Entropy rate estimation for vector processes: Application to complex FMRI analysis

Abstract

When characterizing the density of a vector process, it is desirable to consider the most general case, hence, account for higher-order statistics, sample dependence, and dependence across entries of the vector process. Entropy rate provides a powerful framework for exploiting all three properties. However, its estimation is a difficult problem in general since it is defined based on the joint distribution of the whole vector process. In this paper, we discuss the vector autoregressive (AR) signal model, and propose an entropy rate estimator based on this model. We use a suite of maximum entropy distributions to form a flexible model with a reasonable model complexity. The new entropy rate estimator is shown to exploit all three statistical properties effectively, and to provide desirable performance in analysis of functional magnetic resonance imaging (fMRI) data.