Reconstruction of Epsilon-Machines in Predictive Frameworks and Decisional States

TL;DR

This paper presents a novel algorithm for reconstructing epsilon-machines and decisional states from data, integrating system structure with user-defined utility functions to identify decision-relevant patterns.

Contribution

It introduces the REMAPF algorithm that reconstructs epsilon-machines and decisional states, bridging system modeling with decision-making based on utility functions.

Findings

Effective reconstruction of epsilon-machines from data

Decisional states align with decision-making patterns

Applications demonstrated in automata filtering and image edge detection

Abstract

This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These 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 form a partition of the lower-level causal states that is defined 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 epsilon-machine and the decisional states from data. Application examples are given for hidden model reconstruction, cellular automata filtering, and edge detection in images.