Maximum likelihood estimation via the ECM algorithm: A general framework

Meng, Xiao Li; Rubin, Donald B.

doi:10.1093/biomet/80.2.267

Cited by 1,513 publications

(839 citation statements)

References 18 publications

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“…If the EM algorithm is used to produce the estimates, then the SEM algorithm can be used for variance estimation. For some contingency table models, the ECM algorithm may be used for estimation (Meng and Rubin, 1993) and variance calculation (Van Dyk et al, 1995). A score test for independence in two-way incomplete contingency tables was proposed by Lipsitz and Fitzmaurice (1996).…”

Section: Literature Review and Existing Methodsmentioning

confidence: 99%

Large tests of independence in incomplete two-way contingency tables using fractional imputation

Kang¹,

Larsen²

2015

Journal of the Korean Data and Information Science Society

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Imputation procedures fill-in missing values, thereby enabling complete data analyses. Fully efficient fractional imputation (FEFI) and multiple imputation (MI) create multiple versions of the missing observations, thereby reflecting uncertainty about their true values. Methods have been described for hypothesis testing with multiple imputation. Fractional imputation assigns weights to the observed data to compensate for missing values. The focus of this article is the development of tests of independence using FEFI for partially classified two-way contingency tables. Wald and deviance tests of independence under FEFI are proposed. Simulations are used to compare type I error rates and Power. The partially observed marginal information is useful for estimating the joint distribution of cell probabilities, but it is not useful for testing association. FEFI compares favorably to other methods in simulations.

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Section: Literature Review and Existing Methodsmentioning

confidence: 99%

Large tests of independence in incomplete two-way contingency tables using fractional imputation

Kang¹,

Larsen²

2015

Journal of the Korean Data and Information Science Society

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“…To perform this maximization, we first use the EM algorithm and then describe an extension based on the ECM algorithm (Meng and Rubin, 1993) as in Liu and Rubin (1995) for a single t distribution, and as in Mclachlan and Peel (1998) and Peel and Mclachlan (2000) for mixture of t-distributions.…”

Section: Maximum Likelihood Estimation Of the Tmoe Modelmentioning

confidence: 99%

“…For the general multivariate case using t mixtures, one can refer to for example the two key papers Mclachlan and Peel (1998); Peel and Mclachlan (2000). The inference in the previously described approaches is performed by maximum likelihood estimation via expectation-maximization (EM) or extensions (Dempster et al, 1977;McLachlan and Krishnan, 2008), in particular the expectation conditional maximization (ECM) algorithm (Meng and Rubin, 1993). For the Bayesian framework, Frühwirth-Schnatter and Pyne (2010) have considered the Bayesian inference for both the univariate and the multivariate skew-normal and skew-t mixtures.…”

Section: Introductionmentioning

confidence: 99%

Robust mixture of experts modeling using thetdistribution

Chamroukhi¹

2016

Neural Networks

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Mixture of Experts (MoE) is a popular framework for modeling heterogeneity in data for regression, classification, and clustering. For regression and cluster analyses of continuous data, MoE usually use normal experts following the Gaussian distribution. However, for a set of data containing a group or groups of observations with heavy tails or atypical observations, the use of normal experts is unsuitable and can unduly affect the fit of the MoE model. We introduce a robust MoE modeling using the t distribution. The proposed t MoE (TMoE) deals with these issues regarding heavy-tailed and noisy data. We develop a dedicated expectation-maximization (EM) algorithm to estimate the parameters of the proposed model by monotonically maximizing the observed data log-likelihood. We describe how the presented model can be used in prediction and in model-based clustering of regression data. The proposed model is validated on numerical experiments carried out on simulated data, which show the effectiveness and the robustness of the proposed model in terms of modeling non-linear regression functions as well as in model-based clustering. Then, it is applied to the real-world data of tone perception for musical data analysis, and the one of temperature anomalies for the analysis of climate change data. The obtained results show the usefulness of the TMoE model for practical applications.

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“…One solution to this problem could be expectation-conditional maximization (ECM) (Meng and Rubin, 1993;Meng, 1994), which replaces the M-step by a series of computationally simplified conditional maximization (CM) steps. The ECM is a class of generalized EM (GEM) algorithms in which the Q-function is increased rather than being maximized (Fessler and Hero, 1994).…”

Section: Estimation Algorithmmentioning

confidence: 99%

Spatiotemporal multi-resolution approximation of the Amari type neural field model

Aram

Freestone

Dewar³

et al. 2013

NeuroImage

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Neural fields are spatially continuous state variables described by integro-differential equations, which are well suited to describe the spatiotemporal evolution of cortical activations on multiple scales. Here we develop a multi-resolution approximation (MRA) framework for the integro-difference equation (IDE) neural field model based on semi-orthogonal cardinal B-spline wavelets. In this way, a flexible framework is created, whereby both macroscopic and microscopic behavior of the system can be represented simultaneously. State and parameter estimation is performed using the expectation maximization (EM) algorithm. A synthetic example is provided to demonstrate the framework.

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Maximum likelihood estimation via the ECM algorithm: A general framework

Cited by 1,513 publications

References 18 publications

Large tests of independence in incomplete two-way contingency tables using fractional imputation

Large tests of independence in incomplete two-way contingency tables using fractional imputation

Robust mixture of experts modeling using thetdistribution

Spatiotemporal multi-resolution approximation of the Amari type neural field model

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