Reconstruction of epsilon-Machines in Predictive Frameworks and Decisional States

This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These are de ned as the internal states of a system that lead to the same decision, based on a user-provided utility or pay-o function. The utility function encodes some a priori knowledge external to the system, it quanti es how bad it is to make mistakes. The intrinsic underlying structure of the system is modeled by an epsilon-machine and its causal states. The decisional states form a partition of the lower-level causal states that is de ned according to the higher-level user's knowledge. In a complex systems perspective, the decisional states are thus the emerging patterns corresponding to the utility function. The transitions between these decisional states correspond to events that lead to a change of decision. The new REMAPF algorithm estimates both the epsilonmachine and the decisional states from data. Application examples are given for hidden model reconstruction, cellular automata ltering, and edge detection in images.