Study of methods for comparing the distribution of functions associated with the Algorithm Context.

• Grant number: 24/06218-2
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: June 01, 2024
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Pablo Augusto Ferrari
• Grantee: Arthur Reis Tabelini
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat, AP.CEPID

Abstract

In Hernández et al. (2021), the authors studied the brain´s ability to identify non-trivialpatterns in Electroencephalogram (EEG) data through an experimental protocol that involvesexposing volunteers to a sequence of stimuli generated by Variable Length Markov Chains(VLMC). Analysis of these data shows that brain processing seems to be capable of learningstructural characteristics of VLMCs. One of the classical methods present in the literature forselecting VLMC models with a finite alphabet is known as the Algorithm Context, introducedby Rissanen (1983). In Duarte et al. (2019), the authors adapted the Algorithm Context forinfinite alphabets using a Projective Method, introduced in Cuesta-Albertos et al. (2006).Although the consistency of this procedure has been proven, the idea of associating theAlgorithm Context with tests of law equality is much more general. Therefore, it is natural toassociate the Algorithm Context with other ways of testing law equalities between functions,as well as comparing different methods. The present project aims to generalize the methodproposed in Duarte et al. (2019) by studying other ways of consistently testing law equalitiesin sets of functions and associating them with the Algorithm Context.