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

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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Reliability estimation of a system subject to condition monitoring with two dependent failure modes

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IIE TRANSACTIONS 2016年第11期48卷 1058-1071页

作者： Khaleghei, Akram Makis, Viliam Univ Toronto Dept Mech & Ind Engn Toronto ON Canada

A new competing risk model is proposed to calculate the Conditional Mean Residual Life (CMRL) and Conditional Reliability Function (CRF) of a system subject to two dependent failure modes, namely, degradation failure and catastrophic failure. The degradation process can be represented by a three-state continuous-time stochastic process having a healthy state, a warning state, and a failure state. The system is subject to condition monitoring at regular sampling times that provides partial information about the system is working state and only the failure state is observable. To model the dependency between two failure modes, it is assumed that the joint distribution of the time to catastrophic failure and sojourn time in the healthy state follow Marshal-Olkin bivariate exponential distributions. The expectation-maximization algorithm is developed to estimate the model's parameters and the explicit formulas for the CRF and CMRL are derived in terms of the posterior probability that the system is in the warning state. A comparison with a previously published model is provided to illustrate the effectiveness of the proposed model using real data.

关键词： Competing risk conditional reliability function dependent failure modes expectation-maximization algorithm mean residual life

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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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Parameters Estimation of Impulse Noise for Channel Coded Systems over Fading Channels

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IEICE TRANSACTIONS ON COMMUNICATIONS 2021年第7期E104B卷 903-912页

作者： Chen, Chun-Yin Chiu, Mao-Ching Natl Chung Cheng Univ Dept Commun Engn Minxiong Township Chia Yi County Taiwan

In this paper, we propose a robust parameters estimation algorithm for channel coded systems based on the low-density parity-check (LDPC) code over fading channels with impulse noise. The estimated parameters are then used to generate bit log-likelihood ratios (LLRs) for a soft-inputLDPC decoder. The expectation-maximization (EM) algorithm is used to estimate the parameters, including the channel gain and the parameters of the Bernoulli-Gaussian (B-G) impulse noise model. The parameters can be estimated accurately and the average number of iterations of the proposed algorithm is acceptable. Simulation results show that over a wide range of impulse noise power, the proposed algorithm approaches the optimal performance under different Rician channel factors and even under Middleton class-A (M-CA) impulse noise models.

关键词： impulse noise parameter estimation expectation-maximization algorithm low-density parity-check code

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Estimating successive cancer risks in Lynch Syndrome families using a progressive three-state model

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STATISTICS IN MEDICINE 2014年第4期33卷 618-638页

作者： Choi, Yun-Hee Briollais, Laurent Green, Jane Parfrey, Patrick Kopciuk, Karen Univ Western Ontario Dept Epidemiol & Biostat London ON N6A 5C1 Canada Mt Sinai Hosp Samuel Lunenfeld Res Inst Toronto ON M5G 1X5 Canada Univ Toronto Dalla Lana Sch Publ Hlth Toronto ON M5S 1A1 Canada Mem Univ Newfoundland Discipline Genet St John NF A1B 3X9 Canada Mem Univ Newfoundland Clin Epidemiol Unit St John NF A1B 3X9 Canada Alberta Hlth Serv Canc Care Populat Hlth Res Calgary AB T2S 3C3 Canada Univ Calgary Dept Math & Stat Calgary AB T2N 1N2 Canada

Lynch Syndrome (LS) families harbor mutated mismatch repair genes,which predispose them to specific types of cancer. Because individuals within LS families can experience multiple cancers over their lifetime, we developed a progressive three-state model to estimate the disease risk from a healthy (state 0) to a first cancer (state 1) and then to a second cancer (state 2). Ascertainment correction of the likelihood was made to adjust for complex sampling designs with carrier probabilities for family members with missing genotype information estimated using their family's observed genotype and phenotype information in a one-step expectation-maximization algorithm. A sandwich variance estimator was employed to overcome possible model misspecification. The main objective of this paper is to estimate the disease risk (penetrance) for age at a second cancer after someone has experienced a first cancer that is also associated with a mutated gene. Simulation study results indicate that our approach generally provides unbiased risk estimates and low root mean squared errors across different family study designs, proportions of missing genotypes, and risk heterogeneities. An application to 12 large LS families from Newfoundland demonstrates that the risk for a second cancer was substantial and that the age at a first colorectal cancer significantly impacted the age at any LS subsequent cancer. This study provides new insights for developing more effective management of mutation carriers in LS families by providing more accurate multiple cancer risk estimates. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： ascertainment correction expectation-maximization algorithm family study designs Lynch Syndrome missing genotypes penetrance

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Joint modeling of linear degradation and failure time data with masked causes of failure under simple step-stress test

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2018年第8期88卷 1603-1615页

作者： Azizi, Fariba Haghighi, Firoozeh Univ Tehran Sch Math Stat & Comp Sci Coll Sci Tehran Iran

In this paper, we propose a method to model the relationship between degradation and failure time for a simple step-stress test where the underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to induce failure experimentally and a tampered failure rate model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates of the model parameters are obtained through the expectation-maximization algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real-world example is analysed to illustrate the application of the proposed methods.

关键词： expectation-maximization algorithm cause of failure intensity linear degradation path masked data reliability function

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Reliability analysis for multi-component systems considering stochastic dependency based on factor analysis

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2022年 169卷

作者： Kong, Xuefeng Yang, Jun Li, Lei Beihang Univ Sch Reliabil & Syst Engn Beijing 100191 Peoples R China

Reliability analysis for engineering systems with multiple components has gained increasing interest in recent. Most existing works assume that components follow identical degradation models and preset joint distributions or link functions to characterize the degradation interactions. However, distinct degradation characteristics of components are commonly observed in practice. Besides, the degradation interactions are usually complex and diverse, making the preset dependency structures not applicable. Confronted with the diverse degradation characteristics and complex degradation interactions, this paper offers a flexible reliability analysis framework for multi-component systems. First, a stochastic process-based general degradation model combining the Wiener process, Gamma process, and inverse Gaussian process is adopted to describe component degradation processes, and the factor analysis is employed to characterize the degradation interactions by seeking the latent common factors that dominate their interdependency. Thus the assumption of the identical degradation process and preset dependency structure can be relaxed, which enhances the robustness of the method. On this basis, we derive the explicit form of the system reliability function. An efficient expectation-maximization algorithm is then utilized for statistical inference to enable a fast computation. Finally, the superiority of the proposed method is demonstrated by two real case studies on lithium-ion battery packs.

关键词： Reliability analysis Multi-component systems Stochastic process Stochastic dependency Factor analysis expectation-maximization algorithm

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Fast Automatic Smoothing for Generalized Additive Models

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JOURNAL OF MACHINE LEARNING RESEARCH 2019年 20卷

作者： El-Bachir, Yousra Davison, Anthony C. Ecole Polytech Fed Lausanne FSB MATH STAT Stn 8 CH-1015 Lausanne Switzerland

Generalized additive models (GAMs) are regression models wherein parameters of probability distributions depend on input variables through a sum of smooth functions, whose degrees of smoothness are selected by L-2 regularization. Such models have become the de-facto standard nonlinear regression models when interpretability and flexibility are required, but reliable and fast methods for automatic smoothing in large data sets are still lacking. We develop a general methodology for automatically learning the optimal degree of L-2 regularization for GAMs using an empirical Bayes approach. The smooth functions are penalized by hyper-parameters that are learned simultaneously by maximization of a marginal likelihood using an approximate expectation-maximization algorithm. The latter involves a double Laplace approximation at the E-step, and leads to an efficient M-step. Empirical analysis shows that the resulting algorithm is numerically stable, faster than the best existing methods and achieves state-of-the-art accuracy. For illustration, we apply it to an important and challenging problem in the analysis of extremal data.

关键词： Automatic L-2 Regularization Empirical Bayes expectation-maximization algorithm Generalized Additive Model Laplace Approximation Marginal Maximum Likelihood

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A hidden Markov model for continuous longitudinal data with missing responses and dropout

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BIOMETRICAL JOURNAL 2023年第5期65卷 e2200016页

作者： Pandolfi, Silvia Bartolucci, Francesco Pennoni, Fulvia Univ Perugia Dept Econ Perugia Italy Univ Milano Bicocca Dept Stat & Quantitat Methods Milan Italy Univ Perugia Dept ofEcon Via A Pascoli 20 I-06123 Perugia Italy

We propose a hidden Markov model for multivariate continuous longitudinal responses with covariates that accounts for three different types of missing pattern: (I) partially missing outcomes at a given time occasion, (II) completely missing outcomes at a given time occasion (intermittent pattern), and (III) dropout before the end of the period of observation (monotone pattern). The missing-at-random (MAR) assumption is formulated to deal with the first two types of missingness, while to account for the informative dropout, we rely on an extra absorbing state. Estimation of the model parameters is based on the maximum likelihood method that is implemented by an expectation-maximization (EM) algorithm relying on suitable recursions. The proposal is illustrated by a Monte Carlo simulation study and an application based on historical data on primary biliary cholangitis.

关键词： expectation-maximization algorithm forward-backward recursion latent Markov model missing values prediction

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