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Statistical learning formulation of the DNA base-calling problem and its solution in a Bayesian EM framework

DISCRETE APPLIED MATHEMATICS 2000年第1-3期104卷 229-258页

作者： Pereira, MS Andrade, L El Difrawy, S Karger, BL Manolakos, ES Northeastern Univ Dept Elect & Comp Engn Commun & Digital Signal Proc Ctr Boston MA 02115 USA Northeastern Univ Barnett Inst Boston MA 02115 USA

A novel formulation of the important DNA sequence base-calling problem as well as algorithms for its solution are introduced. The proposed approach is to bring DNA base-calling within the framework of a powerful statistical learning paradigm, which allows the incorporation of prior knowledge about the structure of the problem directly into the base-calling algorithms, without resorting to heuristics. Use of prior knowledge provides constraints which help disambiguate the different possible interpretations that the data may have at regions of low SNR, and is shown to lead to a substantial increase of the number of DNA bases that can be accurately called in such regions. Our experimental results suggest that the proposed algorithms, without being optimized, can achieve base-calling performance that matches, and often exceeds, that of commercially available software. Furthermore,due to their statistical basis, they also provide confidence estimates (in the form of posterior probabilities) for the produced base call decisions, which can be used for sequence assembly and mutation detection purposes. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： DNA base-calling statistical learning expectation-maximization algorithm

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EM estimation for the mixed Pareto regression model for claim severities

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2024年第15期53卷 5507-5523页

作者： Aradhye, Girish Tzougas, George Bhati, Deepesh Cent Univ Rajasthan Dept Stat Ajmer India Heriot Watt Univ Dept Actuarial Math & Stat Edinburgh Scotland

This article presents a mixed Pareto model and examines its suitability for modeling non life insurance claim severity data sets which exhibit peculiar characteristics that cannot be captured by the Pareto distribution. Furthermore, we introduce regression specifications for both the mean and the dispersion parameters of the mixed Pareto model. Our main achievement is that we develop a novel expectation-maximization (EM) algorithm for finding the maximum likelihood (ML) estimates of the parameters of the mixed Pareto regression model which is used for demonstration purposes. Finally, a real-data application based on motor insurance claim size data is provided.

关键词： expectation-maximization algorithm mixed model Inverse Gaussian distribution regression models Motor insurance claim severity data

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Hybrid system of ART and RBF neural networks for online clustering

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APPLIED SOFT COMPUTING 2017年 58卷 1-10页

作者： Bielecki, Andrzej Wojcik, Mateusz AGH Univ Sci & Technol Fac Elect Engn Automat Comp Sci & Biomed Engn Chair Appl Comp Sci Al Mickiewicza 30 PL-30059 Krakow Poland

An online clustering task is considered for machine state monitoring purpose. In the previous authors researches a classical ART-2 network was tested for online classification of operational states in the context of a wind turbine monitoring. Some drawbacks, however, were found when a data stream size had been increased. This case is investigated in this paper. Classical ART-2 network can cluster data incorrectly when data points are compared by using Euclidean distance. Furthermore, ART-2 network can lose accuracy when data stream is processed for long time. The way of improving the ART-2 network is considered and two main steps of that are taken. At first, the stereographic projection is implemented. At the second step, a new type of hybrid neural system which consists of ART-2 and RBF networks with data processed by using the stereographic projection is introduced. Tests contained elementary scenarios for low-dimensional cases as well as higher dimensional real data from wind turbine monitoring. All the tests implied that an efficient system for online clustering had been found. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Online classification Hybrid system ART-2 neural network RBF neural network expectation-maximization algorithm

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Robust stochastic configuration networks for industrial data modelling with Student's-t mixture distribution

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INFORMATION SCIENCES 2022年 607卷 493-505页

作者： Yan, Aijun Guo, Jingcheng Wang, Dianhui Beijing Univ Technol Fac Informat Technol Beijing 100124 Peoples R China Minist Educ Engn Res Ctr Digital Community Beijing 100124 Peoples R China Beijing Lab Urban Mass Transit Beijing 100124 Peoples R China China Univ Min & Technol Artificial Intelligence Res Inst Xuzhou 221116 Peoples R China Northeastern Univ State Key Lab Synthet Automation Proc Ind Shenyang 110819 Peoples R China La Trobe Univ Dept Comp Sci & Informat Technol Melbourne VIC 3086 Australia China Univ Artificial Intelligence Res Inst Xuzhou Peoples R China

Data collected from industrial sites commonly contains outliers or noise that obey unknown distributions, making it challenging to establish an accurate data-driven model. Therefore, this paper proposes a novel robust stochastic configuration network based on a Student's-t mixture distribution (termed as SM-RSC). Firstly, a stochastic configuration algorithm is employed to determine the number of hidden nodes, the input weights and biases. Secondly, the maximum a posteriori (MAP) estimate is used to evaluate the output weights of the SCN learner model under the assumption that outliers or noises obey the Student's-t mixture distribution. Because the output weights cannot be solved directly due to the unknown hyper-parameters of the mixture distribution, we apply the well-known expectation-maximization (EM) algorithm for optimizing the hyper-parameters of the mixture distribution and update the output weights iteratively. The proposed algo-rithm is evaluated by a function approximation, four benchmark datasets, and a case study on industrial data modelling for a waste incineration process. The results show that SM-RSC performs favorably compared with other methods.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Stochastic configuration networks Robust data modeling Student?s-t mixture distribution expectation-maximization algorithm

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Statistical Inference for a New Class of Multivariate Pareto Distributions

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2016年第2期45卷 456-471页

作者： Asimit, Alexandru V. Furman, Edward Vernic, Raluca City Univ London Cass Business Sch London EC1Y 8TZ England York Univ Dept Math & Stat Toronto ON M3J 2R7 Canada Ovidius Univ Constanta Fac Math & Informat Constanta Romania Univ Bucharest Inst Math Stat & Appl Math Bucharest Romania

Various solutions to the parameter estimation problem of a recently introduced multivariate Pareto distribution are developed and exemplified numerically. Namely, a density of the aforementioned multivariate Pareto distribution with respect to a dominating measure, rather than the corresponding Lebesgue measure, is specified and then employed to investigate the maximum likelihood estimation (MLE) approach. Also, in an attempt to fully enjoy the common shock origins of the multivariate model of interest, an adapted variant of the expectation-maximization (EM) algorithm is formulated and studied. The method of moments is discussed as a convenient way to obtain starting values for the numerical optimization procedures associated with the MLE and EM methods.

关键词： Common shock model expectation-maximization algorithm Maximum likelihood estimation Method of moments Multivariate Pareto distribution 62F10 62H12 60E05

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Rainfall data simulation by hidden Markov model and discrete wavelet transformation

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2009年第7期23卷 863-877页

作者： Jayawardena, A. W. Xu, P. C. Li, W. K. Publ Works Res Inst Int Ctr Water Hazard & Risk Management Tsukuba Ibaraki Japan Chinese Acad Sci Acad Math & Syst Sci Beijing Peoples R China Univ Hong Kong Dept Stat & Actuarial Sci Hong Kong Hong Kong Peoples R China

In many regions, monthly (or bimonthly) rainfall data can be considered as deterministic while daily rainfall data may be treated as random. As a result, deterministic models may not sufficiently fit the daily data because of the strong stochastic nature, while stochastic models may also not reliably fit into daily rainfall time series because of the deterministic nature at the large scale (i.e. coarse scale). Although there are different approaches for simulating daily rainfall, mixing of deterministic and stochastic models (towards possible representation of both deterministic and stochastic properties) has not hitherto been proposed. An attempt is made in this study to simulate daily rainfall data by utilizing discrete wavelet transformation and hidden Markov model. We use a deterministic model to obtain large-scale data, and a stochastic model to simulate the wavelet tree coefficients. The simulated daily rainfall is obtained by inverse transformation. We then compare the accumulated simulated and accumulated observed data from the Chao Phraya Basin in Thailand. Because of the stochastic nature at the small scale, the simulated daily rainfall on a point to point comparison show deviations with the observed data. However the accumulated simulated data do show some level of agreement with the observed data.

关键词： Daily rainfall Discrete wavelet transformation Hidden Markov model expectation-maximization algorithm False nearest neighbours Phase space reconstruction

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Process monitoring using a Gaussian mixture model via principal component analysis and discriminant analysis

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COMPUTERS & CHEMICAL ENGINEERING 2004年第8期28卷 1377-1387页

作者： Choi, SW Park, JH Lee, IB Pohang Univ Sci & Technol Dept Chem Engn Pohang 790784 South Korea Pohang Univ Sci & Technol Sch Environm Sci & Engn Pohang 790784 South Korea Pohang Univ Sci & Technol P&I Consulting Co Ltd Pohang 790784 South Korea

Conventional process monitoring based on principal component analysis (PCA) has been applied to many industrial chemical processes. However, such PCA-based approaches assume that the process is operating in a steady state and consequently that the process data are normally distributed and contain no time correlations. These assumptions significantly limit the applicability of PCA-based approaches to the monitoring of real processes. In this paper, we propose a more exact and realistic process monitoring method that does not require that the process data be normally distributed. Specifically, the concept of conventional PCA is expanded such that a Gaussian mixture model (GMM) is used to approximate the data pattern in the model subspace obtained by PCA. The use of a mixture of local Gaussian models means that the proposed approach can be applied to arbitrary datasets, not just those showing a normal distribution. To use the GMM for monitoring, the overall T-2 and Q statistics were used as the monitoring guidelines for fault detection. The proposed approach significantly relaxes the restrictions inherent in conventional PCA-based approaches in regard to the raw data pattern, and can be expanded to dynamic process monitoring without developing a complicated dynamic model. In addition, a GMM via discriminant analysis is proposed to isolate faults. The proposed monitoring method was successfully applied to three case studies: (1) simple two-dimensional toy problems, (2) a simulated 4 x 4 dynamic process, and (3) a simulated non-isothermal continuous stirred tank reactor (CSTR) process. These application studies demonstrated that, in comparison to conventional PCA-based monitoring, the proposed fault detection and isolation (FDI) scheme is more accurate and efficient. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： principal component analysis Gaussian mixture model expectation-maximization algorithm overall T-2 discriminant analysis ARL

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Empirical Bayes matrix completion

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 137卷 195-210页

作者： Matsuda, Takeru Komaki, Fumiyasu Univ Tokyo Grad Sch Informat Sci & Technol Dept Math Informat Bunkyo Ku 7-3-1 Hongo Tokyo 1138656 Japan RIKEN Ctr Brain Sci 2-1 Hirosawa Wako Saitama 3510198 Japan

We develop an empirical Bayes (EB) algorithm for the matrix completion problems. The EB algorithm is motivated from the singular value shrinkage estimator for matrix means by Efron and Morris. Since the EB algorithm is derived as the expectation-maximization algorithm applied to a simple model, it does not require heuristic parameter tuning other than tolerance. Also, it can account for the heterogeneity in variance of observation noise. Numerical results demonstrate that the EB algorithm attains at least comparable accuracy to existing algorithms for matrices not close to square and that it works particularly well when the rank is relatively large or the proportion of observed entries is small. Application to real data also shows the practical utility of the EB algorithm. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Empirical Bayes expectation-maximization algorithm Matrix completion Singular value shrinkage

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A Robust Point Set Registration Approach With Multiple Effective Constraints

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2020年第12期67卷 10931-10941页

作者： Sun, Jing Sun, Zhan-Li Lam, Kin-Man Zeng, Zhigang Anhui Univ Key Lab Intelligent Comp & Signal Proc Minist Educ Hefei 230601 Peoples R China Anhui Univ Sch Elect Engn & Automat Hefei 230601 Peoples R China Hong Kong Polytech Univ Dept Elect & Informat Engn Hong Kong Peoples R China Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan 430074 Peoples R China

How to accurately register point sets still remains a challenging task, due to some unfavorable factors. In this article, a robust point set registration approach is proposed based on the Gaussian mixture model (GMM) with multiple effective constraints. The GMM is established by wrapping a model point set to a target point set, via a spatial transformation. Instead of a displacement model, the spatial transformation is decomposed as two types of transformations, an affine transformation and a nonaffine deformation. For the affine transformation, a constraint term of the parameter vector is applied to improve the robustness and efficiency. In order to enforce the smoothness, the square norm of the kernel Hilbert space is adopted as a coherent constraint for the nonaffine deformation. Moreover, the manifold regularization is utilized as a constraint in the proposed model, to capture the spatial geometry of point sets. In addition, the expectation-maximization algorithm is developed to solve the unknown variables of the proposed model. Compared to the state-of-the-art approaches, the proposed model is more robust to deformation and rotation, due to the use of multiple effective constraints. Experimental results on several widely used data sets demonstrate the effectiveness of the proposed model.

关键词： Strain Shape Kernel Sun Gaussian mixture model Deformable models expectation-maximization algorithm Gaussian mixture model point set registration

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BLIND DECONVOLUTION OF FLUORESCENCE MICROGRAPHS BY MAXIMUM-LIKELIHOOD-ESTIMATION

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APPLIED OPTICS 1995年第29期34卷 6633-6647页

作者： KRISHNAMURTHI, V LIU, YH BHATTACHARYYA, S TURNER, JN HOLMES, TJ YALE UNIV CARDIOL SECT NEW HAVEN CT USA RENSSELAER POLYTECH INST DEPT BIOMED ENGN TROY NY 12180 USA NEW YORK STATE DEPT HLTH WADSWORTH CTR LABS & RES ANAT PATHOL LAB ALBANY NY 12201 USA

We report some recent algorithmic refinements and the resulting simulated and real image reconstructions of fluorescence micrographs by using a blind-deconvolution algorithm based on maximum-likelihood estimation. Blind-deconvolution methods encompass those that do not require either calibrated or theoretical predetermination of the point-spread function (PSF). Instead, a blind deconvolution reconstructs the PSF concurrently with deblurring of the image data. Two-dimensional computer simulations give some definitive evidence of the integrity of the reconstructions of both the fluorescence concentration and the PSF. A reconstructed image and a reconstructed PSF from a two-dimensional fluorescent data set show that the blind version of the algorithm produces images that are comparable with those previously produced by a precursory nonblind version of the algorithm. They furthermore show a remarkable similarity, albeit not perfectly identical, with a PSF measurement taken for the same data set, provided by Agard and colleagues. A reconstructed image of a three-dimensional confocal data set shows a substantial axial smear removal. There is currently an existing trade-off in using the blind deconvolution in that it converges at a slightly slower rate than the nonblind approach. Future research, of course, will address this present limitation.

关键词： BLIND DECONVOLUTION MAXIMUM-LIKELIHOOD ESTIMATION expectation-maximization algorithm CONFOCAL FLUORESCENCE DEBLURRING DECONVOLUTION 3-DIMENSIONAL LIGHT MICROSCOPY

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