Finite Mixture Models

McLachlan, Geoffrey J.; Peel, David

doi:10.1002/0471721182

Cited by 7,326 publications

(6,464 citation statements)

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“…In the one-component case there is no entropy by definition, and therefore the ICL coincides with the BIC. While there is no theoretical justification for this approach, simulations show a superior performance compared to other heuristic criteria, such as the N EC (Biernacki, Celeux, and Govaert, 2000), as well as compared to AIC and BIC (McLachlan and Peel, 2000).…”

Section: Descriptive Statisticsmentioning

confidence: 97%

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Risk and Rationality: Uncovering Heterogeneity in Probability Distortion

2009

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It has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types. We present a parsimonious characterization of risk taking behavior by estimating a finite mixture regression model for three different experimental data sets, two Swiss and one Chinese, over a large number of real gains and losses. We find two distinct types of individuals: In all three data sets, the choices of roughly 80% of the subjects exhibit significant deviations from linear probability weighting, consistent with prospect theory. 20% of the subjects weight probabilities near linearly and behave essentially as expected value maximizers. Moreover, individuals are cleanly assigned to one type with probabilities close to unity. The reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling.

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Section: Descriptive Statisticsmentioning

confidence: 97%

“…may encounter several problems, even if it is in principle feasible (for a general treatise see for example McLachlan and Peel (2000)). First, the highly nonlinear form of the log likelihood causes the optimization algorithm to be rather slow or even incapable of finding the maximum.…”

Section: A Estimation Of the Finite Mixture Regression Modelmentioning

confidence: 99%

Risk and Rationality: Uncovering Heterogeneity in Probability Distortion

2009

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“…The Gaussian mixture model has been extensively studied in the last decades and used in many situations (see [3] and [31] for a review). Therefore, if the Gaussian model is chosen, f k (x; θ k ) will denote the density of a multivariate Gaussian density parametrized by θ k = {µ k , Σ k } where µ k and Σ k are respectively the mean and covariance matrix of kth component of the mixture.…”

Section: Generative Supervised Classificationmentioning

confidence: 99%

“…In the case of the discovery phase of the inductive approach, the maximization of Q(X * ; Θ) according to the parameters µ k and Σ k can be done classically except that parameters µ k and Σ k have only to be estimated for k = C + 1, ..., K. We therefore refer to [31] for ML inference for µ k and Σ k in finite mixture models. The estimation of the mixture proportions π k can unfortunately not be done classically and must be done sequentially.…”

Section: A2 Inductive Approachmentioning

confidence: 99%

Adaptive Mixture Discriminant Analysis for Supervised Learning with Unobserved Classes

Bouveyron

2014

J Classif

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International audienceIn supervised learning, an important issue usually not taken into account by classical methods is the possibility of having in the test set individuals belonging to a class which has not been observed during the learning phase. Classical supervised algorithms will automatically label such observations as belonging to one of the known classes in the training set and will not be able to detect new classes. This work introduces a model-based discriminant analysis method, called adaptive mixture discriminant analysis (AMDA), which is able to detect several unobserved groups of points and to adapt the learned classifier to the new situation. Two EM-based procedures are proposed for parameter estimation and model selection criteria are used for selecting the actual number of classes. Experiments on artificial and real data demonstrate the ability of the proposed method to deal with complex and real word problems. The proposed approach is also applied to the detection of unobserved communities in social network analysis

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“…Identifiability for mixture distributions is defined slightly different in that distinct values of the parameters determine distinct members of the mixture family, allowing permutations of the component labels, i.e. the indicator variables; see, for example, McLachlan and Peel [15].…”

Section: General Formulae For Obtaining the Mlesmentioning

confidence: 99%

Use of the EM algorithm to detect QTL affecting multiple-traits in an across half-sib family analysis

2005

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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. QTL / EM algorithm / interval mapping / half-sib families

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Finite Mixture Models

Cited by 7,326 publications

References 0 publications

Risk and Rationality: Uncovering Heterogeneity in Probability Distortion

Risk and Rationality: Uncovering Heterogeneity in Probability Distortion

Adaptive Mixture Discriminant Analysis for Supervised Learning with Unobserved Classes

Use of the EM algorithm to detect QTL affecting multiple-traits in an across half-sib family analysis

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