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MACHINE LEARNING 2001年第3期45卷 279-299页

作者： Thiesson, B Meek, C Heckerman, D Microsoft Corp Res Redmond WA 98052 USA

The EM algorithm is a popular method for parameter estimation in a variety of problems involving missing data. However, the EM algorithm often requires significant computational resources and has been dismissed as impractical for large databases. We present two approaches that significantly reduce the computational cost of applying the EM algorithm to databases with a large number of cases, including databases with large dimensionality. Both approaches are based on partial E-steps for which we can use the results of Neal and Hinton (In Jordan, M. (Ed.), Learning in Graphical Models, pp. 355-371. The Netherlands: Kluwer Academic Publishers) to obtain the standard convergence guarantees of EM. The first approach is a version of the incremental EM algorithm, described in Neal and Hinton (1998), which cycles through data cases in blocks. The number of cases in each block dramatically effects the efficiency of the algorithm. We provide a method for selecting a near optimal block size. The second approach, which we call lazy EM, will, at scheduled iterations, evaluate the significance of each data case and then proceed for several iterations actively using only the significant cases. We demonstrate that both methods can significantly reduce computational costs through their application to high-dimensional real-world and synthetic mixture modeling problems for large databases.

关键词： expectation maximization algorithm incremental EM lazy EM online EM data blocking mixture models clustering

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Analysis and probabilistic modeling of wind characteristics of an arch bridge using structural health monitoring data during typhoons

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STRUCTURAL ENGINEERING AND MECHANICS 2017年第6期63卷 809-824页

作者： Ye, X. W. Xi, P. S. Su, Y. H. Chen, B. Zhejiang Univ Dept Civil Engn Hangzhou 310058 Zhejiang Peoples R China

The accurate evaluation of wind characteristics and wind-induced structural responses during a typhoon is of significant importance for bridge design and safety assessment. This paper presents an expectation maximization (EM) algorithm-based angular-linear approach for probabilistic modeling of field-measured wind characteristics. The proposed method has been applied to model the wind speed and direction data during typhoons recorded by the structural health monitoring (SHM) system instrumented on the arch Jiubao Bridge located in Hangzhou, China. In the summer of 2015, three typhoons, i.e., Typhoon Chan-hom, Typhoon Soudelor and Typhoon Goni, made landfall in the east of China and then struck the Jiubao Bridge. By analyzing the wind monitoring data such as the wind speed and direction measured by three anemometers during typhoons, the wind characteristics during typhoons are derived, including the average wind speed and direction, turbulence intensity, gust factor, turbulence integral scale, and power spectral density (PSD). An EM algorithm-based angular-linear modeling approach is proposed for modeling the joint distribution of the wind speed and direction. For the marginal distribution of the wind speed, the finite mixture of two-parameter Weibull distribution is employed, and the finite mixture of von Mises distribution is used to represent the wind direction. The parameters of each distribution model are estimated by use of the EM algorithm, and the optimal model is determined by the values of R-2 statistic and the Akaike's information criterion (AIC). The results indicate that the stochastic properties of the wind field around the bridge site during typhoons are effectively characterized by the proposed EM algorithm-based angular-linear modeling approach. The formulated joint distribution of the wind speed and direction can serve as a solid foundation for the purpose of accurately evaluating the typhoon-induced fatigue damage of long-span bridges.

关键词： structural health monitoring wind characteristics typhoon joint distribution function angular-linear approach expectation maximization algorithm

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Robust Low-Rank Matrix Factorization Under General Mixture Noise Distributions

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2016年第10期25卷 4677-4690页

作者： Cao, Xiangyong Zhao, Qian Meng, Deyu Chen, Yang Xu, Zongben Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China Xi An Jiao Tong Univ Minist Educ Key Lab Intelligent Networks & Network Secur Xian 710049 Peoples R China

Many computer vision problems can be posed as learning a low-dimensional subspace from high-dimensional data. The low rank matrix factorization (LRMF) represents a commonly utilized subspace learning strategy. Most of the current LRMF techniques are constructed on the optimization problems using L-1-norm and L-2-norm losses, which mainly deal with the Laplace and Gaussian noises, respectively. To make LRMF capable of adapting more complex noise, this paper proposes a new LRMF model by assuming noise as mixture of exponential power (MoEP) distributions and then proposes a penalized MoEP (PMoEP) model by combining the penalized likelihood method with MoEP distributions. Such setting facilitates the learned LRMF model capable of automatically fitting the real noise through MoEP distributions. Each component in this mixture distribution is adapted from a series of preliminary super-or sub-Gaussian candidates. Moreover, by facilitating the local continuity of noise components, we embed Markov random field into the PMoEP model and then propose the PMoEP-MRF model. A generalized expectation maximization (GEM) algorithm and a variational GEM algorithm are designed to infer all parameters involved in the proposed PMoEP and the PMoEP-MRF model, respectively. The superiority of our methods is demonstrated by extensive experiments on synthetic data, face modeling, hyperspectral image denoising, and background subtraction.

关键词： Low-rank matrix factorization mixture of exponential power distributions expectation maximization algorithm face modeling hyperspectral image denoising background subtraction

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Learning mixtures of point distribution models with the EM algorithm

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PATTERN RECOGNITION 2003年第12期36卷 2805-2818页

作者： Al-Shaher, AA Hancock, ER Univ York Dept Comp Sci York YO1 5DD N Yorkshire England

This paper demonstrates how the EM algorithm can be used for learning and matching mixtures of point distribution models. We make two contributions. First, we show how shape-classes can be learned in an unsupervised manner. We present a fast procedure for training point distribution models using the EM algorithm. Rather than estimating the class means and covariance matrices needed to construct the PDM, the method iteratively refines the eigenvectors of the covariance matrix using a gradient ascent technique. Second, we show how recognition by alignment can be realised by fitting a mixture of linear shape deformations. We evaluate the method on the problem of learning the class-structure and recognising Arabic characters. (C) 2003 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

关键词： point distribution models expectation maximization algorithm unsupervised learning alignment shape recognition Arabic character

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Unified Statistical Channel Model for Turbulence-Induced Fading in Underwater Wireless Optical Communication Systems

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IEEE TRANSACTIONS ON COMMUNICATIONS 2019年第4期67卷 2893-2907页

作者： Zedini, Emna Oubei, Hassan Makine Kammoun, Abla Hamdi, Mounir Ooi, Boon S. Alouini, Mohamed-Slim Hamad Bin Khalifa Univ Coll Sci & Engn Doha Qatar King Abdullah Univ Sci & Technol Comp Elect & Math Sci & Engn Div Thuwal 23955 Saudi Arabia

A unified statistical model is proposed to characterize turbulence-induced fading in underwater wireless optical communication (UWOC) channels in the presence of air bubbles and temperature gradient for fresh and salty waters, based on experimental data. In this model, the channel irradiance fluctuations are characterized by the mixture exponential-generalized gamma (EGG) distribution. We use the expectation-maximization algorithm to obtain the maximum likelihood parameter estimation of the new model. Interestingly, the proposed model is shown to provide a perfect fit with the measured data under all channel conditions for both types of water. The major advantage of the new model is that it has a simple mathematical form making it attractive from a performance analysis point of view. Indeed, we show that the application of the EGG model leads to closed-form and analytically tractable expressions for key UWOC system performance metrics such as the outage probability, the average bit-error rate, and the ergodic capacity. To the best of our knowledge, this is the first-ever comprehensive channel model addressing the statistics of optical beam irradiance fluctuations in underwater wireless optical channels due to both air bubbles and temperature gradient.

关键词： Underwater wireless optical communication (UWOC) channel modeling distribution fitting maximum likelihood estimation expectation maximization algorithm mixture models performance analysis outage probability bit-error rate (BER) ergodic capacity

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Combining mixed effects hidden Markov models with latent alternating recurrent event processes to model diurnal active-rest cycles

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BIOMETRICS 2023年第4期79卷 3402-3417页

作者： Ren, Benny Barnett, Ian Univ Penn Dept Biostat Epidemiol & Informat Philadelphia PA 19104 USA

Data collected from wearable devices can shed light on an individual's pattern of behavioral and circadian routine. Phone use can be modeled as alternating processes, between the state of active use and the state of being idle. Markov chains and alternating recurrent event models are commonly used to model state transitions in cases such as these, and the incorporation of random effects can be used to introduce diurnal effects. While state labels can be derived prior to modeling dynamics, this approach omits informative regression covariates that can influence state memberships. We instead propose an alternating recurrent event proportional hazards (PH) regression to model the transitions between latent states. We propose an expectation-maximization algorithm for imputing latent state labels and estimating parameters. We show that our E-step simplifies to the hidden Markov model (HMM) forward-backward algorithm, allowing us to recover an HMM with logistic regression transition probabilities. In addition, we show that PH modeling of discrete-time transitions implicitly penalizes the logistic regression likelihood and results in shrinkage estimators for the relative risk. This new estimator favors an extended stay in a state and is useful for modeling diurnal rhythms. We derive asymptotic distributions for our parameter estimates and compare our approach against competing methods through simulation as well as in a digital phenotyping study that followed smartphone use in a cohort of adolescents with mood disorders.

关键词： alternating recurrent event processes expectation maximization algorithm hidden Markov models latent variable modeling longitudinal data

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Remaining Useful Life Prediction of Lithium-Ion Batteries Based on the Wiener Process with Measurement Error

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ENERGIES 2014年第2期7卷 520-547页

作者： Tang, Shengjin Yu, Chuanqiang Wang, Xue Guo, Xiaosong Si, Xiaosheng High Tech Inst Xian Xian 710025 Shaanxi Peoples R China Tsinghua Univ Dept Precis Instrument Beijing 100084 Peoples R China

Remaining useful life (RUL) prediction is central to the prognostics and health management (PHM) of lithium-ion batteries. This paper proposes a novel RUL prediction method for lithium-ion batteries based on the Wiener process with measurement error (WPME). First, we use the truncated normal distribution (TND) based modeling approach for the estimated degradation state and obtain an exact and closed-form RUL distribution by simultaneously considering the measurement uncertainty and the distribution of the estimated drift parameter. Then, the traditional maximum likelihood estimation (MLE) method for population based parameters estimation is remedied to improve the estimation efficiency. Additionally, we analyze the relationship between the classic MLE method and the combination of the Bayesian updating algorithm and the expectation maximization algorithm for the real time RUL prediction. Interestingly, it is found that the result of the combination algorithm is equal to the classic MLE method. Inspired by this observation, a heuristic algorithm for the real time parameters updating is presented. Finally, numerical examples and a case study of lithium-ion batteries are provided to substantiate the superiority of the proposed RUL prediction method.

关键词： lithium-ion batteries remaining useful life the Wiener process measurement error prediction truncated normal distribution maximum likelihood estimation Bayesian expectation maximization algorithm

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Validity index for crisp and fuzzy clusters

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PATTERN RECOGNITION 2004年第3期37卷 487-501页

作者： Pakhira, MK Bandyopadhyay, S Maulik, U Kalyani Govt Engn Coll Dept Comp Sci & Technol Kalyani 741235 W Bengal India Indian Stat Inst Machine Intelligence Unit Kolkata 700108 W Bengal India Kalyani Govt Engn Coll Dept Comp Sci & Technol Kalyani 741235 W Bengal India

In this article, a cluster validity index and its fuzzification is described, which can provide a measure of goodness of clustering on different partitions of a data set. The maximum value of this index, called the PBM-index, across the hierarchy provides the best partitioning. The index is defined as a product of three factors, maximization of which ensures the formation of a small number of compact clusters with large separation between at least two clusters. We have used both the k-means and the expectation maximization algorithms as underlying crisp clustering techniques. For fuzzy clustering, we have utilized the well-known fuzzy c-means algorithm. Results demonstrating the superiority of the PBM-index in appropriately determining the number of clusters, as compared to three other well-known measures, the Davies-Bouldin index, Dunn's index and the Xie-Beni index, are provided for several artificial and real-life data sets. (C) 2003 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

关键词： clustering expectation maximization algorithm fuzzy c-means algorithm k-means algorithm unsupervised classification validity index

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Time discretization of continuous-time filters and smoothers for HMM parameter estimation

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IEEE TRANSACTIONS ON INFORMATION THEORY 1996年第2期42卷 593-605页

作者： James, MR Krishnamurthy, V LeGland, F UNIV MELBOURNE DEPT ELECT & ELECTR ENGNPARKVILLEVIC 3052AUSTRALIA INST NATL RECH INFORMAT & AUTOMAT INST RECH INFORMAT & SYST ALEATOIRESF-35042 RENNESFRANCE

In this paper we propose algorithms for parameter estimation of fast-sampled homogeneous Markov chains observed in white Gaussian noise. Our algorithms are obtained by the robust discretization of stochastic differential equations involved in the estimation of continuous-time Hidden Markov Models (HMM's) via the EM algorithm. We present two algorithms: The first is based on the robust discretization of continuous-time filters that were recently obtained by Elliott to estimate quantities used in the EM algorithm. The second is based on the discretization of continuous-time smoothers, yielding essentially the well-known Baum-Welch re-estimation equations. The smoothing formulas for continuous-time HMM's are new, and their derivation involves two sided stochastic integrals. The choice of discretization results in equations which are identical to those obtained by deriving the results directly in discrete time. The filter-based EM algorithm has negligible memory requirements;indeed, independent of the number of observations. In comparison the smoother-based discrete-time EM algorithm require the use of the forward-backward algorithm, which is a fixed-interval smoothing algorithm and has memory requirements proportional to the number of observations. On the other hand, the computational complexity of the filter-based EM algorithm is greater than that of the smoother-based scheme. However, the filters may be suitable for parallel implementation. Using computer simulations we compare the smoother-based and filter-based EM algorithms for HMM estimation. We provide also estimates for the discretization error.

关键词： Hidden Markov Models robust discretization expectation maximization algorithm parameter estimation

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Probability graph complementation contrastive learning

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NEURAL NETWORKS 2024年 179卷 106522页

作者： Jiang, Wenhao Bai, Yuebin Beihang Univ Sch Comp Sci & Engn Beijing 100191 Peoples R China

Graph Neural Network (GNN) has achieved remarkable progress in the field of graph representation learning. The most prominent characteristic, propagating features along the edges, degrades its performance in most heterophilic graphs. Certain researches make attempts to construct KNN graph to improve the graph homophily. However, there is no prior knowledge to choose proper K and they may suffer from the problem of Inconsistent Similarity Distribution (ISD). To accommodate this issue, we propose Probability Graph Complementation Contrastive Learning (PGCCL) which adaptively constructs the complementation graph. We employ Beta Mixture Model (BMM) to distinguish intra-class similarity and inter-class similarity. Based on the posterior probability, we construct Probability Complementation Graphs to form contrastive views. The contrastive learning prompts the model to preserve complementary information for each node from different views. By combining original graph embedding and complementary graph embedding, the final embedding is able to capture rich semantics in the finetuning stage. At last, comprehensive experimental results on 20 datasets including homophilic and heterophilic graphs firmly verify the effectiveness of our algorithm as well as the quality of probability complementation graph compared with other state-of-the-art methods.

关键词： Heterophily Graph contrastive learning Graph complementation Beta mixture model expectation maximization algorithm

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