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A varying-coefficient generalized odds rate model with time-varying exposure: An application to fitness and cardiovascular disease mortality

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BIOMETRICS 2019年第3期75卷 853-863页

作者： Zhou, Jie Zhang, Jiajia Mclain, Alexander C. Lu, Wenbin Sui, Xuemei Hardin, James W. Univ South Carolina Dept Epidemiol & Biostat Columbia SC 29208 USA North Carolina State Univ Dept Stat Raleigh NC USA Univ South Carolina Dept Exercise Columbia SC 29208 USA

Varying-coefficient models have become a common tool to determine whether and how the association between an exposure and an outcome changes over a continuous measure. These models are complicated when the exposure itself is time-varying and subjected to measurement error. For example, it is well known that longitudinal physical fitness has an impact on cardiovascular disease (CVD) mortality. It is not known, however, how the effect of longitudinal physical fitness on CVD mortality varies with age. In this paper, we propose a varying-coefficient generalized odds rate model that allows flexible estimation of age-modified effects of longitudinal physical fitness on CVD mortality. In our model, the longitudinal physical fitness is measured with error and modeled using a mixed-effects model, and its associated age-varying coefficient function is represented by cubic B-splines. An expectation-maximization algorithm is developed to estimate the parameters in the joint models of longitudinal physical fitness and CVD mortality. A modified pseudoadaptive Gaussian-Hermite quadrature method is adopted to compute the integrals with respect to random effects involved in the E-step. The performance of the proposed method is evaluated through extensive simulation studies and is further illustrated with an application to cohort data from the Aerobic Center Longitudinal Study.

关键词： B-splines expectation-maximization algorithm generalized odds rate model joint modeling varying coefficient

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Noise can speed backpropagation learning and deep bidirectional pretraining

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NEURAL NETWORKS 2020年 129卷 359-384页

作者： Kosko, Bart Audhkhasi, Kartik Osoba, Osonde Univ Southern Calif Dept Elect & Comp Engn Signal & Image Proc Inst Los Angeles CA 90089 USA RAND Corp Santa Monica CA 90401 USA Google Inc New York NY USA

We show that the backpropagation algorithm is a special case of the generalized expectation-maximization (EM) algorithm for iterative maximum likelihood estimation. We then apply the recent result that carefully chosen noise can speed the average convergence of the EM algorithm as it climbs a hill of probability or log-likelihood. Then injecting such noise can speed the average convergence of the backpropagation algorithm for both the training and pretraining of multilayer neural networks. The beneficial noise adds to the hidden and visible neurons and related parameters. The noise also applies to regularized regression networks. This beneficial noise is just that noise that makes the current signal more probable. We show that such noise also tends to improve classification accuracy. The geometry of the noise-benefit region depends on the probability structure of the neurons in a given layer. The noise-benefit region in noise space lies above the noisy-EM (NEM) hyperplane for classification and involves a hypersphere for regression. Simulations demonstrate these noise benefits using MNIST digit classification. The NEM noise benefits substantially exceed those of simply adding blind noise to the neural network. We further prove that the noise speed-up applies to the deep bidirectional pretraining of neural-network bidirectional associative memories (BAMs) or their functionally equivalent restricted Boltzmann machines. We then show that learning with basic contrastive divergence also reduces to generalized EM for an energy-based network probability. The optimal noise adds to the input visible neurons of a BAM in stacked layers of trained BAMs. Global stability of generalized BAMs guarantees rapid convergence in pretraining where neural signals feed back between contiguous layers. Bipolar coding of inputs further improves pretraining performance. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Backpropagation Noise benefit Stochastic resonance expectation-maximization algorithm Bidirectional associative memory Contrastive divergence

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Survival analysis for a new compounded bivariate failure time distribution in shock and competing risk models via an EM algorithm

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2020年第21期49卷 5123-5153页

作者： Shoaee, Shirin Khorram, Esmaile Shahid Beheshti Univ Fac Math Sci Dept Actuarial Sci Tehran Iran Amirkabir Univ Technol Fac Math & Comp Sci Dept Stat Tehran Iran

In this paper, two bivariate models based on the proposed methods of Marshall and Olkin are introduced. In the first model, the new bivariate distribution is presented based on the proposed method of Marshall and Olkin (1967) which has natural interpretations, and it can be applied in fatal shock models or in competing risks models. In the second model, the proposed method of Marshall and Olkin (1997) is generalized to bivariate case and a new bivariate distribution is introduced. We call these new distributions as the bivariate Gompertz (BGP) distribution and bivariate Gompertz-geometric (BGPG) distribution, respectively. Moreover, the BGP model can be obtained as a special case of the BGPG model. Then, we present various properties of the new bivariate models. In this regard, the joint and conditional density functions, the joint cumulative distribution function can be obtained in compact forms. Also, the aging properties and the bivariate hazard gradient are discussed. This model has five unknown parameters and the maximum likelihood estimators cannot be obtained in explicit form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters, and it is computationally quite tractable. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze three real data sets for illustrative purposes.

关键词： Bivariate model competing risks model expectation-maximization algorithm gompertz distribution shock model

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Estimating random-intercept models on data streams

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2016年 104卷 169-182页

作者： Ippel, L. Kaptein, M. C. Vermunt, J. K. Tilburg Univ Warandelaan 2POB 90153 NL-5000 LE Tilburg Netherlands

Multilevel models are often used for the analysis of grouped data. Grouped data occur for instance when estimating the performance of pupils nested within schools or analyzing multiple observations nested within individuals. Currently, multilevel models are mostly fit to static datasets. However, recent technological advances in the measurement of social phenomena have led to data arriving in a continuous fashion (i.e., data streams). In these situations the data collection is never "finished". Traditional methods of fitting multilevel models are ill-suited for the analysis of data streams because of their computational complexity. A novel algorithm for estimating random-intercept models is introduced. The Streaming EM Approximation (SEMA) algorithm is a fully-online (row-by-row) method enabling computationally-efficient estimation of random-intercept models. SEMA is tested in two simulation studies, and applied to longitudinal data regarding individuals' happiness collected continuously using smart phones. SEMA shows competitive statistical performance to existing static approaches, but with large computational benefits. The introduction of this method allows researchers to broaden the scope of their research, by using data streams. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Data streams expectation-maximization algorithm Multilevel models Online learning Random-intercept model

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An EM approach to multiple-access interference mitigation in asynchronous slow FHSS systems

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2008年第7期7卷 2661-2670页

作者： Tan, Xing Shea, John M. Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA

In this paper, we apply the EM algorithm for mitigation of multi-access interference (MAI) in asynchronous slow frequency-hop spread spectrum (FHSS) systems that employ binary frequency-shift keying (BFSK) modulation. MAI occurs if the hopping patterns of the users are not orthogonal. We show that when FSK signals arrive asynchronously, the time offset exposes portions of the desired and interfering signals in a way that can be exploited to improve the decoder performance. We develop an iterative detection, estimation, and decoding scheme to recover the desired signal in the presence of MAI. We compare the performance of this algorithm with that of a conventional noncoherent BFSK transceiver and show that the EM-based algorithm is particularly effective in the presence of strong interfering signals and allows more users in a FHSS system.

关键词： multiple-access interference mitigation frequency hop communication iterative detection and estimation expectation-maximization algorithm multiuser detection

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Noise-boosted bidirectional backpropagation and adversarial learning

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NEURAL NETWORKS 2019年 120卷 9-31页

作者： Adigun, Olaoluwa Kosko, Bart Univ Southern Calif Dept Elect & Comp Engn Signal & Image Proc Inst Los Angeles CA 90089 USA

Bidirectional backpropagation trains a neural network with backpropagation in both the backward and forward directions using the same synaptic weights. Special injected noise can then improve the algorithm's training time and accuracy because backpropagation has a likelihood structure. Training in each direction is a form of generalized expectation-maximization because backpropagation itself is a form of generalized expectation-maximization. This requires backpropagation invariance in each direction: The gradient log-likelihood in each direction must give back the original update equations of the backpropagation algorithm. The special noise makes the current training signal more probable as bidirectional backpropagation climbs the nearest hill of joint probability or log-likelihood. The noise for injection differs for classification and regression even in the same network because of the constraint of backpropagation invariance. The backward pass in a bidirectionally trained classifier estimates the centroid of the input pattern class. So the feedback signal that arrives back at the input layer of a classifier tends to estimate the local pattern-class centroid. Simulations show that noise speeded convergence and improved the accuracy of bidirectional backpropagation on both the MNIST test set of hand-written digits and the CIFAR-10 test set of images. The noise boost further applies to regular and Wasserstein bidirectionally trained adversarial networks. Bidirectionality also greatly reduced the problem of mode collapse in regular adversarial networks. (C) 2019 Published by Elsevier Ltd.

关键词： Bidirectional backpropagation Neural networks Noise benefit Stochastic resonance expectation-maximization algorithm Bidirectional associative memory Noise benefit

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Maximum likelihood estimation of Gaussian models with missing data-Eight equivalent formulations

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AUTOMATICA 2012年第9期48卷 1955-1962页

作者： Hansson, Anders Wallin, Ragnar Linkoping Univ Div Automat Control SE-58183 Linkoping Sweden

In this paper we derive the maximum likelihood problem for missing data from a Gaussian model. We present in total eight different equivalent formulations of the resulting optimization problem, four out of which are nonlinear least squares formulations. Among these formulations are also formulations based on the expectation-maximization algorithm. Expressions for the derivatives needed in order to solve the optimization problems are presented. We also present numerical comparisons for two of the formulations for an ARMAX model. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Maximum likelihood estimation Missing data expectation-maximization algorithm ARMAX models

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Genetic-based EM algorithm to improve the robustness of Gaussian mixture models for damage detection in bridges

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STRUCTURAL CONTROL & HEALTH MONITORING 2017年第3期24卷 1-9页

作者： Santos, Adam Figueiredo, Eloi Silva, Moises Santos, Reginaldo Sales, Claudomiro Costa, Joao C. W. A. Fed Univ Para Appl Electromagnetism Lab R Augusto CorreaGuama 01 BR-66075110 Belem Para Brazil Univ Lusofona Humanidades & Tecnol Fac Engn Campo Grande 376 P-1749024 Lisbon Portugal

During the service life of bridges, the bridge management systems (BMSs) seek to handle all performed assessment activities by controlling regular inspections, evaluations, and maintenance of these structures. However, the BMSs still rely heavily on qualitative and visual bridge inspections, which compromise the structural evaluation and, consequently, the maintenance decisions as well as the avoidance of bridge collapses. The structural health monitoring appears as a natural field to aid the bridge management, providing more reliable and quantitative information. Herein, the machine learning algorithms have been used to unveil structural anomalies from monitoring data. In particular, the Gaussian mixture models (GMMs), supported by the expectation-maximization (EM) on the parameter estimation, have been proposed to model the main clusters that correspond to the normal and stable state conditions of a bridge, even when it is affected by unknown sources of operational and environmental variations. Unfortunately, the performance of the EM algorithm is strongly dependent on the choice of the initial parameters. This paper proposes a hybrid approach based on a standard genetic algorithm (GA) to improve the stability of the EM algorithm on the searching of the optimal number of clusters and their parameters, strengthening the damage classification performance. The superiority of the GA-EM-GMM approach, over the classic EMGMM one, is tested on a damage detection strategy implemented through the Mahalanobis-squared distance, which permits one to track the outlier formation in relation to the chosen main group of states, using real-world data sets from the Z-24 Bridge, in Switzerland. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： Structural health monitoring Data normalization Damage detection Gaussian mixture models expectation-maximization algorithm Genetic algorithms Operational and environmental conditions

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Statistical inference for masked interval data with Weibull distribution under simple step-stress test and tampered failure rate model

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART O-JOURNAL OF RISK AND RELIABILITY 2017年第6期231卷 654-665页

作者： Azizi, Fariba Haghighi, Firoozeh Ghadiri, Elahe Torabi, Leila Univ Tehran Dept Math Stat & Comp Sci Tehran Iran

In this article, we consider the planning of simple step-stress life test in the presence of competing risks with the possibility of masked causes of failure and interval censoring. It is assumed that the competing risks have independent Weibull distribution with the common shape parameter, but different scale parameters and a tampered failure rate model is hold. Maximum likelihood estimates of the model parameters are obtained for both cases, with and without masking. An expectation-maximization algorithm is used to estimate maximum likelihood estimates based on the masked data. For the case without masking, the Fisher information matrix is derived, and the problem of choosing the optimal test plan is considered using variance-optimality as well as determinant-optimality criteria. Through Monte Carlo simulations, the precision of the estimates is assessed and the optimal test plans are compared. Finally, the results are illustrated with an example.

关键词： Competing risks determinant optimality expectation-maximization algorithm interval censoring masked data optimal plan tampered failure rate model variance optimality Weibull distribution

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Frequency Domain Identification of Multivariable Model for Aero-Engine using an Improved Maximum Likelihood Method

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INTERNATIONAL JOURNAL OF TURBO & JET-ENGINES 2015年第3期32卷 247-255页

作者： Liu, Nan Huang, Jinquan Lu, Feng Pan, Muxuan Nanjing Univ Aeronaut & Astronaut Jiangsu Prov Key Lab Aerosp Power Syst Nanjing 210016 Peoples R China Collaborat Innovat Ctr Adv Aeroengine Beijing 100191 Peoples R China Commercial Aircraft Corp China Shanghai Aircraft Design & Res Inst Shanghai 200232 Peoples R China

For the linear modeling problem of multivariable system of aero-engine, considering the coupling between parameters, a multivariable maximum likelihood (ML) estimation method is researched. An improved expectation-maximization (EM) algorithm integrated genetic algorithm (GA) is proposed and applied to the process of ML identification of frequency domain. The amplitude, harmonic and phase vectors of odd-odd multi-sine exciting signal are designed and optimized. With the application of the proposed method, multivariable linear models of aero-engine at different operation states in flight envelope are established from nonlinear component-level model. The precision is demonstrated through simulations comparing to nonlinear model.

关键词： aero-engine multivariable model frequency domain maximum likelihood estimation expectation-maximization algorithm genetic algorithm

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