Title :
On model selection and concavity for finite mixture models
Author :
Cadez, Igor V. ; Smyth, Padhraic
Author_Institution :
Dept. of Inf. & Comput. Sci., California Univ., Irvine, CA, USA
Abstract :
We show that the log-likelihood of finite mixture models is approximately concave as a function of the number of mixture components k. A corollary of this result is that the penalized log-likelihood will also be approximately concave (as a function of k) if the penalty term is itself strictly concave or linear in k (true, for example, for BIC). These results have a number of significant practical implications for parameter estimation and model selection in a mixture context
Keywords :
computational complexity; parameter estimation; probability; complexity model; concave penalty term; concavity; finite mixture models; linear penalty term; log-likelihood; mixture components; model selection; parameter estimation; penalized log-likelihood; probability density function; Clustering methods; Computer science; Context modeling; Engineering profession; Parameter estimation; Probability density function; Statistical analysis; Statistical distributions;
Conference_Titel :
Information Theory, 2000. Proceedings. IEEE International Symposium on
Conference_Location :
Sorrento
Print_ISBN :
0-7803-5857-0
DOI :
10.1109/ISIT.2000.866621
