Retrieving a Context Tree from EEG Data

Aline Duarte,Antonio Galves,Guilherme Ost,Claudia D Vargas,Ricardo Fraiman

doi:10.3390/math7050427

Abstract

It has been repeatedly conjectured that the brain retrieves statistical regularities from stimuli. Here, we present a new statistical approach allowing to address this conjecture. This approach is based on a new class of stochastic processes, namely, sequences of random objects driven by chains with memory of variable length.

Highlights

EEG data, we introduce a new class of stochastic processes
We assume that at each time step a new EEG chunk is chosen according to a probability measure which depends only on the context assigned to the sequence of auditory units generated up to that time. This implies that to describe the new class of stochastic chains introduced in this paper, we need to consider a family of probability measures on the set of functions corresponding to the EEG chunks, indexed by the contexts of the context tree characterizing the chain of auditory stimuli
Is the brain able to identify the context tree generating the sample of auditory stimuli? From an experimental point of view, the question is whether it is possible to retrieve the tree presented in Figure 1 from the corresponding EEG data

Summary

Introduction

We assume that at each time step a new EEG chunk is chosen according to a probability measure (defined on suitable class of functions) which depends only on the context assigned to the sequence of auditory units generated up to that time This implies that to describe the new class of stochastic chains introduced in this paper, we need to consider a family of probability measures on the set of functions corresponding to the EEG chunks, indexed by the contexts of the context tree characterizing the chain of auditory stimuli. In this probabilistic framework, the neurobiological question can be rigorously addressed as follows.

Informal Presentation of Our Approach

Notation and Definitions

Simulation Study

Proof of Theorem 1