On 08-Apr-09 23:39:36, Ted Harding wrote: > On 08-Apr-09 22:10:26, Ravi Varadhan wrote: >> EM algorithm is a better approach for maximum likelihood estimation >> of finite-mixture models than direct maximization of the mixture >> log-likelihood. Due to its ascent properties, it is guaranteed to >> converge to a local maximum. By theoretical construction, it also >> automatically ensures that all the parameter constraints are >> satisfied. >> [snip] >> Be warned >> that EM convergence can be excruciatingly slow. Acceleration methods >> can be of help in large simulation studies or for bootstrapping. >> >> Best, >> Ravi. > > [snip] > As to acceleration: agreed, EM can be slow. Aitken acceleration > can be dramatically faster. Several outlines of the Aitken procedure > can be found by googling on "aitken acceleration". > > I recently wrote a short note, describing its general principle > and outlining its application to the EM algorithm, using the Probit > model as illustration (with R code). For fitting the location > parameter alone, Raw EM took 59 iterations, Aitken-accelerated EM > took 3. For fitting the location and scale paramaters, Raw EM took > 108, and Aitken took 4. > > If anyone would like a copy (PS or PDF) of this, drop me a line.
I have now placed a PDF copy of this, if anyone is interested (it was intended as a brief expository note), at: http://www.zen89632.zen.co.uk/R/EM_Aitken/em_aitken.pdf Best wishes to all, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <ted.hard...@manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 10-Apr-09 Time: 17:15:06 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
