Assessment of the Number of Components in Gaussian Mixture Models in the Presence of Multiple Likelihood Local Maximizers

• Activity Number: 284
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Daeyoung Kim*+ and Byungtae Seo
• Companies: University of Massachusetts, Amherst and Sungkyunkwan University
• Keywords: Gaussian mixture ; Maximum likelihood ; Spurious local maximizer ; Unbounded likelihood

Abstract

Gaussian mixtures are very flexible in representing the underlying structure in the data. However, the likelihood inference for Gaussian mixtures with unrestricted covariances is challenging because the likelihood function is unbounded and often has multiple local maximizers including spurious local maximizers. In this talk we first show that the presence of multiple local maximizers including spurious local maximizers affects the performances of model selection criteria used to choose the number of components in Gaussian mixture models. We then propose a likelihood-based method designed to avoid spurious local maximizers and choose a statistically desirable local maximizer in the presence of multiple local maximizers. We investigate, by a real-data example and simulation studies, the performance of the proposed method in the likelihood-based model selection criteria commonly used to assess the number of components.