38,748 research outputs found
Regularized Maximum Likelihood Estimation and Feature Selection in Mixtures-of-Experts Models
Mixture of Experts (MoE) are successful models for modeling heterogeneous
data in many statistical learning problems including regression, clustering and
classification. Generally fitted by maximum likelihood estimation via the
well-known EM algorithm, their application to high-dimensional problems is
still therefore challenging. We consider the problem of fitting and feature
selection in MoE models, and propose a regularized maximum likelihood
estimation approach that encourages sparse solutions for heterogeneous
regression data models with potentially high-dimensional predictors. Unlike
state-of-the art regularized MLE for MoE, the proposed modelings do not require
an approximate of the penalty function. We develop two hybrid EM algorithms: an
Expectation-Majorization-Maximization (EM/MM) algorithm, and an EM algorithm
with coordinate ascent algorithm. The proposed algorithms allow to
automatically obtaining sparse solutions without thresholding, and avoid matrix
inversion by allowing univariate parameter updates. An experimental study shows
the good performance of the algorithms in terms of recovering the actual sparse
solutions, parameter estimation, and clustering of heterogeneous regression
data
EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis
Data clustering has received a lot of attention and numerous methods,
algorithms and software packages are available. Among these techniques,
parametric finite-mixture models play a central role due to their interesting
mathematical properties and to the existence of maximum-likelihood estimators
based on expectation-maximization (EM). In this paper we propose a new mixture
model that associates a weight with each observed point. We introduce the
weighted-data Gaussian mixture and we derive two EM algorithms. The first one
considers a fixed weight for each observation. The second one treats each
weight as a random variable following a gamma distribution. We propose a model
selection method based on a minimum message length criterion, provide a weight
initialization strategy, and validate the proposed algorithms by comparing them
with several state of the art parametric and non-parametric clustering
techniques. We also demonstrate the effectiveness and robustness of the
proposed clustering technique in the presence of heterogeneous data, namely
audio-visual scene analysis.Comment: 14 pages, 4 figures, 4 table
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