81,758 research outputs found
Robust mixtures of regression models
Doctor of PhilosophyDepartment of StatisticsKun Chen and Weixin YaoThis proposal contains two projects that are related to robust mixture models. In the robust project,
we propose a new robust mixture of regression models (Bai et al., 2012). The existing methods for tting
mixture regression models assume a normal distribution for error and then estimate the regression param-
eters by the maximum likelihood estimate (MLE). In this project, we demonstrate that the MLE, like the
least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust
estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte
Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works
much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the
proposed robust method works comparably to the MLE when there are no outliers and the error is normal.
In the second project, we propose a new robust mixture of linear mixed-effects models. The traditional
mixture model with multiple linear mixed effects, assuming Gaussian distribution for random and error
parts, is sensitive to outliers. We will propose a mixture of multiple linear mixed t-distributions to robustify
the estimation procedure. An EM algorithm is provided to and the MLE under the assumption of t-
distributions for error terms and random mixed effects. Furthermore, we propose to adaptively choose the
degrees of freedom for the t-distribution using profile likelihood. In the simulation study, we demonstrate
that our proposed model works comparably to the traditional estimation method when there are no outliers
and the errors and random mixed effects are normally distributed, but works much better if there are outliers
or the distributions of the errors and random mixed effects have heavy tails
Robust mixture modeling
Doctor of PhilosophyDepartment of StatisticsWeixin Yao and Kun ChenOrdinary least-squares (OLS) estimators for a linear model are very sensitive to unusual
values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. In this proposal, we first review and describe some available and popular robust techniques, including some recent developed ones, and compare them in terms of breakdown point and efficiency. In addition, we also use a simulation study and a real data application to compare the performance of existing robust methods under different scenarios. Finite mixture models are widely applied in a variety of random phenomena. However, inference of mixture models is a challenging work when the outliers exist in the data. The traditional maximum likelihood estimator (MLE) is sensitive to outliers. In this proposal, we propose a Robust Mixture via Mean shift penalization (RMM) in mixture models and Robust Mixture Regression via Mean shift penalization (RMRM) in mixture regression, to achieve simultaneous outlier detection and parameter estimation. A mean shift parameter is added to the mixture models, and penalized by a nonconvex penalty function. With this model setting, we develop an iterative thresholding embedded EM algorithm to maximize the penalized objective function. Comparing with other existing robust methods, the proposed methods show outstanding performance in both identifying outliers and estimating the parameters
Modelling Background Noise in Finite Mixtures of Generalized Linear Regression Models
In this paper we show how only a few outliers can completely break down EM-estimation of mixtures of regression models. A simple, yet very effective way of dealing with this problem, is to use a component where all regression parameters are fixed to zero to model the background noise. This noise component can be easily defined for different types of generalized linear models, has a familiar interpretation as the empty regression model, and is not very sensitive with respect to its own parameters
Robust EM algorithm for model-based curve clustering
Model-based clustering approaches concern the paradigm of exploratory data
analysis relying on the finite mixture model to automatically find a latent
structure governing observed data. They are one of the most popular and
successful approaches in cluster analysis. The mixture density estimation is
generally performed by maximizing the observed-data log-likelihood by using the
expectation-maximization (EM) algorithm. However, it is well-known that the EM
algorithm initialization is crucial. In addition, the standard EM algorithm
requires the number of clusters to be known a priori. Some solutions have been
provided in [31, 12] for model-based clustering with Gaussian mixture models
for multivariate data. In this paper we focus on model-based curve clustering
approaches, when the data are curves rather than vectorial data, based on
regression mixtures. We propose a new robust EM algorithm for clustering
curves. We extend the model-based clustering approach presented in [31] for
Gaussian mixture models, to the case of curve clustering by regression
mixtures, including polynomial regression mixtures as well as spline or
B-spline regressions mixtures. Our approach both handles the problem of
initialization and the one of choosing the optimal number of clusters as the EM
learning proceeds, rather than in a two-fold scheme. This is achieved by
optimizing a penalized log-likelihood criterion. A simulation study confirms
the potential benefit of the proposed algorithm in terms of robustness
regarding initialization and funding the actual number of clusters.Comment: In Proceedings of the 2013 International Joint Conference on Neural
Networks (IJCNN), 2013, Dallas, TX, US
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