Decisional States

This article introduces the decisional states of system, and provides a practical algorithm for computing them. The decisional states are defined as the internal states of a system that lead to the same decision, based on a user-provided utility or pay-off function. The utility function encodes some a priori knowledge external to the system, it quantifies 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 are the emerging patterns corresponding to the utility function. In a complex systems perspective, these patterns thus form a partition of the lower-level system states that is defined according to the higher-level user's knowledge. The transitions between these decisional states correspond to events that lead to a change of decision. An algorithm is provided so as to estimate the states and their transitions from data. Application examples are given for hidden model reconstruction, cellular automata filtering, and edge detection in images.