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A Discrete Time Event-History Approach to Informative Drop-Out in Mixed Latent Markov Models with Covariates

BIOMETRICS 2015年第1期71卷 80-89页

作者： Bartolucci, Francesco Farcomeni, Alessio Univ Perugia IT Dept Econ Perugia Italy Sapienza Univ Rome IT Dept Publ Hlth & Infect Dis Rome Italy

Mixed latent Markov (MLM) models represent an important tool of analysis of longitudinal data when response variables are affected by time-fixed and time-varying unobserved heterogeneity, in which the latter is accounted for by a hidden Markov chain. In order to avoid bias when using a model of this type in the presence of informative drop-out, we propose an event-history (EH) extension of the latent Markov approach that may be used with multivariate longitudinal data, in which one or more outcomes of a different nature are observed at each time occasion. The EH component of the resulting model is referred to the interval-censored drop-out, and bias in MLM modeling is avoided by correlated random effects, included in the different model components, which follow common latent distributions. In order to perform maximum likelihood estimation of the proposed model by the expectation-maximization algorithm, we extend the usual forward-backward recursions of Baum and Welch. The algorithm has the same complexity as the one adopted in cases of non-informative drop-out. We illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest, one continuous and the other binary.

关键词： Discrete latent variables expectation-maximization algorithm Hidden Markov models Shared-parameter models

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Lifetime Inference for Highly Reliable Products Based on Skew-Normal Accelerated Destructive Degradation Test Model

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IEEE TRANSACTIONS ON RELIABILITY 2015年第4期64卷 1340-1355页

作者： Tsai, Chih-Chun Lin, Chien-Tai Tamkang Univ Dept Math New Taipei City Taiwan

The accelerated destructive degradation test (ADDT) method provides an effective way to assess the reliability information of highly reliable products whose quality characteristics degrade over time, and can be taken only once on each tested unit during the measurement process. Conventionally, engineers assume that the measurement error follows the normal distribution. However, degradation models based on this normality assumption often do not apply in practical applications. To relax the normality assumption, the skew-normal distribution is adopted in this study because it preserves the advantages of the normal distribution with the additional benefit of flexibility with regard to skewness and kurtosis. Here, motivated by polymer data, we propose a skew-normal nonlinear ADDT model, and derive the analytical expressions for the product's lifetime distribution along with its corresponding 100pth percentile. Then, the polymer data are used to illustrate the advantages gained by the proposed model. Finally, we addressed analytically the effects of model mis-specification when the skewness of measurement error are mistakenly treated, and the obtained results reveal that the impact from the skewness parameter on the accuracy and precision of the prediction of the lifetimes of products is quite significant.

关键词： Accelerated destructive degradation tests expectation-maximization algorithm highly reliable products skew-normal distribution model mis-specification

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FITTING MIXTURES OF ERLANGS TO CENSORED AND TRUNCATED DATA USING THE EM algorithm

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ASTIN BULLETIN-THE JOURNAL OF THE INTERNATIONAL ACTUARIAL ASSOCIATION 2015年第3期45卷 729-758页

作者： Verbelen, Roel Gong, Lan Antonio, Katrien Badescu, Andrei Lin, Sheldon Katholieke Univ Leuven Fac Econ & Business LStat Leuven Belgium Univ Toronto Dept Stat Sci Toronto ON M5S 1A1 Canada Univ Amsterdam Fac Econ & Business NL-1012 WX Amsterdam Netherlands

We discuss how to fit mixtures of Erlangs to censored and truncated data by iteratively using the EM algorithm. Mixtures of Erlangs form a very versatile, yet analytically tractable, class of distributions making them suitable for loss modeling purposes. The effectiveness of the proposed algorithm is demonstrated on simulated data as well as real data sets.

关键词： Mixture of Erlang distributions with a common scale parameter censoring truncation expectation-maximization algorithm maximum likelihood

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Model-Based Clustering for Conditionally Correlated Categorical Data

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JOURNAL OF CLASSIFICATION 2015年第2期32卷 145-175页

作者： Marbac, Matthieu Biernacki, Christophe Vandewalle, Vincent Inria Lille F-59000 Lille France DGA F-59000 Lille France Univ Lille 1 CNRS F-59650 Villeneuve Dascq France Inria F-59650 Villeneuve Dascq France EA 2694 Univ Lille 2 F-59000 Lille France Inria F-59000 Lille France

An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and intra-dependent blocks, in order to consider the main intra-class correlations. The dependency between variables grouped inside the same block of a class is taken into account by mixing two extreme distributions, which are respectively the independence and the maximum dependency. When the variables are dependent given the class, this approach is expected to reduce the biases of the latent class model. Indeed, it produces a meaningful dependency model with only a few additional parameters. The parameters are estimated, by maximum likelihood, by means of an EM algorithm. Moreover, a Gibbs sampler is used for model selection in order to overcome the computational intractability of the combinatorial problems involved by the block structure search. Two applications on medical and biological data sets show the relevance of this new model. The results strengthen the view that this model is meaningful and that it reduces the biases induced by the conditional independence assumption of the latent class model.

关键词： Categorical data Clustering Correlation expectation-maximization algorithm Gibbs sampler Mixture model Model selection

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Estimating the dynamics and dependencies of accumulating mutations with applications to HIV drug resistance

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BIOSTATISTICS 2015年第4期16卷 713-726页

作者： Montazeri, Hesam Guenthard, Huldrych F. Yang, Wan-Lin Kouyos, Roger Beerenwinkel, Niko Swiss Fed Inst Technol Dept Biosyst Sci & Engn CH-4058 Basel Switzerland SIB CH-4058 Basel Switzerland Univ Zurich Univ Zurich Hosp Div Infect Dis & Hosp Epidemiol CH-8091 Zurich Switzerland Univ Zurich Inst Med Virol CH-8057 Zurich Switzerland

We introduce a new model called the observed time conjunctive Bayesian network (OT-CBN) that describes the accumulation of genetic events (mutations) under partial temporal ordering constraints. Unlike other CBN models, the OT-CBN model uses sampling time points of genotypes in addition to genotypes themselves to estimate model parameters. We developed an expectation-maximization algorithm to obtain approximate maximum likelihood estimates by accounting for this additional information. In a simulation study, we show that the OT-CBN model outperforms the continuous time CBN (CT-CBN) (Beerenwinkel and Sullivant, 2009. Markov models for accumulating mutations. Biometrika 96(3), 645-661), which does not take into account individual sampling times for parameter estimation. We also show superiority of the OT-CBN model on several datasets of HIV drug resistance mutations extracted from the Swiss HIV Cohort Study database.

关键词： Conjunctive Bayesian networks expectation-maximization algorithm Genetic progression HIV drug resistance Maximum likelihood estimation

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expectation-maximization algorithm with Local Adaptivity

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SIAM JOURNAL ON IMAGING SCIENCES 2009年第3期2卷 834-857页

作者： Leung, Shingyu Liang, Gang Solna, Knut Zhao, Hongkai Hong Kong Univ Sci & Technol Dept Math Hong Kong Hong Kong Peoples R China Univ Calif Irvine Dept Stat Irvine CA 92697 USA Univ Calif Irvine Dept Math Irvine CA 92697 USA

We develop an expectation-maximization algorithm with local adaptivity for image segmentation and classification. The key idea of our approach is to combine global statistics extracted from the Gaussian mixture model or other proper statistical models with local statistics and geometrical information, such as local probability distribution, orientation, and anisotropy. The combined information is used to design an adaptive local classification strategy that improves the robustness of the algorithm and also keeps fine features in the image. The proposed methodology is flexible and can be easily generalized to deal with other inferred information/quantities and statistical methods/models.

关键词： expectation-maximization algorithm Gaussian mixture model posterior probability local adaptivity image segmentation

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Load spectrum modeling for tracked vehicles based on variational Bayesian inference

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART B-JOURNAL OF ENGINEERING MANUFACTURE 2015年第1-Sup期229卷 178-188页

作者： Wang, Yanzhong Zhu, Chengli Beihang Univ Sch Mech Engn & Automat Beijing 10083 Peoples R China

The load spectrum is the basis of performing the reliability and fatigue life analysis for the structures of tracked vehicles. In order to obtain the load spectrum, the load cycles should be extracted from the measured or simulated load time history using rainflow counting method. After that, the distribution of the load cycles can be modeled by a continuous distribution function. For the purpose of finding a common modeling method and effective parameters' estimation method for the load spectrum, we used a mixture of multivariate Gaussian functions to model the probability density function of general load time history on the basis of extracted load cycles. Additionally, we proposed an approach for unknown parameters' estimation based on variational Bayesian inference. This parameter estimation method can automatically infer the number of components from the observed data set. Numerical examples were given to illustrate the effectiveness of our proposed modeling method and unknown parameters' estimation method. We compared the distributions of the load cycles reconstructed by the load spectrum models with those of the original load cycles. At the same time, we obtained the quantitative optimal results of the parameters for the load cases. The results showed that the mixture Gaussian functions can model complex distribution of the rainflow load cycles for tracked vehicles by choosing suitable number of components and suitable parameters of them, and the variational Bayesian inference is an effective unknown parameters' estimation method for the mixture models which have latent variables.

关键词： Load spectrum mixture Gaussians expectation-maximization algorithm variational Bayesian inference

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Spatially regularized mixture model for lesion segmentation with application to stroke patients

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BIOSTATISTICS 2015年第3期16卷 580-595页

作者： Ozenne, Brice Subtil, Fabien Ostergaard, Leif Maucort-Boulch, Delphine Hosp Civils Lyon Serv Biostat Lyon France Univ Lyon 1 CNRS UMR 5558 Equipe Biostat Sante F-69100 Villeurbanne France Aarhus Univ Ctr Functionally Integrat Neurosci DK-8000 Aarhus Denmark

In medical imaging, lesion segmentation (differentiation between lesioned and non-lesioned tissue) is a crucial and difficult task. Automated segmentation algorithms based on intensity analysis have been already proposed and recent developments have shown that integrating spatial information enhances automatic image segmentation. However, spatial modeling is often limited to short-range spatial interactions that deal only with noise or small artifacts. Previous tissue alterations (e.g. white matter disease (WMD)) similar in intensity with the lesion of interest require a broader-scale approach to be corrected. On the other hand, imaging techniques offer now a multiparametric voxel characterization that may help differentiating lesioned from non-lesioned voxels. We developed an unsupervised multivariate segmentation algorithm based on finite mixture modeling that incorporates spatial information. We extended the usual spatial Potts model to the regional scale using a 'multi-order' neighborhood potential, with internal adjustment of the regional scale according to the lesion size. We validate the ability of this new algorithm to deal with noise and artifacts (linear and spherical) using artificial data. We then assess its performance on real magnetic resonance imaging brain scans of stroke patients with history of WMD and show that regional regularization was able to remove large-scale WMD artifacts.

关键词： expectation-maximization algorithm Finite mixture models Image segmentation Markov random fields Mean-field approximation

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SubspaceEM: A fast maximum-a-posteriori algorithm for cryo-EM single particle reconstruction

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JOURNAL OF STRUCTURAL BIOLOGY 2015年第2期190卷 200-214页

作者： Dvornek, Nicha C. Sigworth, Fred J. Tagare, Hemant D. Yale Univ Sch Med Dept Diagnost Radiol New Haven CT 06510 USA Yale Univ Dept Biomed Engn New Haven CT 06520 USA Yale Univ Sch Med Dept Cellular & Mol Physiol New Haven CT 06510 USA Yale Univ Dept Elect Engn New Haven CT 06520 USA

Single particle reconstruction methods based on the maximum-likelihood principle and the expectation-maximization (E-M) algorithm are popular because of their ability to produce high resolution structures. However, these algorithms are computationally very expensive, requiring a network of computational servers. To overcome this computational bottleneck, we propose a new mathematical framework for accelerating maximum-likelihood reconstructions. The speedup is by orders of magnitude and the proposed algorithm produces similar quality reconstructions compared to the standard maximum-likelihood formulation. Our approach uses subspace approximations of the cryo-electron microscopy (cryo-EM) data and projection images, greatly reducing the number of image transformations and comparisons that are computed. Experiments using simulated and actual cryo-EM data show that speedup in overall execution time compared to traditional maximum-likelihood reconstruction reaches factors of over 300. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Cryo-electron microscopy Single particle reconstruction Maximum-likelihood Maximum-a-posteriori expectation-maximization algorithm Fast image processing

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MODELING SPEECH PARAMETER SEQUENCES WITH LATENT TRAJECTORY HIDDEN MARKOV MODEL 25

MODELING SPEECH PARAMETER SEQUENCES WITH LATENT TRAJECTORY H...

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IEEE International Workshop on Machine Learning for Signal Processing

作者： Kameoka, Hirokazu NTT Corp Tokyo Japan Univ Tokyo Tokyo 1138654 Japan

ISBN: (纸本)9781467374545

This paper proposes a probabilistic generative model of a sequence of vectors called the latent trajectory hidden Markov model (HMM). While a conventional HMM is only capable of describing piecewise stationary sequences of data vectors, the proposed model is capable of describing continuously time-varying sequences of data vectors, governed by discrete hidden states. This feature is noteworthy in that it can be used to model many kinds of time series data that are continuous in nature such as speech spectra. Given a sequence of observed data, the optimal state sequence can be decoded using the expectation-maximization (EM) algorithm. Given a set of training examples, the underlying model parameters can be trained by either the expectation-maximization algorithm or the variational inference algorithm.

关键词： Sequential modeling Hidden Markov model (HMM) Trajectory HMM Latent trajectory HMM expectation-maximization algorithm variational inference

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