EM algorithms for multivariate Gaussian mixture models with truncated and censored data

Lee, Gyemin; Scott, Clayton

doi:10.1016/j.csda.2012.03.003

Cited by 122 publications

(80 citation statements)

References 20 publications

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“…Citing Lee and Scott (2012), data are said to be censored when the exact values of measurements are not reported. For example, the needle of a scale that does not provide a reading over 200 kg will show 200 kg for all the objects that weigh more than the limit.…”

Section: The Modelmentioning

confidence: 99%

Linear censored regression models with scale mixtures of normal distributions

et al. 2015

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In the framework of censored regression models the random errors are routinely assumed to have a normal distribution, mainly for mathematical convenience. However, this method has been criticized in the literature because of its sensitivity to deviations from the normality assumption. Here, we first establish a new link between the censored regression model and a recently studied class of symmetric distributions, which extend the normal one by the inclusion of kurtosis, called scale mixtures of normal (SMN) distributions. The Student-t, Pearson type VII, slash, contaminated normal, among others distributions, are contained in this class. A member of this class can be a good alternative to model this kind of data, because they have been shown its flexibility in several applications. In this work, we develop an analytically simple and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closedform expressions at the E-step, that rely on formulas for the mean and variance of certain truncated SMN distributions. The proposed algorithm is implemented in the R package SMNCensReg. Applications with simulated and a real data set are reported, illustrating the usefulness of the new methodology.

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Section: The Modelmentioning

confidence: 99%

Linear censored regression models with scale mixtures of normal distributions

et al. 2015

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“…Lee et al [18] developed for fitting multivariate Gaussian mixture models to data that is truncated. By applying these algorithms to the data, parameters π k , µ k and Σ k of the multivariate Gaussian mixture model can be calculated.…”

Section: B Algorithmsmentioning

confidence: 99%

Evaluation of automated vehicles encountering pedestrians at unsignalized crossings

Chen

Zhao

Peng

2017

2017 IEEE Intelligent Vehicles Symposium (IV)

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Abstract-Interactions between vehicles and pedestrians have always been a major problem in traffic safety. Experienced human drivers are able to analyze the environment and choose driving strategies that will help them avoid crashes. What is not yet clear, however, is how automated vehicles will interact with pedestrians. This paper proposes a new method for evaluating the safety and feasibility of the driving strategy of automated vehicles when encountering unsignalized crossings. MobilEye ® sensors installed on buses in Ann Arbor, Michigan, collected data on 2,973 valid crossing events. A stochastic interaction model was then created using a multivariate Gaussian mixture model. This model allowed us to simulate the movements of pedestrians reacting to an oncoming vehicle when approaching unsignalized crossings, and to evaluate the passing strategies of automated vehicles. A simulation was then conducted to demonstrate the evaluation procedure.

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“…However, the absence of a global maximizer of the likelihood is not an obstacle to apply the EM algorithm in the finite mixtures context, as we can see in the works of Celeux et al (1996), Peel andMcLachlan (2000), Fraley and Raftery (2002), Wang et al (2004), Lin et al (2007), Lin and Lin (2010), Lee and Scott (2012), Lo and Gottardo (2012), Wei (2012), and Lee and McLachlan (2014), to name a few. In general, the unboundedness problem is solved by imposing some restriction on the parameter space or by using a maximum penalized likelihood estimator, see Hathaway (1985Hathaway ( , 1986 and Chen et al (2008), for example.…”

Section: Discussionmentioning

confidence: 93%

Robust mixture regression modeling based on scale mixtures of skew-normal distributions

Zeller

Cabral

Lachos

2015

TEST

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The traditional estimation of mixture regression models is based on the assumption of normality (symmetry) of component errors and thus is sensitive to outliers, heavy-tailed errors and/or asymmetric errors. In this work we present a proposal to deal with these issues simultaneously in the context of the mixture regression by extending the classic normal model by assuming that the random errors follow a scale mixtures of skew-normal distributions. This approach allows us to model data with great flexibility, accommodating skewness and heavy tails. The main virtue of considering the mixture regression models under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows easy implementation of inference. We develop a simple EM-type algorithm to perform maximum likelihood inference of the parameters of the proposed model. In order to examine the robust aspect of this flexible model against outlying observations, some Electronic supplementary material The online version of this article (

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EM algorithms for multivariate Gaussian mixture models with truncated and censored data

Cited by 122 publications

References 20 publications

Linear censored regression models with scale mixtures of normal distributions

Linear censored regression models with scale mixtures of normal distributions

Evaluation of automated vehicles encountering pedestrians at unsignalized crossings

Robust mixture regression modeling based on scale mixtures of skew-normal distributions

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