Non-Parametric Finite Multivariate Mixture Models with Applications
Open Access
- Author:
- ZHU, XIAOTIAN
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- September 26, 2014
- Committee Members:
- David Russell Hunter, Dissertation Advisor/Co-Advisor
David Russell Hunter, Committee Chair/Co-Chair
Bruce G Lindsay, Committee Member
Le Bao, Committee Member
John C Liechty, Committee Member
Stephanie Trea Lanza, Committee Member
Runze Li, Committee Member - Keywords:
- mixture model
conditional independence
nonparametric estimation
penalized smoothed likelihood
independent component analysis - Abstract:
- This research set out to investigate and build upon the foundation for the nonparametric estimation of finite multivariate mixture models given the conditional independence assumption, set forth in a series of studies over the last decade. We proposed a novel formulation of the objective function in terms of penalized smoothed Kullback-Leibler divergence under a reduced parameter space. A special optimization landscape and scheme was discovered in working out the majorizationminimization method for the estimation problem which leads to a closed form of the nonlinearly smoothed majorization-minimization (NSMM) algorithm. We established a sharpened monotonicity property that precisely measures the distance between successive iterates of the algorithm and proved the existence of a solution to the main optimization problem for the first time in literature. The estimation theory for this basic model together with the special optimization scheme can be adapted to the investigation of an important extension of the model that incorporates component-wise independent component analysis (ICA). The NSMMICA algorithm has been developed and a discretized version of it, which interweaves NSMM and weighted FastICA has been implemented in the R package icamix as a model-based clustering tool. We demonstrated the use of the newly developed methods/algorithms by applications in image analysis and unsupervised learning.