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Multi-rate Gaussian Bayesian network soft sensor development with noisy input and missing data

JOURNAL OF PROCESS CONTROL 2021年 105卷 48-61页

作者： Khosbayar, Anudari Valluru, Jayaram Huang, Biao Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2G6 Canada

For efficient process control and monitoring, accurate real-time information of quality variables is essential. To predict these quality (or slow-rate) variables at a fast-rate, in the industry, inferential/soft sensors are often used. However, most of the conventional methods for soft sensors do not utilize prior process knowledge even if it is available. The prediction accuracy of these inferential sensors depends mainly on the quality of available data, which can be affected by significant noise and possible sensor failures. To address these issues, in this work, a generic Gaussian Bayesian network based soft-sensor framework is developed, which can account multiple hidden states and multirate/missing data. In the proposed framework, due to the presence of hidden variables and missing data, posterior probability of these variables in E-step of the em algorithm is evaluated using Bayesian inference. Compared to the existing soft-sensors, the proposed approach will allow users to integrate prior knowledge into the BN structure. Moreover, due to the probabilistic nature of BNs, variances of measurement noises and disturbances between hidden states are simultaneously estimated. The proposed framework is generic and can be used for any multi-layered structure. Its performance is demonstrated for two different structures, two-layer and multilayered structures, on a benchmark flow-network problem and an industrial process. It is observed that the proposed Gaussian Bayesian network based soft sensors are able to give significantly better and more reliable estimates compared to the conventional approaches. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Gaussian Bayesian networks Soft-sensors em algorithm Multirate data

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On mixture periodic Integer-Valued ARCH models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2021年第12期50卷 3931-3957页

作者： Ouzzani, Fares Bentarzi, Mohamed Univ Sci & Technol Houari Boumediene Fac Math Dept Operat Res Algiers 16111 Algeria

This paper deals with the study of Mixture Periodic Integer-Valued Autoregressive Conditionally Heteroskedastic models. Some theoretical properties of the model, such as the first and the second moment periodically stationary conditions, are established. Moreover, closed-forms of these moments are, under these conditions, derived. The estimation is done by the maximum likelihood via the iterative em algorithm and the performance of this method is shown via an intensive simulation study. A comparative real data study is performed on a Campylobacteriosis time series.

关键词： Periodically correlated integer-valued process Mixture Periodic Integer-Valued (MPINARCH) periodically stationary condition em algorithm Campylobacteriosis

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On inference and design under progressive type-I interval censoring scheme for inverse Gaussian lifetime model

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INTERNATIONAL JOURNAL OF QUALITY & RELIABILITY MANAGemENT 2022年第8期39卷 1937-1962页

作者： Roy, Soumya Pradhan, Biswabrata Purakayastha, Annesha Indian Inst Management Kozhikode Quantitat Methods & Operat Management Area Kozhikode India Indian Stat Inst SQC & OR Unit Kolkata India Model Risk Management Div Mumbai Maharashtra India

Purpose This article considers Inverse Gaussian distribution as the basic lifetime model for the test units. The unknown model parameters are estimated using the method of moments, the method of maximum likelihood and Bayesian methods. As part of maximum likelihood analysis, this article employs an expectation-maximization algorithm to simplify numerical computation. Subsequently, Bayesian estimates are obtained using the Metropolis-Hastings algorithm. This article then presents the design of optimal censoring schemes using a design criterion that deals with the precision of a particular system lifetime quantile. The optimal censoring schemes are obtained after taking into account budget constraints. Design/methodology/approach This article first presents classical and Bayesian statistical inference for Progressive Type-I Interval censored data. Subsequently, this article considers the design of optimal Progressive Type-I Interval censoring schemes after incorporating budget constraints. Findings A real dataset is analyzed to demonstrate the methods developed in this article. The adequacy of the lifetime model is ensured using a simulation-based goodness-of-fit test. Furthermore, the performance of various estimators is studied using a detailed simulation experiment. It is observed that the maximum likelihood estimator relatively outperforms the method of moment estimator. Furthermore, the posterior median fares better among Bayesian estimators even in the absence of any subjective information. Furthermore, it is observed that the budget constraints have real implications on the optimal design of censoring schemes. Originality/value The proposed methodology may be used for analyzing any Progressive Type-I Interval Censored data for any lifetime model. The methodology adopted to obtain the optimal censoring schemes may be particularly useful for reliability engineers in real-life applications.

关键词： em algorithm Goodness of fit Metropolis-hastings algorithm Optimal censoring scheme Simulation

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Multiple arbitrarily inflated Poisson regression analysis

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Abusaif, Ihab Kayaci, Burak Kus, Coskun Selcuk Univ Fac Sci Dept Stat Konya Turkiye

In this paper, a new flexible count regression analysis is proposed. For this purpose, a new modification of the Poisson distribution is introduced which generalizes the Poisson, zero-inflated Poisson, zero-one inflated Poisson, and zero-one-two inflated Poisson distributions. Some distributional properties are discussed for the proposed distribution. The Fisher scoring and em algorithms are derived to attain the maximum likelihood estimates of the unknown parameters. An expected Fisher information matrix is provided to construct an approximate confidence interval for the parameters. Using the modified Poisson distribution, an arbitrary multiply inflated counting regression model is proposed. The performance of the maximum likelihood methodology is investigated with a simulation study for the distribution and count regression model. Finally, two practical data sets are analyzed and the superiority of the proposed model is demonstrated among others.

关键词： Count data em algorithm Fisher scoring algorithm Inflated count regression model Zero-inflated Poisson distribution

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Advanced inference techniques for two-parameter Topp-Leone models under unified progressively hybrid censoring

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Bayoud, Husam A. Almathkour, Fatmah B. Raqab, Mohammad Z. Qatar Fdn Acad Bridge Program Doha Qatar Fahad Bin Sultan Univ Coll Sci & Humanities Tabuk Saudi Arabia Kuwait Univ Dept Stat & Operat Res Al Shadadiyya Kuwait Univ Jordan Dept Math Amman Jordan

In this study, we examine the unified progressive hybrid censoring scheme from Topp-Leone models, and we show that while the maximum likelihood estimates of the model parameters are uniquely exist, they cannot be obtained in a closed form. To obtain these estimates, we utilize two frequentist algorithms-the Expectation-Maximization method and an Expectation-Maximization type method. We also derive confidence intervals for the unknown parameters using both asymptotic distributions of the maximum likelihood estimators and bootstrap approaches. Furthermore, we develop sample-based Bayes estimates for the model parameters under different error loss functions, such as square, LINEX, and entropy loss functions. To approximate the Bayes estimates, we apply importance sampling and Metropolis-Hastings algorithms. We also construct Bayes credible intervals for the estimates. To assess the performance of the proposed methods, we conduct a numerical simulation study. Finally, we analyze a real data set to illustrate the practical application of our proposed methods and their findings. The study highlights the usefulness of hybrid censoring schemes and the applicability of various statistical methods for parameter estimation and inference.

关键词： Bayes estimation confidences em algorithm Importance sampling method Maximum likelihood estimation Metropolis-Hastings method Topp-Leone models Unified progressive censoring scheme

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Adaptive Harmony Learning and Optimization for Attributed Graph Clustering

Adaptive Harmony Learning and Optimization for Attributed Gr...

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IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) / IEEE World Congress on Computational Intelligence (IEEE WCCI) / International Joint Conference on Neural Networks (IJCNN) / IEEE Congress on Evolutionary Computation (IEEE CEC)

作者： Wu, Daqing Guo, Xiangyang Luo, Xiao Qiao, Ziyue Ma, Jinwen Peking Univ Sch Math Sci Dept Informat & Comp Sci Beijing Peoples R China Peking Univ Sch Math Sci Dept Probabil & Stat Beijing Peoples R China Chinese Acad Sci Comp Network Informat Ctr Beijing Peoples R China

ISBN: (数字)9781728186719

ISBN: (纸本)9781728186719

Graph clustering aiming to partition nodes into several disjoint subsets is a fundamental task for graph-structured learning. Traditional graph clustering methods only consider the adjacency information. In recent years, inspired by the homophily assumption that the adjacent nodes tend to have similar features and labels, most existing graph clustering approaches leverage node attribute information to improve graph clustering performance. These works have mainly focused on node embedding learning via the various combinations of auto-encoder and graph neural networks. As for clustering learning, they introduce a self-optimizing strategy that assumes that all clusters are homogeneous. However, this assumption usually does not hold since the size and variance of different clusters can be quite different, and self-optimizing strategy is incompetent in dealing with this heterogeneous clusters. In this work, we propose a novel method named Adaptive Harmony Learning and Optimization (AHLO) for attributed graph clustering, which models the node embeddings with the mixture of von Mises-Fisher distributions on the unit hypersphere and develops an alternating learning strategy. Specifically, we take the node embeddings as the supervisory signals for the update of the mixture parameters, and the mixture distribution as the supervisory signals for the update of the node embeddings. To prevent small clusters from annexing by large clusters, we develop the regularized harmony loss to enhance the prediction on small clusters. In the mixture parameter optimization stage, we utilize em algorithm and heuristically design a center update scheme with consideration of the posterior probability confidence and the impact of other centers. Hence, AHLO can simultaneously improve the intra-cluster compactness and inter-cluster separability. Extensive experiments on four benchmark attributed graph datasets have demonstrated the effectiveness of our proposed AHLO.

关键词： Graph Clustering Graph Neural Networks Harmony Learning em algorithm

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Identification of Wiener state-space models utilizing Gaussian sum smoothing

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AUTOMATICA 2024年 166卷

作者： Cedeno, Angel L. Gonzalez, Rodrigo A. Carvajal, Rodrigo Aguero, Juan C. Univ Tecn Federico Santa Maria Elect Engn Dept Valparaiso Chile AC3E Adv Ctr Elect & Elect Engn Valparaiso Chile Eindhoven Univ Technol Dept Mech Engn Eindhoven Netherlands Pontificia Univ Catolica Valparaiso Sch Elect Engn Valparaiso Chile

In this paper, we address the problem of system identification for Wiener state-space models. Our approach is based on the Maximum Likelihood method and the Expectation-Maximization algorithm. In the problem of interest, we model the output nonlinearity as a piecewise polynomial function and we jointly estimate the parameters of the linear system with the coefficients of each polynomial section. In our proposal, the computation of the cost function in the Expectation-Maximization algorithm requires the computation of the joint distribution of the state and the output of the linear system given the output of the nonlinear block. These quantities are obtained from an approximation that leads to a novel Gaussian sum smoothing algorithm. Additionally, we show that our method also addresses the identification of state-space systems in which the output is produced by a known quantizer. We present numerical examples to illustrate the benefits of the proposed identification technique. (c) 2024 Elsevier Ltd. All rights reserved.

关键词： Wiener system identification em algorithm Maximum likelihood Piecewise polynomial

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t distribution-based robust semiparametric mixture regression model

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Ge, Yan Xiang, Sijia Yao, Weixin Zhejiang Univ Finance & Econ Sch Data Sci Hangzhou 310018 Zhejiang Peoples R China Univ CA Dept Stat Riverside CA USA

Semiparametric mixture of regression (SMR) models provide a popular and flexible framework for modeling heterogeneous data that violates some of the parametric assumptions assumed in traditional finite mixture of regressions models. The majority of applications of SMR models assume normality for their error terms. As is well known, Gaussian distribution is sensitive to outliers or heavy-tailed distribution. In this article, we propose a more robust approach of SMR by modeling the error distribution as t distributions. By combining the em algorithm and kernel density estimator, two algorithms are proposed to fit the robust SMR models and are proven to monotonically increase the likelihood function. We further investigate a modified version based on trimming for high leverage outliers. In real applications, a data adaptive mechanism is discussed to choose the degrees of freedom. A simulation study and three real data analyses show the superiority of the new methodology.

关键词： Distribution em algorithm Robust regression t Varying coefficient

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A multi-step kernel-based regression estimator that adapts to error distributions of unknown form

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2021年第24期50卷 6211-6230页

作者： De Gooijer, Jan G. Reichardt, Hugo Univ Amsterdam Amsterdam Sch Econ Amsterdam Netherlands London Sch Econ London England

For linear regression models, we propose and study a multi-step kernel density-based estimator that is adaptive to unknown error distributions. We establish asymptotic normality and almost sure convergence. An efficient em algorithm is provided to implement the proposed estimator. We also compare its finite sample performance with five other adaptive estimators in an extensive Monte Carlo study of eight error distributions. Our method generally attains high mean-square-error efficiency. An empirical example illustrates the gain in efficiency of the new adaptive method when making statistical inference about the slope parameters in three linear regressions.

关键词： Adaptive estimation em algorithm kernel density estimate least squares estimate linear regression

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Quantile modeling through multivariate log-normal/independent linear regression models with application to newborn data

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BIOMETRICAL JOURNAL 2021年第6期63卷 1290-1308页

作者： Moran-Vasquez, Raul Alejandro Mazo-Lopera, Mauricio A. Ferrari, Silvia L. P. Univ Antioquia Inst Matemat Calle 67 53-108 Medellin 050010 Colombia Univ Nacl Colombia Escuela Estadist Medellin Colombia Univ Sao Paulo Dept Estat Sao Paulo Brazil

In this article, we propose and study the class of multivariate log-normal/independent distributions and linear regression models based on this class. The class of multivariate log-normal/independent distributions is very attractive for robust statistical modeling because it includes several heavy-tailed distributions suitable for modeling correlated multivariate positive data that are skewed and possibly heavy-tailed. Besides, expectation-maximization (em)-type algorithms can be easily implemented for maximum likelihood estimation. We model the relationship between quantiles of the response variables and a set of explanatory variables, compute the maximum likelihood estimates of parameters through em-type algorithms, and evaluate the model fitting based on Mahalanobis-type distances. The satisfactory performance of the quantile estimation is verified by simulation studies. An application to newborn data is presented and discussed.

关键词： em algorithm multivariate linear regression multivariate normal independent distribution newborn quantile modeling

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