Methods for selecting mixture models

• Grant number: 24/00413-8
• Support Opportunities: Regular Research Grants
• Duration: May 01, 2024 - April 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal Investigator: Daiane Aparecida Zuanetti
• Grantee: Daiane Aparecida Zuanetti
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

Mixture models have gained a lot of visibility in the last two decades and have been widely used in many areas of research due to their flexibility in accommodating heterogeneous, independent or dependent, structured or unstructured data. With the availability of high-dimensional data and an increasing amount of information, two major challenges have been identifying the ideal number of components (groups) in the mixture and selecting the variables (covariates or predictors) which, in some cases, are used in a regression function to define some parameters involved in the model. This project, therefore, consists of two simultaneous sub-projects. One of them is focused on proposing more efficient frequentist and Bayesian methodologies for selecting variables in non-homogeneous hidden Markov models, which are mixture models with dependent data over time. The objective of the second sub-project is to compare the performance of several known metrics for selecting the number of topics in mixture models for textual analysis and latent Dirichlet allocation, which can be seen as a flexibilization of mixture models in the analysis and clustering of texts. The performance of the proposed and studied methods will be analyzed and compared in simulated and real data. (AU)