A mutual information based distance for multivariate Gaussian processes

In this paper a distance on the set of multivariate Gaussian linear stochastic processes is proposed based on the concept of mutual information. The definition of the distance is inspired by various properties of the mutual information of past and future of a stochastic process. For two special classes of models a link exists between this mutual information distance and a previously defined scalar cepstral distance. Finally, it is demonstrated that the distance shows similar behavior to an ad hoc defined multivariate cepstral distance.