This article tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (em) algorithm for Gaussian mixture models, has shown interestin...
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This article tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (em) algorithm for Gaussian mixture models, has shown interesting properties when compared to other popular approaches such as those based on k-nearest neighbors or on multiple imputations by chained equations. However, Gaussian mixture models are known to be non-robust to heterogeneous data, which can lead to poor estimation performance when the data is contaminated by outliers or have non-Gaussian distributions. To overcome this issue, a new em algorithm is investigated for mixtures of elliptical distributions with the property of handling potential missing data. This paper shows that this problem reduces to the estimation of a mixture of angular Gaussian distributions under generic assumptions (i.e., each sample is drawn from a mixture of elliptical distributions, which is possibly different for one sample to another). In that case, the complete-data likelihood associated with mixtures of elliptical distributions is well adapted to the em framework with missing data thanks to its conditional distribution, which is shown to be a multivariate t-distribution. Experimental results on synthetic data demonstrate that the proposed algorithm is robust to outliers and can be used with non-Gaussian data. Furthermore, experiments conducted on real-world datasets show that this algorithm is very competitive when compared to other classical imputation methods.
Among recent methods designed for accelerating the em algorithm without any modification in the structure of em or in the statistical model, the parabolic acceleration (P-em) has proved its efficiency. It does not inv...
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Among recent methods designed for accelerating the em algorithm without any modification in the structure of em or in the statistical model, the parabolic acceleration (P-em) has proved its efficiency. It does not involve any computation of gradient or hessian matrix and can be used as an additional software component of any fixed point algorithm maximizing some objective function. The vector epsilon algorithm was introduced to reach the same goals. Through geometric considerations, the relationships between the outputs of an improved version of P-em and those of the vector epsilon algorithm are established. This sheds some light on their different behaviours and explains why the parabolic acceleration of em outperforms its competitor in most numerical experiments. A detailed analysis of its trajectories in a variety of real or simulated data shows the ability of P-em to choose the most efficient paths to the global maximum of the likelihood. (C) 2012 Elsevier B.V. All rights reserved.
This paper describes how relational graph matching can be effected using the expectation and maximisation algorithm. According to this viewpoint, matching is realised as a two-step iterative em-like process. Firstly, ...
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This paper describes how relational graph matching can be effected using the expectation and maximisation algorithm. According to this viewpoint, matching is realised as a two-step iterative em-like process. Firstly, updated symbolic matches are located so as to minimise the divergence between the model and data graphs. Secondly, with the updated matches to hand probabilities describing the affinity between nodes in the model and data graphs may be computed. The probability distributions underpinning this study are computed using a simple model of uniform matching errors. As a result, the expected likelihood function is defined over a family of exponential distributions of Hamming distance. We evaluate our matching method and offer comparison with both mean-field annealing and quadratic assignment. (C) 1998 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.
A stochastic representation with a latent variable often enables us to make an em algorithm to obtain the maximum likelihood estimate. The skew-normal distribution has such a simple stochastic representation with a la...
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A stochastic representation with a latent variable often enables us to make an em algorithm to obtain the maximum likelihood estimate. The skew-normal distribution has such a simple stochastic representation with a latent variable, and consequently one expects to have a convenient em algorithm. However, even for the univariate skew-normal distribution, existing em algorithms constructed using a stochastic representation require a solution of a complicated estimating equation for the skewness parameter, making it difficult to extend such an idea to the multivariate skew-normal distribution. A stochastic representation with overparameterization is proposed, which has not been discussed yet. The approach allows the construction of an efficient em algorithm in a closed form, which can be extended to a mixture of multivariate skew-normal distributions. The proposed em algorithm can be regarded as an accelerated version with momentum (which is known as an acceleration technique of the algorithm in optimization) of a recently proposed em algorithm. The novel em algorithm is applied to real data and compared with the command msn. mle from the R package sn. (C) 2021 EcoSta Econometrics and Statistics. Published by Elsevier B.V. All rights reserved.
The aim of this study is to find the maximum likelihood estimate (MLE) among frequency count data by using the expectation-maximization (em) algorithm in which is useful to impute the missing or hidden values. Two for...
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The aim of this study is to find the maximum likelihood estimate (MLE) among frequency count data by using the expectation-maximization (em) algorithm in which is useful to impute the missing or hidden values. Two forms of missing count data in both zero truncation and right censoring situations are illustrated for estimating the population size on drug use. The results show that a truncated and censored Poisson likelihood performs well with good estimates corresponding to the em algorithm with a numerically stable convergence, a monotone increasing likelihood, and providing local maxima, so the expected global maximum of the MLE depends on the initial value. (C) 2016 The Authors. Published by Elsevier B.V.
Context: Although independent imputation techniques are comprehensively studied in software effort prediction, there are few studies on embedded methods in dealing with missing data in software effort prediction. Obje...
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Context: Although independent imputation techniques are comprehensively studied in software effort prediction, there are few studies on embedded methods in dealing with missing data in software effort prediction. Objective: We propose BRem (Bayesian Regression and Expectation Maximization) algorithm for software effort prediction and two embedded strategies to handle missing data. Method: The MDT (Missing Data Toleration) strategy ignores the missing data when using BRem for software effort prediction and the MDI (Missing Data Imputation) strategy uses observed data to impute missing data in an iterative manner while elaborating the predictive model. Results: Experiments on the ISBSG and CSBSG datasets demonstrate that when there are no missing values in historical dataset, BRem outperforms LR (Linear Regression), BR (Bayesian Regression), SVR (Support Vector Regression) and M5' regression tree in software effort prediction on the condition that the test set is not greater than 30% of the whole historical dataset for ISBSG dataset and 25% of the whole historical dataset for CSBSG dataset. When there are missing values in historical datasets, BRem with the MDT and MDI strategies significantly outperforms those independent imputation techniques, including MI, BMI, CMI, MINI and M5'. Moreover, the MDI strategy provides BRem with more accurate imputation for the missing values than those given by the independent missing imputation techniques on the condition that the level of missing data in training set is not larger than 10% for both ISBSG and CSBSG datasets. Conclusion: The experimental results suggest that BRem is promising in software effort prediction. When there are missing values, the MDI strategy is preferred to be embedded with BRem. (C) 2014 Elsevier B.V. All rights reserved.
It is well-known that the em algorithm generally converges to a local maximum likelihood estimate. However, there have been many evidences to show that the em algorithm can converge correctly to the true parameters as...
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It is well-known that the em algorithm generally converges to a local maximum likelihood estimate. However, there have been many evidences to show that the em algorithm can converge correctly to the true parameters as long as the overlap of Gaussians in the sample data is small enough. This paper studies this correct convergence problem asymptotically on the em algorithm for Gaussian mixtures. It has been proved that the em algorithm becomes a contraction mapping of the parameters within a neighborhood of the consistent solution of the maximum likelihood when the measure of average overlap among Gaussians in the original mixture is small enough and the number of samples is large enough. That is, if the initial parameters are set within the neighborhood, the em algorithm will always converge to the consistent solution, i.e., the expected result. Moreover, the simulation results further demonstrate that this correct convergence neighborhood becomes larger as the average overlap becomes smaller. (c) 2005 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
We consider the problem of estimation of the parameters of the Marshall-Olkin Bivariate Weibull distribution in the presence of random censoring. Since the maximum likelihood estimators of the parameters cannot be exp...
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We consider the problem of estimation of the parameters of the Marshall-Olkin Bivariate Weibull distribution in the presence of random censoring. Since the maximum likelihood estimators of the parameters cannot be expressed in a closed form, we suggest an em algorithm to compute the same. Extensive simulations are carried out to conclude that the estimators perform efficiently under random censoring. (C) 2010 Elsevier B.V. All rights reserved.
This paper addresses the problems of parameter estimation of multivariable stationary stochastic systems on the basis of observed output *** main contribution is to employ the expectation-maximisation(em)method as a m...
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This paper addresses the problems of parameter estimation of multivariable stationary stochastic systems on the basis of observed output *** main contribution is to employ the expectation-maximisation(em)method as a means for computation of the maximum-likelihood(ML)parameter estimation of the *** form of the expectation of the studied system subjected to Gaussian distribution noise is derived and parameter choice that maximizes the expectation is also *** results in an iterative algorithm for parameter estimation and the robust algorithm implementation based on technique of QR-factorization and Cholesky factorization is also ***,algorithmic properties such as non-decreasing likelihood value,necessary and sufficient conditions for the algorithm to arrive at a local stationary parameter,the convergence rate and the factors affecting the convergence rate are *** study shows that the proposed algorithm has attractive properties such as numerical stability,and avoidance of difficult initial conditions.
Mixture models implemented via the expectation-maximization (em) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the em algorithm requires ...
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Mixture models implemented via the expectation-maximization (em) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the em algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the em algorithm could improve its rate of convergence. In this paper, we show how this modified em algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the em algorithm for segmenting MR images of the human brain. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
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