Paper Info
Title
The EM algorithm with gradient function update for discrete mixtures with known (fixed) number of components
Abstract
The paper is focussing on some recent developments in nonparametric mixture distributions. It discusses nonparametric maximum likelihood estimation of the mixing distribution and will emphasize gradient type results, especially in terms of global results and global convergence of algorithms such as vertex direction or vertex exchange method. However, the NPMLE (or the algorithms constructing it) provides also an estimate of the number of components of the mixing distribution which might be not desirable for theoretical reasons or might be not allowed from the physical interpretation of the mixture model. When the number of components is fixed in advance, the before mentioned algorithms can not be used and globally convergent algorithms do not exist up to now. Instead, the EM algorithm is often used to find maximum likelihood estimates. However, in this case multiple maxima are often occuring. An example from a meta-analyis of vitamin A and childhood mortality is used to illustrate the considerable, inferential importance of identifying the correct global likelihood. To improve the behavior of the EM algorithm we suggest a combination of gradient function steps and EM steps to achieve global convergence leading to the EM algorithm with gradient function update (EMGFU). This algorithms retains the number of components to be exactly k and typically converges to the global maximum. The behavior of the algorithm is highlighted at hand of several examples.
Year
DOI
Venue
2003
10.1023/A:1024222817645
Statistics and Computing
Keywords
Field
DocType
mixture models,globally convergent algorithms,multiple maxima
Convergence (routing),Mathematical optimization,Vertex (geometry),Expectation–maximization algorithm,Maximum likelihood,Nonparametric statistics,Nonparametric maximum likelihood,Statistics,Maxima,Mixture model,Mathematics
Journal
Volume
Issue
ISSN
13
3
1573-1375
Citations 
PageRank 
References 
5
1.54
0
Authors
1
Name
Order
Citations
PageRank
Dankmar Böhning15013.62