This work proposes an exponential computation with low-computational complexity and applies this technique to the expectation-maximization (em) algorithm for Gaussian mixture model (GMM). For certain machine-learning ...
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This work proposes an exponential computation with low-computational complexity and applies this technique to the expectation-maximization (em) algorithm for Gaussian mixture model (GMM). For certain machine-learning techniques, such as the em algorithm for the GMM, fast and low-cost implementations are preferred over high precision ones. Since the exponential function is frequently used in machine-learning algorithms, this work proposes reducing computational complexity by transforming the function into powers of two and introducing a look-up table. Moreover, to improve efficiency the look-up table is scaled. To verify the validity of the proposed technique, this work obtains simulation results for the em algorithm used for parameter estimation and evaluates the performances of the results in terms of the mean absolute error and computational time. This work compares our proposed method against the Taylor expansion and the exp() function in a standard C library, and shows that the computational time of the em algorithm is reduced while maintaining comparable precision in the estimation results.
In this paper, we study the techniques of blast wave field reconstruction based on Tomography. Overpressure field is reconstructed by inverting the velocity field in the process of shock wave transmission. Since the r...
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ISBN:
(纸本)9781479948604
In this paper, we study the techniques of blast wave field reconstruction based on Tomography. Overpressure field is reconstructed by inverting the velocity field in the process of shock wave transmission. Since the reconstruction process is difficult due to the insufficient number of excitation sources and detectors, we propose an em algorithm based on prior information. Appropriate models are constructed using the proposed methods, and a simulation example is put forward at last. The result reveals that compared with the traditional methods, this method has higher precision and converges faster. It also shows the validity and practicality of the developed algorithm in solving the problem of incomplete data reconstruction.
The em algorithm of Dempster, Laird and Rubin [1977. Maximum likelihood from incomplete data via the em algorithm. J. Roy. Statist. Soc. Ser. B 39, 1-22] is a very general and popular iterative computational algorithm...
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The em algorithm of Dempster, Laird and Rubin [1977. Maximum likelihood from incomplete data via the em algorithm. J. Roy. Statist. Soc. Ser. B 39, 1-22] is a very general and popular iterative computational algorithm that is used to find maximum likelihood estimates from incomplete data and is widely used to perform statistical analysis with missing data, because of its stability, flexibility and simplicity. However, a common criticism is that the convergence of the em algorithm is slow. Various algorithms to accelerate the convergence of the em algorithm have been proposed. In this paper, we propose the "epsilon-accelerated em algorithm" that speeds up the convergence of the em sequence via the vector epsilon algorithm of Wynn [1962. Acceleration techniques for iterated vector and matrix problems. Math. Comp. 16, 304-322]. We also demonstrate its theoretical properties. The epsilon-accelerated em algorithm has been successfully extended to the em algorithm without affecting its stability, flexibility and simplicity. Numerical experiments illustrate the potential of the epsilon-accelerated em algorithm. (c) 2006 Elsevier B.V. All rights reserved.
This paper proposes an improved computation method of maximum likelihood (ML) estimation for phase-type (PH) distributions with a number of phases. We focus on the em (expectation-maximization) algorithm proposed by A...
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This paper proposes an improved computation method of maximum likelihood (ML) estimation for phase-type (PH) distributions with a number of phases. We focus on the em (expectation-maximization) algorithm proposed by Asmussen et al. [27] and refine it in terms of time complexity. Two ideas behind our method are a uniformization-based procedure for computing a convolution integral of the matrix exponential and an improvement of the forward-backward algorithm using time intervals. Compared with the differential-equation-based em algorithm discussed in Asmussen et al. [27], our approach succeeds in the reduction of computation time for the PH fitting with a moderate to large number of phases. In addition to the improvement of time complexity, this paper discusses how to estimate the canonical form by applying the em algorithm. In numerical experiments, we examine computation times of the proposed and differential-equation-based em algorithms. Furthermore, the proposed em algorithm is also compared with the existing PH fitting methods in terms of computation time and fitting accuracy. (C) 2011 Elsevier B.V. All rights reserved.
Joint modeling of survival and longitudinal data has been studied extensively in the recent literature. The likelihood approach is one of the most popular estimation methods employed within the joint modeling framewor...
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Joint modeling of survival and longitudinal data has been studied extensively in the recent literature. The likelihood approach is one of the most popular estimation methods employed within the joint modeling framework. Typically, the parameters are estimated using maximum likelihood, with computation performed by the expectation maximization (em) algorithm. However, one drawback of this approach is that standard error (SE) estimates are not automatically produced when using the em algorithm. Many different procedures have been proposed to obtain the asymptotic covariance matrix for the parameters when the number of parameters is typically small. In the joint modeling context, however, there may be an infinite-dimensional parameter, the baseline hazard function, which greatly complicates the problem, so that the existing methods cannot be readily applied. The profile likelihood and the bootstrap methods overcome the difficulty to some extent;however, they can be computationally intensive. In this paper, we propose two new methods for SE estimation using the em algorithm that allow for more efficient computation of the SE of a subset of parametric components in a semiparametric or high-dimensional parametric model. The precision and computation time are evaluated through a thorough simulation study. We conclude with an application of our SE estimation method to analyze an HIV clinical trial dataset.
QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect ...
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QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect associations between phenotype and genotype measured on the progeny. When family sizes are limiting experimenters may wish to incorporate as much information as possible into a single analysis. However, combining information across sires is problematic because of incomplete linkage disequilibrium between the markers and the QTL in the population. This study describes formulae for obtaining MLEs via the expectation maximization (em) algorithm for use in a multiple-trait, multiple-family analysis. A model specifying a QTL with only two alleles, and a common within sire error variance is assumed. Compared to single-family analyses, power can be improved up to fourfold with multi-family analyses. The accuracy and precision of QTL location estimates are also substantially improved. With small family sizes, the multi-family, multi-trait analyses reduce substantially, but not totally remove, biases in QTL effect estimates. In situations where multiple QTL alleles are segregating the multi-family analysis will average out the effects of the different QTL alleles.
The expectation-maximization (em) algorithm is applied to a mixture of central and non-central eta(2) distributions. The derivation is based on the writing of this mixture as an infinite mixture of exponential distrib...
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The expectation-maximization (em) algorithm is applied to a mixture of central and non-central eta(2) distributions. The derivation is based on the writing of this mixture as an infinite mixture of exponential distributions for which the em algorithm takes a simple form. (C) 2004 Elsevier B.V. All rights reserved.
The Expectation-Maximization (em) algorithm is widely used also in industry for parameter estimation within a Maximum Likelihood (ML) framework in case of missing data. It is well-known that em shows good convergence ...
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The Expectation-Maximization (em) algorithm is widely used also in industry for parameter estimation within a Maximum Likelihood (ML) framework in case of missing data. It is well-known that em shows good convergence in several cases of practical interest. To the best of our knowledge, results showing under which conditions em converges fast are only available for specific cases. In this paper, we analyze the connection of the em algorithm to other ascent methods as well as the convergence rates of the em algorithm in general including also nonlinear models and apply this to the PMHT model. We compare the em with other known iterative schemes such as gradient and Newton-type methods. It is shown that em reaches Newton-convergence in case of well-separated objects and a Newton-em combination turns out to be robust and efficient even in cases of closely-spaced targets.
This paper is devoted to a novel hyperparameters estimator for bayesian denoising of images using the Bessel K Forms prior which we recently developed.(1, 2) More precisely, this approach is based on the em algorithm....
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ISBN:
(纸本)9780819484079
This paper is devoted to a novel hyperparameters estimator for bayesian denoising of images using the Bessel K Forms prior which we recently developed.(1, 2) More precisely, this approach is based on the em algorithm. The simulation results show that this estimator offers good performances and is slightly better compared to the cumulant-based estimator suggested in.(1, 2) A comparative study is carried to show the effectiveness of our bayesian denoiser based on em algorithm compared to other denoisers developed in both classical and bayesian contexts. Our study has been effected on natural and medical images for gaussian and poisson noise removal.
Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets an...
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Although many clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called block mixture model which takes into account this situation. This model allows one to embed simultaneous clustering of objects and variables in a mixture approach. We have studied this probabilistic model under the classification likelihood approach and developed a new algorithm for simultaneous partitioning based on the Classification em algorithm. In this paper, we consider the block clustering problem under the maximum likelihood approach and the goal of our contribution is to estimate the parameters of this model. Unfortunately, the application of the em algorithm for the block mixture model cannot be made directly;difficulties arise due to the dependence structure in the model and approximations are required. Using a variational approximation, we propose a generalized em algorithm to estimate the parameters of the block mixture model and, to illustrate our approach, we study the case of binary data by using a Bernoulli block mixture.
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