A stochastic EM algorithm for a semiparametric mixture model

Abstract

To cite this version:Abstract. Recently several authors considered finite mixture models with semi-/nonparametric component distributions. Identifiability of such model parameters is generally not obvious, and when it occurs, inference methods are rather specific to the mixture model under consideration. In this paper we propose a generalization of the EM algorithm to semiparametric mixture models. Our approach is methodological and can be applied to a wide class of semiparametric mixture models. The behavior of the EM type estimators we propose is studied numerically through several Monte Carlo experiments but also by comparison with alternative methods existing in the literature. In addition to these numerical experiments we provide applications to real data showing that our estimation methods behaves well, that it is fast and easy to be implemented.

An EM-Like Algorithm for Semi- and Nonparametric Estimation in Multivariate Mixtures

“…Here, we take a different approach and adapt an algorithm of Bordes et al (2007), which is presented by those authors as a stochastic algorithm for the particular univariate case of model (1) under the assumption that φ j (x) = f (x − µ j ) for some symmetric density f (x). We demonstrate how to extend the algorithm to model (4) and eliminate the stochasticity.…”

Model based labeling for mixture models

“…For the semi-parametric model, similar to Bordes, Chauveau, and Vandekerkhove (2007) and Benaglia, Chauveau, and Hunter (2009), the convergence property of the Algorithm 2 has not been established and needs further research, although empirically, the Algorithm 2 worked quite well and did converge for all the data sets we tried. One might also use one-step of Algorithm 2 to speed up the MBLSP method if one starts the Algorithm 2 from some good labels (such as NORMLH labels (Yao and Lindsay 2009)).…”

“…We will call such mixture model a semi-parametric mixture model due to the symmetric restriction (equal mixing proportions and permutation symmetric component density functions). By extending the semi-parametric EM algorithm proposed by Bordes, Chauveau, and Vandekerkhove (2007) and Benaglia, Chauveau, and Hunter (2009), we propose the following EM-like algorithm to fit the model (2).…”

Application of Polynomial Spline Independent Component Analysis to fMRI Data

“…From the observations that are separated by the k-means method, those having a larger mean are used to initialize f 1 . It is possible that the stochastic EM algorithm may not converge but be stable (Bordes et al, 2007;Celeux & Diebolt, 1992). Therefore, we use a large number of iterations so as to stabilize the estimate of f .…”

“…A version of this algorithm called a stochastic EM algorithm was introduced in (Celeux & Diebolt, 1992) to avoid stabilization on saddle points in parametric mixture models by incorporating the stochastic step (S-step) into the EM algorithm. (Bordes et al, 2007) generalized it to semiparametric mixture models by using kernel density estimation.…”