Exponential Curvature of Markov Models

Abstract

We prove that the non FSMX tree model is not an exponential family. It is noted in [Weinberger et al., 95] that the tree source is classified into two classes; a FSMX source or not, depending on shape of the context tree. The FSMX source is a tree source and a finite state machine. It is known that the FSMX model is an exponential family. In this situation our concern is whether the non FSMX tree model is an exponential family or not. This paper's contribution is to show that the non FSMX tree model is not an exponential family. Hence, for the tree model, to be an FSMX model is a necessary and sufficient condition for to be an exponential family.