No. 920

Title:

Whitening as a tool for estimating mutual information in spatiotemporal data sets

Author(s):

Galka, Andreas (Institute of Statistical Mathematics, University of Kiel); Ozaki, Tohru (Institute of Statistical Mathematics); Bosch Bayard, Jorge (Cuban Neuroscience Center); Yamashita, Okito /(nstitute of Statistical Mathematics)

Key words:

Time series analysis; mutual information; fMRI; maximum likelihood; whitening; spatiotemporal modelling .

Abstract:

We address the issue of inferring the connectivity structure of spatially extended dynamical systems by estimation of mutual information between pairs of sites. The well-known problem of correlated data is approached by explicit temporal and spatial modelling steps which aim at removing approximately all spatial and temporal correlations, i.e. at whitening the data, such that it is replaced by spatiotemporal innovations; this approach provides a link to the maximum-likelihood method and, for appropriately chosen models, removes the problem of estimating probability distributions of unknown shape. Consequently mutual information can be reinterpreted in the framework of dynamical model comparison, since it is shown to be equivalent to the difference of the log-likelihoods of coupled and uncoupled models for a pair of sites. This work is motivated by the analysis of fMRI data sets arising in brain research and neurological diagnosis. The practical application of this methodology is demonstrated for simulated data generated by a stochastic coupled-map lattice.