Gaussian mixture models represent a conceptually and mathematically elegant class of models for casting the density of a heterogeneous population where the observed data is collected from a population composed of a finite set of G homogeneous subpopulations with a Gaussian distribution. A limitation of these models is that they suffer from the curse of dimensionality, and the number of parameters becomes easily extremely large in the presence of high-dimensional data. In this paper, we propose a class of parsimonious Gaussian mixture models with constrained extended ultrametric covariance structures that are capable of exploring hierarchical relations among variables. The proposal shows to require a reduced number of parameters to be fit and includes constrained covariance structures across and within components that further reduce the number of parameters of the model.
Cavicchia, C., Vichi, M., Zaccaria, G. (2024). Parsimonious ultrametric Gaussian mixture models. STATISTICS AND COMPUTING, 34(3 (June 2024)), 1-23 [10.1007/s11222-024-10405-9].
Parsimonious ultrametric Gaussian mixture models
Zaccaria, G
2024
Abstract
Gaussian mixture models represent a conceptually and mathematically elegant class of models for casting the density of a heterogeneous population where the observed data is collected from a population composed of a finite set of G homogeneous subpopulations with a Gaussian distribution. A limitation of these models is that they suffer from the curse of dimensionality, and the number of parameters becomes easily extremely large in the presence of high-dimensional data. In this paper, we propose a class of parsimonious Gaussian mixture models with constrained extended ultrametric covariance structures that are capable of exploring hierarchical relations among variables. The proposal shows to require a reduced number of parameters to be fit and includes constrained covariance structures across and within components that further reduce the number of parameters of the model.File | Dimensione | Formato | |
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