Study of models with latent variables: optimal estimation in high dimensions

• Grant number: 25/14038-7
• Support Opportunities: Scholarships abroad - Research
• Start date: July 01, 2026
• End date: June 30, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Florencia Graciela Leonardi
• Grantee: Florencia Graciela Leonardi
• Host Investigator: Catherine Matias
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Université Paris-Sorbonne (Paris 4), France
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

Latent variable models comprise a broad class of statistical models that have been widely used to represent various types of data. Within this class, we can highlight models such as random graph models with community structure, hidden Markov models, and mixture models. Despite their differing structures and definitions, these models share certain key features. The most important of these is that the dimension of the parameter space depends on the number of possible values of the latent variables, a quantity that is unobserved in the data and is commonly referred to as the "order" of the model.A central problem in statistical modeling with latent variable models is the consistent and efficient determination of the model order, given a sample from the observed process. This is a particularly challenging issue, both theoretically and in practice, due to the unobserved nature of the latent variables. Other open problems include determining the minimal regularization of cost functions that yield consistent estimators-thus avoiding underestimation of the model-and developing computationally efficient methods for approximating these estimators.This proposal builds upon successful recent research in the theoretical study of latent variable models, such as the Stochastic Block Model for random networks. It aims to develop model selection methods for the order in high-dimensional settings, i.e., without assuming known upper bounds on the order. Practical solutions to these problems could have a direct impact in application areas such as data science and artificial intelligence, where model order is often assumed to be known.This proposal is aligned with the objectives of the thematic project "Modeling of Stochastic Systems" (FAPESP grant 2023/13453-5) and the CEPID NeuroMat project (FAPESP grant 2013/07699-0), in which the proponent participates as a principal investigator. (AU)