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Randomized mixture models for probability density approximation and estimation

INFORMATION SCIENCES 2018年 467卷 135-148页

作者： Nguyen, Hien D. Wang, Dianhui McLachlan, Geoffrey J. La Trobe Univ Dept Math & Stat Melbourne Vic 3086 Australia La Trobe Univ Dept Comp Sci & Informat Technol Melbourne Vic 3086 Australia Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Liaoning Peoples R China Univ Queensland Sch Math & Phys St Lucia Qld 4072 Australia

Neural networks (NNs) with random weights are an interesting alternative to conventional NNs that are used more for data modeling. The random vector functional-link (RVFL) network is an established and theoretically well-grounded randomized learner. A key theoretical result for RVFL networks is that they provide universal approximation for continuous maps, in expectation, with respect to the square-integral norm. We specialize and modify this result, and show that RFVL networks can provide functional approximations that converge in Kullback-Leibler divergence, when the target function is a probability density function. Expanding on the approximation results, we demonstrate the RFVL networks lead to a simple randomized mixture model (MM) construction for density estimation from sample data. An expectation-maximization (EM) algorithm is derived for the maximum likelihood estimation of our randomized MM. The EM algorithm is proved to be globally convergent and the maximum likelihood estimator is proved to be consistent. A set of simulation studies is given to provide empirical evidence towards our approximation and density estimation results. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Density estimation expectation-maximization algorithm Functional approximation Mixture models Neural networks Random vector functional-link networks

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Gaussian Mixture Learning for LDPC Coded BICM Receivers With Blanking Nonlinearity

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IEEE ACCESS 2019年 7卷 168720-168727页

作者： He, Yuan Jiang, Ming Zhao, Chunming Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China Purple Mt Labs Nanjing 210096 Peoples R China

With the aid of blanking nonlinearity, the low density parity check (LDPC) coded bit-interleaved coded modulation (BICM) has been jointly considered as a robust mitigation for the impulsive interference in orthogonal frequency division multiplexing (OFDM) systems. However, the Gaussian assumption for the nonlinear channel conditional probability induces the mismatched L-values in the conventional MAP demodulator. In this paper, combined with the pulse blanking optimization via the PEXIT analysis, we propose a novel MAP demodulator based on the Gaussian mixture model (GMM) and estimate the parameters with the expectation-maximization (EM) algorithm. Taking the L-band Digital Aeronautical Communication System Type1 (L-DACS1) as an example, the GMM-based MAP demodulator can obtain the PEXIT thresholds that match the decoding curves well and provide the better BER performance in the interference-limit channel environment.

关键词： LDPC code BICM blanking nonlinearity Gaussian mixture model expectation-maximization algorithm

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Weld bead bead recognition using laser vision with model-based classification

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ROBOTICS AND COMPUTER-INTEGRATED MANUFACTURING 2018年 52卷 9-16页

作者： Ye, Guoliang Guo, Jianwen Sun, Zhenzhong Li, Chuan Zho, Shouyan Dongguan Univ Technol Sch Mech Engn Dongguan Guangdong Peoples R China

Weld bead recognition is important for providing information for automatic control of welding process and also for post-weld inspection. Bead geometry profiles can be measured by a laser-line profile sensor projecting a laser line onto the welding surface and receiving the reflection to calculate the height of the surface. As the bead is usually very small, it may be easily covered by the sensor noise or distorted by the bending of the work pieces after welding. In addition, it is difficult to estimate the parameters of bead width and bead height while moving the laser sensor to cover a 3D surface, since the movement may cause unstable measurements. This work investigates using a model-based classification method to automatically segment the bead from the welding surface regardless of the distance and the angle of the scanner to the welding surface. It firstly uses a polynomial model together with the expectation-Maximisation (EM) algorithm fitting into the distance profiles measured by the laser sensor, and then automatically removes the surface curvature. Consequently the shape of the bead can be easily extracted from the welding surface by applying a small value of threshold depending on the noise level of the data. Experimental results show that the Butt welding bead parameters of bead width and height can be extracted successfully. The method is robust to the bending of the welding surface and the unstable movement of the laser sensor. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Bead geometry Segmentation Laser vision expectation-maximization algorithm

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Type I multivariate zero-truncated/adjusted Poisson distributions with applications

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2018年 344卷 132-153页

作者： Tian, Guo-Liang Liu, Yin Tang, Man-Lai Jiang, Xuejun Southern Univ Sci & Technol Dept Math Shenzhen 518055 Guangdong Peoples R China Zhongnan Univ Econ & Law Sch Stat & Math Wuhan 430073 Hubei Peoples R China Hang Seng Management Coll Sch Business Dept Math & Stat Shatin Hong Kong Peoples R China

Although there is substantial literature on the univariate zero-truncated Poisson (ZTP) distributions, few works have been done for developing multivariate ZTP distributions with dimension larger than two. In this paper, we first propose a new Type I multivariate ZTP distribution to model multivariate zero-truncated count data and develop its important distributional properties, while providing efficient statistical inference methods. The key idea for extending the univariate ZTP distribution to a multivariate version is to identify a new stochastic representation of the ZTP random variable, resulting in a novel expectation-maximization algorithm with a feature that the introduced latent variables are independent of the observed variables. Since the ZTP distribution is closely related with the zero-adjusted Poisson (ZAP) distribution, the second objective of this paper is to propose a new family of Type I multivariate ZAP distributions (including the Type I multivariate ZTP distribution, the Type I multivariate zero-inflated Poisson (ZIP) distribution, the Type I multivariate zero-deflated Poisson (ZDP) distribution as its special cases) by accounting for truncation, inflation and deflation at zero. The corresponding distributional properties are explored and the associated statistical methods are provided. Finally, three real data sets are used to illustrate the proposed distributions and corresponding analysis methods. (C) 2018 Elsevier B.V. All rights reserved.

关键词： expectation-maximization algorithm Multivariate zero-adjusted Poisson model Multivariate zero-truncated Poisson model Stochastic representation

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An imputation-regularized optimization algorithm for high dimensional missing data problems and beyond

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 2018年第5期80卷 899-926页

作者： Liang, Faming Jia, Bochao Xue, Jingnan Li, Qizhai Luo, Ye Purdue Univ W Lafayette IN 47907 USA Univ Florida Gainesville FL USA Houzz Palo Alto CA USA Chinese Acad Sci Beijing Peoples R China

Missing data are frequently encountered in high dimensional problems, but they are usually difficult to deal with by using standard algorithms, such as the expectation-maximization algorithm and its variants. To tackle this difficulty, some problem-specific algorithms have been developed in the literature, but there still lacks a general algorithm. This work is to fill the gap: we propose a general algorithm for high dimensional missing data problems. The algorithm works by iterating between an imputation step and a regularized optimization step. At the imputation step, the missing data are imputed conditionally on the observed data and the current estimates of parameters and, at the regularized optimization step, a consistent estimate is found via the regularization approach for the minimizer of a Kullback-Leibler divergence defined on the pseudocomplete data. For high dimensional problems, the consistent estimate can be found under sparsity constraints. The consistency of the averaged estimate for the true parameter can be established under quite general conditions. The algorithm is illustrated by using high dimensional Gaussian graphical models, high dimensional variable selection and a random-coefficient model.

关键词： expectation-maximization algorithm Gaussian graphical model Gibbs sampler Imputation consistency Random-coefficient model Variable selection

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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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Stochastic parameterization identification using ensemble Kalman filtering combined with maximum likelihood methods

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TELLUS SERIES A-DYNAMIC METEOROLOGY AND OCEANOGRAPHY 2018年第1期70卷 1-17页

作者： Pulido, Manuel Tandeo, Pierre Bocquet, Marc Carrassi, Alberto Lucini, Magdalena Univ Nacl Nordeste Dept Phys FaCENA Corrientes Argentina CNRS CONICET IFAECI IMIT Buenos Aires DF Argentina IMT Atlantique UBL Lab STICC Brest France Univ Paris Est Joint Lab Ecole Ponts ParisTech & EDF R&D CEREA Champs Sur Marne France Nansen Environm & Remote Sensing Ctr Bergen Norway Univ Nacl Nordeste FaCENA Dept Math Corrientes Argentina Consejo Nacl Invest Cient & Tecn Corrientes Argentina

For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the best possible stochastic parameterization from noisy data. State-of-the-art sequential estimation methods such as Kalman and particle filters do not achieve this goal successfully because both suffer from the collapse of the posterior distribution of the parameters. To overcome this intrinsic limitation, we propose two statistical learning methods. They are based on the combination of the ensemble Kalman filter (EnKF) with either the expectation-maximization (EM) or the Newton-Raphson (NR) used to maximize a likelihood associated to the parameters to be estimated. The EM and NR are applied primarily in the statistics and machine learning communities and are brought here in the context of data assimilation for the geosciences. The methods are derived using a Bayesian approach for a hidden Markov model and they are applied to infer deterministic and stochastic physical parameters from noisy observations in coarse-grained dynamical models. Numerical experiments are conducted using the Lorenz-96 dynamical system with one and two scales as a proof of concept. The imperfect coarse-grained model is modelled through a one-scale Lorenz-96 system in which a stochastic parameterization is incorporated to represent the small-scale dynamics. The algorithms are able to identify the optimal stochastic parameterization with good accuracy under moderate observational noise. The proposed EnKF-EM and EnKF-NR are promising efficient statistical learning methods for developing stochastic parameterizations in high-dimensional geophysical models.

关键词： parameter estimation model error estimation stochastic parameterization expectation-maximization algorithm

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Small area estimation via unmatched sampling and linking models

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TEST 2018年第2期27卷 407-427页

作者： Sugasawa, Shonosuke Kubokawa, Tatsuya Rao, J. N. K. Risk Anal Res Ctr Inst Stat Math Tokyo Japan Univ Tokyo Fac Econ Tokyo Japan Carleton Univ Sch Math & Stat Ottawa ON Canada

The authors use an empirical Bayes (EB) approach to small area estimation under area-level unmatched sampling and linking models. Model parameters are estimated by a unified expectation and maximization (EM) algorithm and used to obtain EB estimators of area parameters. Results are extended to a nonparametric linking model based on a spline approximation. Approximate EB estimators that are computationally simpler are also obtained. Different bootstrap approaches to estimating the mean squared error (MSE) of the EB estimators are proposed. Results of a simulation study on the performance of the proposed methods are presented. Proposed methods are applied to data from a survey of family income and expenditure in Japan and poverty rates in Spanish provinces.

关键词： Bootstrap Empirical Bayes expectation-maximization algorithm Fay-Herriot model Mean squared error Penalized spline

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Model selection in multivariate semiparametric regression

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STATISTICAL METHODS IN MEDICAL RESEARCH 2018年第10期27卷 3026-3038页

作者： Li, Zhuokai Liu, Hai Tu, Wanzhu Duke Clin Res Inst Durham NC USA Gilead Sci Inc 353 Lakeside Dr Foster City CA 94404 USA Indiana Univ Sch Med Dept Biostat 410 West 10th St Indianapolis IN 46202 USA

Variable selection in semiparametric mixed models for longitudinal data remains a challenge, especially in the presence of multiple correlated outcomes. In this paper, we propose a model selection procedure that simultaneously selects fixed and random effects using a maximum penalized likelihood method with the adaptive least absolute shrinkage and selection operator penalty. Through random effects selection, we determine the correlation structure among multiple outcomes and therefore address whether a joint model is necessary. Additionally, we include a bivariate nonparametric component, as approximated by tensor product splines, to accommodate the joint nonlinear effects of two independent variables. We use an adaptive group least absolute shrinkage and selection operator to determine whether the bivariate nonparametric component can be reduced to additive components. To implement the selection and estimation method, we develop a two-stage expectation-maximization procedure. The operating characteristics of the proposed method are assessed through simulation studies. Finally, the method is illustrated in a clinical study of blood pressure development in children.

关键词： Adaptive least absolute shrinkage and selection operator adaptive group least absolute shrinkage and selection operator expectation-maximization algorithm mixed effects multivariate data

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Latent Ignorability and Item Selection for Nursing Home Case-Mix Evaluation

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JOURNAL OF CLASSIFICATION 2018年第1期35卷 172-193页

作者： Bartolucci, Francesco Montanari, Giorgio E. Pandolfi, Silvia Univ Perugia Perugia Italy

In the social, behavioral, and health sciences it is often of interest to identify latent or unobserved groups in the population with the group membership of the individuals depending on a set of observed variables. In particular, we focus on the field of nursing home assessment in which the response variables typically come from the administration of questionnaires made of categorical items. These types of data may suffer from missing values and the use of lengthy questionnaires may be problematic as a large number of items could have a negative impact on the responses. In such a context, we introduce an extended version of the Latent Class (LC) model aimed at dealing with missing values, by assuming a form of latent ignorability. Moreover, we propose an item selection algorithm, based on the LC model, for finding the smallest subset of items providing an amount of information close to that of the initial set. The proposed approach is illustrated through an application to a dataset collected within an Italian project on the quality-of-life of nursing home patients.

关键词： expectation-maximization algorithm Missing responses Polytomous items Quality-of-life ULISSE project

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