19,691 research outputs found
The use of mixtures for dealing with non-normal regression errors
In many situations, the distribution of the error terms of a linear regression model departs significantly from normality. It is shown, through a simulation study, that an effective strategy
to deal with these situations is fitting a regression model based on the assumption that the error terms follow a mixture of normal distributions. The main advantage, with respect to the usual approach based on the least-squares method is a greater precision of the parameter estimates and confidence intervals. For the parameter estimation we make use of the EM algorithm, while confidence intervals are constructed through a bootstrap method
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
High-Dimensional Regression with Gaussian Mixtures and Partially-Latent Response Variables
In this work we address the problem of approximating high-dimensional data
with a low-dimensional representation. We make the following contributions. We
propose an inverse regression method which exchanges the roles of input and
response, such that the low-dimensional variable becomes the regressor, and
which is tractable. We introduce a mixture of locally-linear probabilistic
mapping model that starts with estimating the parameters of inverse regression,
and follows with inferring closed-form solutions for the forward parameters of
the high-dimensional regression problem of interest. Moreover, we introduce a
partially-latent paradigm, such that the vector-valued response variable is
composed of both observed and latent entries, thus being able to deal with data
contaminated by experimental artifacts that cannot be explained with noise
models. The proposed probabilistic formulation could be viewed as a
latent-variable augmentation of regression. We devise expectation-maximization
(EM) procedures based on a data augmentation strategy which facilitates the
maximum-likelihood search over the model parameters. We propose two
augmentation schemes and we describe in detail the associated EM inference
procedures that may well be viewed as generalizations of a number of EM
regression, dimension reduction, and factor analysis algorithms. The proposed
framework is validated with both synthetic and real data. We provide
experimental evidence that our method outperforms several existing regression
techniques
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