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Mixture model analysis of DNA microarray images

IEEE TRANSACTIONS ON MEDICAL IMAGING 2005年第7期24卷 901-909页

作者： Blekas, K Galatsanos, NP Likas, A Lagaris, IE Univ Ioannina Dept Comp Sci GR-45110 Ioannina Greece

In this paper, we propose a new methodology for analysis of microarray images. First, a new gridding algorithm is proposed for determining the individual spots and their borders. Then, a Gaussian mixture model (GMM) approach is presented for the analysis of the individual spot images. The main advantages of the proposed methodology are modeling flexibility and adaptability to the data, which are well-known strengths of GMM. The maximum likelihood and maximum a posteriori approaches are used to estimate the GMM parameters via the expectation maximization algorithm. The proposed approach has the ability to detect and compensate for artifacts that might occur in microarray images. This is accomplished by a model-based criterion that selects the number of the mixture components. We present numerical experiments with artificial and real data where we compare the proposed approach with previous ones and existing software tools for microarray image analysis and demonstrate its advantages.

关键词： cross-validated likelihood DNA microarray image analysis expectation-maximization algorithm Gaussian mixture models Markov random fields maximum a posteriori maximum likelihood microarray gridding

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Robust algorithms for multiphase regression models

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APPLIED MATHEMATICAL MODELLING 2020年第Part2期77卷 1643-1661页

作者： Lu, Kang-Ping Chang, Shao-Tung Natl Taichung Univ Sci & Technol Dept Appl Stat Taichung Taiwan Natl Taiwan Normal Univ Dept Math Taipei Taiwan

This paper proposes a robust procedure for solving multiphase regression problems that is efficient enough to deal with data contaminated by atypical observations due to measurement errors or those drawn from heavy-tailed distributions. Incorporating the expectation and maximization algorithm with the M-estimation technique, we simultaneously derive robust estimates of the change-points and regression parameters, yet as the proposed method is still not resistant to high leverage outliers we further suggest a modified version by first moderately trimming those outliers and then implementing the new procedure for the trimmed data. This study sets up two robust algorithms using the Huber loss function and Tukey's biweight function to respectively replace the least squares criterion in the normality-based expectation and maximization algorithm, illustrating the effectiveness and superiority of the proposed algorithms through extensive simulations and sensitivity analyses. Experimental results show the ability of the proposed method to withstand outliers and heavy-tailed distributions. Moreover, as resistance to high leverage outliers is particularly important due to their devastating effect on fitting a regression model to data, various real-world applications show the practicability of this approach. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Multiphase regression models Change-point Outliers Robust regression expectation-maximization algorithm

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Estimation and Prediction for the Generalized Half Normal Distribution under Hybrid Censoring

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JOURNAL OF TESTING AND EVALUATION 2020年第2期48卷 1071-1094页

作者： Sultana, Farha Tripathi, Yogesh Mani Indian Inst Technol Patna Dept Math Bihta 801106 Bihar India

In this article, we make estimation and prediction inferences for the generalized half normal distribution. The maximum likelihood and Bayes estimators of unknown parameters are obtained based on hybrid Type I censored samples. We obtain asymptotic intervals using the observed Fisher information matrix and also construct bootstrap intervals of unknown parameters. Bayes estimators are obtained under the squared error loss function using different approximation methods. We also construct the highest posterior density intervals of unknown parameters. Further one- and two-sample predictors and prediction intervals of censored observations are discussed. A Monte Carlo simulation study is conducted to compare the performance of the proposed methods. We further analyze a real data set for illustrative purposes. Finally, conclusions are presented.

关键词： Bayes estimates expectation-maximization algorithm hybrid Type I censoring importance sampling scheme Bayesian prediction Tierney and Kadane method

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Factor-augmented transformation models for interval-censored failure time data

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BIOMETRICS 2024年第3期80卷 ujae078页

作者： Li, Hongxi Li, Shuwei Sun, Liuquan Song, Xinyuan Guangzhou Univ Sch Econ & Stat Guangzhou 510006 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100190 Peoples R China Chinese Univ Hong Kong Dept Stat Hong Kong 999077 Peoples R China

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

关键词： expectation-maximization algorithm factor analysis interval censoring joint model nonparametric maximum likelihood estimation

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A Unified Model-Based Image Analysis Framework for Automated Detection of Precancerous Lesions in Digitized Uterine Cervix Images

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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2009年第1期3卷 101-111页

作者： Srinivasan, Yeshwanth Corona, Enrique Nutter, Brian Mitra, Sunanda Bhattacharya, Sonal Ambrado Inc Richardson TX 75080 USA Texas Tech Univ Dept Elect & Comp Engn Lubbock TX 79409 USA

A unified framework for a fully automated diagnostic system for cervical intraepithelial neoplasia (CIN) is proposed. CIN is a detectable and treatable precursor pathology of cancer of the uterine cervix. algorithms based on mathematical morphology, and clustering based on Gaussian mixture modeling (GMM) in a joint color and geometric feature space, are used to segment macro regions. A non-parametric technique, based on the transformation and analysis of the D(R) (distortion-rate) curve is proposed to assess the model order. This technique provides good starting points to infer the GMM parameters via the expectation-maximization (EM) algorithm, reducing the segmentation time and the chances of getting trapped in local optima. The classification of vascular abnormalities in CIN, such as mosaicism and punctations, is modeled as a texture classification problem, and a solution is attempted by characterizing the neighborhood gray-tone dependences and co-occurrence statistics of the textures. The model presented in this paper provides a sequential framework for translating digital images of the cervix into a complete diagnostic tool, with minimal human intervention. In its current form, the research presented in this work may be used to aid physicians to locate abnormalities due to CIN and assess the best areas for a biopsy.

关键词： Cervical cancer cervical intraepithelial neoplasia expectation-maximization algorithm Gaussian mixture model rate-distortion theory

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A toll evasion recognition method based on Gaussian mixture clustering

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2022年第7期51卷 3901-3911页

作者： Zhao, Yong-He Shi, Hui-feng Ren, Xiao-Chen Jiao, Bing-Jie North China Elect Power Univ Sch Math & Phys Baoding 071003 Peoples R China

The phenomenon of toll evasion on expressway is universal and recognition of evasion phenomena has become a necessary means to reduce property losses. In view of this situation, a clustering method based Gaussian mixture model(GMM) of load weight is applied to identify the toll evasion by transportation vehicles. Firstly, based on the Kolmogorov-Smirnov and Quantile-Quantile plot test of the load weight in different driving cycles, it is definite that the load in a certain driving cycle is approximately Gaussian mixture distribution(GMD) and there are significant differences among load distributions in different driving cycles. Then, the load during historical vehicles in a certain driving cycle is clustered by GMM. expectation-maximization(EM) algorithm is used to calculate the parameters of GMM. Based on the clustering results, the GMD of the load in a certain driving cycle is clear. Finally, according to the criterion of Gaussian distribution, we scientifically obtain a reasonable load interval and distinguish the toll evasion by transportation vehicles. In addition, the concrete practice procedures of the toll evasion recognition method are discussed. Empirical results demonstrate that could achieve satisfactory results when the proposed method is applied to model the toll data of six-axis trucks of south of Baoding City station in Hebei province of China.

关键词： expectation-maximization algorithm Gaussian mixture clustering Kolmogorov-Smirnov test Quantile-quantile plot Toll evading recognition

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A mixture of experts network structure for modelling Doppler ultrasound blood flow signals

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COMPUTERS IN BIOLOGY AND MEDICINE 2005年第7期35卷 565-582页

作者： Güler, I Übeyli, ED Gazi Univ Fac Tech Educ Dept Elect & Comp Engn TR-06500 Ankara Turkey

Mixture of experts (ME) is a modular neural network architecture for supervised learning. This paper illustrates the use of ME network structure to guide modelling Doppler ultrasound blood flow signals. expectation-maximization (EM) algorithm was used for training the ME so that the learning process is decoupled in a manner that fits well with the modular structure. The ophthalmic and internal carotid arterial Doppler signals were decomposed into time-frequency representations using discrete wavelet transform and statistical features were calculated to depict their distribution. The ME network structures were implemented for diagnosis of ophthalmic and internal carotid arterial disorders using the statistical features as inputs. To improve diagnostic accuracy, the outputs of expert networks were combined by a gating network simultaneously trained in order to stochastically select the expert that is performing the best at solving the problem. The ME network structure achieved accuracy rates which were higher than that of the stand-alone neural network models. (c) 2004 Elsevier Ltd. All rights reserved.

关键词： mixture of experts expectation-maximization algorithm diagnostic accuracy discrete wavelet transform Doppler signal ophthalmic artery internal carotid artery

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Robust Probabilistic Multivariate Calibration Model

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TECHNOMETRICS 2008年第3期50卷 305-316页

作者： Fang, Yi Jeong, Myong K. Purdue Univ Dept Comp Sci W Lafayette IN 47907 USA Rutgers State Univ Ctr Operat Res Piscataway NJ 08853 USA Rutgers State Univ Dept Ind & Syst Engn Piscataway NJ 08853 USA

In this article we propose a robust probabilistic multivariate calibration (RPMC) model in an attempt to identify linear relationships between two sets of observed variables contaminated with outliers Instead of the Gaussian assumptions that predominate in classical statistical models, RPMC is closely related with the multivariate Student t-distribution over noises and latent variables. Thus RPMC diminishes the effect Of Outlying data points by regulating the thickness of the distribution tails. RPMC is essentially a robustified version of the supervised probabilistic principal component analysis (SPPCA) that has emerged recently, We show that RPMC encompasses probabilistic principal component analysis and SPPCA as limiting cases. We also derive an efficient EM algorithm for parameter estimation in RPMC. Based on a probabilistic description of latent variables, we present a procedure for the detection of Outliers. The experimental results from both simulated examples and real life data sets demonstrate the effectiveness and robustness of our proposed approach.

关键词： expectation-maximization algorithm Latent variable model Multivariate Student t-distribution Outlier detection Probabilistic principal component analysis Supervised probabilistic principal component analysis

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Estimating parameters from the generalized inverse Lindley distribution under hybrid censoring scheme

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2024年第7期53卷 2483-2515页

作者： Sarkar, Mojammel Haque Tripathy, Manas Ranjan Kundu, Debasis Natl Inst Technol Rourkela Dept Math Rourkela India Indian Inst Technol Kanpur Dept Math & Stat Kanpur India Natl Inst Technol Rourkela Dept Math Rourkela 769008 India

Estimation of parameters of the generalized inverse Lindley (GIL) distribution is considered under a hybrid censoring scheme. The point estimators, such as the maximum likelihood estimators using the expectation-maximization (E-M) algorithm, have been derived. The two approximate Bayes estimators using Tierney and Kadane's method and Gibbs sampling procedure, using the gamma prior and the general entropy loss (GEL) function, have been obtained. Several confidence intervals are proposed, such as the asymptotic confidence intervals (ACIs), bootstrap confidence intervals, and the highest posterior density (HPD) credible intervals. The prediction for future observations has been considered under one and two-sample Bayesian prediction methods using the type-i hybrid censoring scheme. An extensive simulation study has been conducted to numerically evaluate all the estimators' performances. The point estimators are compared through their biases and mean squared errors (MSEs). The performances of confidence intervals are evaluated using coverage probability (CP), average length (AL), and probability coverage density (PCD). Two real-life datasets have been considered for illustrative purposes.

关键词： Approximate Bayes estimator asymptotic confidence interval Bayesian prediction bootstrap confidence interval expectation-maximization algorithm Gibbs sampling maximum likelihood estimator numerical comparison

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Accelerated Life Tests of a Series System With Masked Interval Data Under Exponential Lifetime Distributions

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IEEE TRANSACTIONS ON RELIABILITY 2012年第3期61卷 798-808页

作者： Fan, Tsai-Hung Hsu, Tsung-Ming Natl Cent Univ Grad Inst Stat Jhongli 32001 Taiwan

We will discuss the reliability analysis of a series system under accelerated life tests when interval data are observed, while the components are assumed to have statistically independent exponential lifetime distributions. In a series system, the system fails if any of the components fails. It is common to include masked data in which the component that causes failure of the system is not observed. First, we apply the maximum likelihood approach via the expectation-maximization algorithm, and use the parametric bootstrap method for the standard error estimation. When the proportion of the masking data is high, the maximum likelihood approach fails due to lack of information. A Bayesian approach is an appropriate alternative in such a case. Hence, we also study the Bayesian approach incorporated with a subjective prior distribution with the aid of the Markov chain Monte Carlo method. We derive statistical inference on the model parameters, as well as the mean lifetimes, and the reliability functions of the system and components. The proposed method is illustrated through a numerical example simulated from the underlying model under various masking levels.

关键词： Accelerated life tests expectation-maximization algorithm interval data Markov chain Monte Carlo masked data parametric bootstrap series system

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