a novel spectrum sensing technique for cognitive radio (CR) is proposed where eigen-values of the covariance matrix of the received signal are used as features for detection with multiple uncalibrated antennas. In the proposed scheme, training decision vectors composed of eigenvalue com-ponents are approximated as Gaussian mixture model (GMM) and underlying distribution parameters are extracted using expectation-maximization (EM) algorithm. Using the obtained parameters, posterior probability of subsequent decision vectors are computed and the channel is classified as either occu-pied or unoccupied. This is different form existing spectrum sensing techniques where elements of the covariance matrix or its eigenvalues are reduced to a single decision statistic resulting in loss of use-ful discriminatory information. Proposed technique overcomes this limitation by forming decision vectors from the eigenvalue features and performing GMM based classification in multidimensional space. Simu-lation results also reveal that proposed method outperforms state-of-the-art techniques for detection of primary user (PU) signal using uncalibrated antennas. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Cognitive radio Spectrum sensing Eigenvalue Gaussian mixture model expectation-maximization algorithm Uncalibrated antennas

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Mapping QTL controlling count traits with excess zeros and ones using a zero-and-one-inflated generalized Poisson regression model

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BIOMETRICAL JOURNAL 2024年第3期66卷 e2200342页

作者： Chi, Jinling Ye, Jimin Zhou, Ying Xidian Univ Sch Math & Stat Xian Peoples R China Heilongjiang Univ Sch Math Sci Harbin Peoples R China Xidian Univ Sch Math & Stat Xian 710071 Peoples R China Heilongjiang Univ Sch Math Sci Harbin 150080 Peoples R China

The research on the quantitative trait locus (QTL) mapping of count data has aroused the wide attention of researchers. There are frequent problems in applied research that limit the application of the conventional Poisson model in the analysis of count phenotypes, which include the overdispersion and excess zeros and ones. In this article, a novel model, that is, the zero-and-one-inflated generalized Poisson (ZOIGP) model, is proposed to deal with these problems. Based on the proposed model, a score test is performed for the inflation parameter, in which the ZOIGP model with a constant proportion of excess zeros and ones is compared with a standard generalized Poisson model. To illustrate the practicability of the ZOIGP model, we extend it to the QTL interval mapping application that underpins count phenotype with excess zeros and excess ones. The genetic effects are estimated utilizing the expectation-maximization algorithm embedded with the Newton-Raphson algorithm, and the genome-wide scan and likelihood ratio test is performed to map and test the potential QTLs. The statistical properties exhibited by the proposed method are investigated through simulation. Finally, a real data analysis example is used to illustrate the utility of the proposed method for QTL mapping.

关键词： expectation-maximization algorithm quantitative trait locus mapping score test zero-and-one-inflated count data zero-and-one-inflated generalized Poisson model

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A new algorithm for inference in HMM's with lower span complexity

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2024年 195卷

作者： Pereira, Diogo Nunes, Claudia Rodrigues, Rui IST Lisbon Portugal CEMAT Lisbon Portugal NOVA FCT Ctr Math & Applicat NOVA Math Caparica Portugal NOVA FCT Dept Math Caparica Portugal

The maximum likelihood problem for Hidden Markov Models is usually numerically solved by the Baum -Welch algorithm, which uses the expectation -maximization algorithm to find the estimates of the parameters. This algorithm has a recursion depth equal to the data sample size and cannot be computed in parallel, which limits the use of modern GPUs to speed up computation time. A new algorithm is proposed that provides the same estimates as the Baum -Welch algorithm, requiring about the same number of iterations, but is designed in such a way that it can be parallelized. As a consequence, it leads to a significant reduction in the computation time. This reduction is illustrated by means of numerical examples, where we consider simulated data as well as real datasets.

关键词： Hidden Markov Models expectation-maximization algorithm Parallel computation Baum-Welch algorithm

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Point Set Registration With a Hybrid Structure Constraint

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IEEE ACCESS 2019年 7卷 164246-164255页

作者： Sun, Jing Chen, Xia Sun, Zhan-Li Lam, Kin-Man Zeng, Zhigang Anhui Univ Sch Elect Engn & Automat Hefei 230039 Anhui Peoples R China Hefei ZC Optoelect Technol Ltd Anhui Prov Key Lab Nondestruct Evaluat Hefei 230031 Anhui Peoples R China Hong Kong Polytech Univ Dept Elect & Informat Engn Hong Kong Peoples R China Huazhong Univ Sci & Technol Sch Automat Wuhan 430074 Hubei Peoples R China Huazhong Univ Sci & Technol Educ Minist China Key Lab Image Proc & Intelligent Control Wuhan 430074 Hubei Peoples R China

Due to some unfavorable factors, how to accurately register point sets is still a challenging task. In this paper, an effective point set registration approach is proposed based on a hybrid structure constrain. In the proposed method, a composite weight coefficient is determined based on the amplitudes of the vector and the corresponding projection of neighbor points. Given the composite weight coefficient, a local structure constraint is constructed as a linear combination of the vectors of neighbor points. A Gaussian mixture model is established by utilizing the local structure constraint and a global structure constraint based on the motion coherence theory. In addition, an expectation-maximization algorithm is derived to solve the unknown variables in the proposed model. For the constraint terms, an update strategy is utilized to obtain the approximately optimal weight coefficients. Compared to the state-of-the-art approaches, the proposed model is more robust due to the use of multiple effective constraints. Experimental results on some widely used data sets demonstrate the effectiveness of the proposed model.

关键词： Point set registration Gaussian mixture model structure constraint expectation-maximization algorithm

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Dynamic Linear Models With Switching

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Journal of the American Statistical Association 1991年第415期86卷 763-769页

作者： Shumway, R. H. Stoffer, D. S. Professor Division of Statistics University of California Davis CA 95616 Associate Professor Department of Mathematics and Statistics University of Pittsburgh Pittsburgh PA 15260

The problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time-varying independent random process. We derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process. A maximum likelihood estimation procedure is given that uses a pseudo-expectation-maximization algorithm in the initial stages and nonlinear optimization. We relate the models to those considered previously in the literature and give an application revolving the tracking of multiple targets. [ABSTRACT FROM AUTHOR]

关键词： Change points expectation-maximization algorithm Nonlinear models State-space Target tracking

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A distributed Kalman filter based fault detection scheme incorporating weighted average consensus algorithm for large-scale interconnected systems ⁎

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IFAC-PapersOnLine 2024年第14期58卷 586-591页

作者： Haozhou Yuan Jingjing Gao Jian Huang Xu Yang Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing 100083 China

Stimulated by the increasing demands for system safety and process reliability in complex industrial processes, this paper investigates a weighted average consensus algorithm based distributed fault detection scheme for large-scale interconnected systems, using a sensor network where each node is equipped with a Kalman filter (KF). To reduce the communication and computation efforts, the proposed distributed fault detection scheme is splitted into two phases: distributed offline training and online fault detection. To this end, the expectation-maximization (EM) algorithm is firstly addressed to identify the unknown measurement matrices and covariance matrices of noise vectors. It is followed by an average consensus algorithm so that the identical Kalman filters can be designed in parallel at all sensor nodes. On this basis, distributed residual generators and test statistics are constructed for fault detection purpose using the average consensus algorithm. Considering that there exist some special conditions, such as the occurrence of node failures, a variation of the distributed Kalman filter based fault detection scheme is proposed by dynamically adjusting the consensus weight. Finally, the feasibility and effectiveness of the proposed scheme are demonstrated through a case study on the waste water treatment plants (WWTPs).

关键词： Distributed fault detection Large-scale systems Distributed Kalman filter Weighted average consensus expectation-maximization algorithm

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Optimizing Parameters for Enhanced Iterative Image Reconstruction Using Extended Power Divergence

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algorithmS 2024年第11期17卷 512-512页

作者： Kojima, Takeshi Yamaguchi, Yusaku Abou Al-Ola, Omar M. Yoshinaga, Tetsuya Tokushima Univ Inst Biomed Sci 3-18-15 Kuramoto Tokushima 7708509 Japan Natl Hosp Org Shikoku Med Ctr Children & Adults 2-1-1 Senyu Zentsuji 7658507 Japan Tanta Univ Fac Sci El Giesh St Tanta 31527 Egypt

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.

关键词： extended power-divergence measure computed tomography iterative reconstruction expectation-maximization algorithm optimization

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Penetrance estimation of Alzheimer disease in SORL1 loss-of-function variant carriers using a family-based strategy and stratification by APOE genotypes (vol 14, 69, 2022)

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GENOME MEDICINE 2022年第1期14卷 69-69页

作者： Schramm, Catherine Charbonnier, Camille Zarea, Aline Lacour, Morgane Wallon, David Boland, Anne Deleuze, Jean-Francois Olaso, Robert Alarcon, Flora Campion, Dominique Nuel, Gregory Nicolas, Gael Normandie Univ UNIROUEN Dept Genet INSERM 22 Blvd Gambetta CS 76183 F-76000 Rouen France CNRMAJ Genom FHU G4 22 Blvd Gambetta CS 76183 F-76000 Rouen France Normandie Univ CHU Rouen UNIROUEN INSERMU1245Dept Neurol F-76000 Rouen France Univ Paris Saclay CEA Ctr Natl Rech Genom Humaine F-91057 Evry France Univ Paris MAP5 UMR CNRS 8145 F-75270 Paris France Rouvray Psychiat Hosp Dept Res F-76681 Sotteville Les Rouen France Sorbonne Univ LPSM CNRS 8001 F-75005 Paris France

Background Alzheimer disease (AD) is a common complex disorder with a high genetic component. Loss-of-function (LoF) SORL1 variants are one of the strongest AD genetic risk factors. Estimating their age-related penetrance is essential before putative use for genetic counseling or preventive trials. However, relative rarity and co-occurrence with the main AD risk factor, APOE-ε4, make such estimations difficult. Methods We proposed to estimate the age-related penetrance of SORL1-LoF variants through a survival framework by estimating the conditional instantaneous risk combining (i) a baseline for non-carriers of SORL1-LoF variants, stratified by APOE-ε4, derived from the Rotterdam study (N = 12,255), and (ii) an age-dependent proportional hazard effect for SORL1-LoF variants estimated from 27 extended pedigrees (including 307 relatives ≥ 40 years old, 45 of them having genotyping information) recruited from the French reference center for young Alzheimer patients. We embedded this model into an expectation-maximization algorithm to accommodate for missing genotypes. To correct for ascertainment bias, proband phenotypes were omitted. Then, we assessed if our penetrance curves were concordant with age distributions of APOE-ε4-stratified SORL1-LoF variant carriers detected among sequencing data of 13,007 cases and 10,182 controls from European and American case-control study consortia. Results SORL1-LoF variants penetrance curves reached 100% (95% confidence interval [99–100%]) by age 70 among APOE-ε4ε4 carriers only, compared with 56% [40–72%] and 37% [26–51%] in ε4 heterozygous carriers and ε4 non-carriers, respectively. These estimates were fully consistent with observed age distributions of SORL1-LoF variant carriers in case-control study data. Conclusions We conclude that SORL1-LoF variants should be interpreted in light of APOE genotypes for future clinical applications.

关键词： Alzheimer SORL1 APOE Penetrance Lifetime risk expectation-maximization algorithm Pedigree Missing genotypes

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BAYESIAN IMAGE-RECONSTRUCTION FOR EMISSION TOMOGRAPHY INCORPORATING GOOD ROUGHNESS PRIOR ON MASSIVELY PARALLEL PROCESSORS

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 1991年第8期88卷 3223-3227页

作者： MILLER, MI ROYSAM, B WASHINGTON UNIV INST BIOMED COMPST LOUISMO 63130 RENSSELAER POLYTECH INST DEPT ELECT COMP & SYST ENGNTROYNY 12180

Since the introduction by Shepp and Vardi [Shepp, L. A. & Vardi, Y. (1982) IEEE Trans. Med. Imaging 1, 113-121] of the expectation-maximization algorithm for the generation of maximum-likelihood images in emission tomography, a number of investigators have applied the maximum-likelihood method to imaging problems. Though this approach is promising, it is now well known that the unconstrained maximum-likelihood approach has two major drawbacks: (i) the algorithm is computationally demanding, resulting in reconstruction times that are not acceptable for routine clinical application, and (ii) the unconstrained maximum-likelihood estimator has a fundamental noise artifact that worsens as the iterative algorithm climbs the likelihood hill. In this paper the computation issue is addressed by proposing an implementation on the class of massively parallel single-instruction, multiple-data architectures. By restructuring the superposition integrals required for the expectation-maximization algorithm as the solutions of partial differential equations, the local data passage required for efficient computation on this class of machines is satisfied. For dealing with the "noise artifact" a Markov random field prior determined by Good's rotationally invariant roughness penalty is incorporated. These methods are demonstrated on the single-instruction multiple-data class of parallel processors, with the computation times compared with those on conventional and hypercube architectures.

关键词： PENALIZED LIKELIHOOD expectation-maximization algorithm PARALLEL COMPUTERS

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