The EM Algorithm: A Guided Tour

Couvreur, Christophe

doi:10.1007/978-1-4612-1996-5_12

Cited by 36 publications

(47 citation statements)

References 24 publications

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“…First, an EM estimator is unbiased and efficient when the missing mechanism is ignorable (ignorability is discussed under the section Missing Data Mechanisms , Graham 2003 ). Second, the EM algorithm is simple, easy to implement ( Dempster et al 1977 ) and stable ( Couvreur 1996 ). Third, it is straightforward in EM to compare different models using the likelihood ratio test, because EM is based on the likelihood function.…”

Section: Expectation-maximization (Em) Algorithmmentioning

confidence: 99%

Principled missing data methods for researchers

2013

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The impact of missing data on quantitative research can be serious, leading to biased estimates of parameters, loss of information, decreased statistical power, increased standard errors, and weakened generalizability of findings. In this paper, we discussed and demonstrated three principled missing data methods: multiple imputation, full information maximum likelihood, and expectation-maximization algorithm, applied to a real-world data set. Results were contrasted with those obtained from the complete data set and from the listwise deletion method. The relative merits of each method are noted, along with common features they share. The paper concludes with an emphasis on the importance of statistical assumptions, and recommendations for researchers. Quality of research will be enhanced if (a) researchers explicitly acknowledge missing data problems and the conditions under which they occurred, (b) principled methods are employed to handle missing data, and (c) the appropriate treatment of missing data is incorporated into review standards of manuscripts submitted for publication.

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Section: Expectation-maximization (Em) Algorithmmentioning

confidence: 99%

Principled missing data methods for researchers

2013

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“…The main advantages of the EM algorithm are its simplicity and ease of implementation. Moreover, the EM algorithm is proven to be stable and robust . In this study, the integral of the nonlinear inverse problem is avoided through an iterative procedure.…”

Section: Bayesian Inference Using Em Algorithmmentioning

confidence: 99%

Sparse Bayesian learning for structural damage detection using expectation–maximization technique

Hou

Xia

Zhou

et al. 2019

Struct Control Health Monit

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Summary Sparse Bayesian learning (SBL) methods have been developed and applied in the context of regression and classification, in which latent variables and hyperparameters are iteratively obtained using type‐II maximization likelihood. However, this method is ineffective in structural damage detection using modal parameters, which have a nonlinear relation with structural damage. Consequently, the analytical solution of the type‐II maximization likelihood is unavailable. In this study, an iterative expectation–maximization (EM) technique is employed to tackle the difficulty. During the iteration, structural damage and hyperparameters are updated through an expectation and maximization processes alternatively. Two sampling methods are utilized during the expectation procedure. Upon convergence, some hyperparameters approach infinity and the associated damage variables become zero, resulting in the sparsity of damage. Numerical and experimental examples demonstrate that the proposed SBL method can accurately locate and quantify the sparse damage. The proposed EM technique is easy to implement while also containing clear physical meaning.

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“…We construct in this section an auxiliary criterion, depending explicitly on the matching matrix, and we use an alternated optimisation scheme. This construction follows EM principles [3,10] and the auxiliary variables framework of [4].…”

Section: From the Maximum Likelihood To The Em Criterionmentioning

confidence: 99%

Rigid Point-Surface Registration Using an EM Variant of ICP for Computer Guided Oral Implantology

Granger

Pennec

Roche

2001

Lecture Notes in Computer Science

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Abstract. We investigate the rigid registration of a set of points onto a surface for computer-guided oral implants surgery. We first formulate the Iterative Closest Point (ICP) algorithm as a Maximum Likelihood (ML) estimation of the transformation and the matches. Then, considering matches as a hidden random variable, we show that the ML estimation of the transformation alone leads to a criterion efficiently solved using an Expectation-Maximisation (EM) algorithm. The experimental section provides evidences that this new algorithm is more robust and accurate than ICP and reaches a global accuracy of 0.2 mm with computation times compatible with a peroperative system.

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The EM Algorithm: A Guided Tour

Cited by 36 publications

References 24 publications

Principled missing data methods for researchers

Principled missing data methods for researchers

Sparse Bayesian learning for structural damage detection using expectation–maximization technique

Rigid Point-Surface Registration Using an EM Variant of ICP for Computer Guided Oral Implantology

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