DIRAC Networks: An Approach to Probabilistic Inference Based Upon the DIRAC Algebra of Quantum Mechanics.

摘要

This report describes how the Dirac algebra of quantum mechanics provides for a robust and self-consistent approach to probabilistic inference system modeling and processing. We call such systems Dirac networks and demonstrate how their use: (1) allows an efficient algebraic encoding of the probabilities and distributions for all possible combinations of truth values for the logical variable in an inference system; (2) employs unitary - rotation, time evolution, and translation operators to model influences upon system variable probabilities and their distributions; (3) guarantees system normalization; (4) admits unambiguously defined linear, as well as cyclic, cause and effect relationships; (5) enables the use of the von Neumann entropy as an informational uncertainty measure; and (6) allows for a variety of 'measurement' operators useful for quantifying probabilistic inferences. Dirac networks should have utility in such diverse application areas as data fusion and analysis, dynamic resource allocation, qualitative analysis of complex systems, automated medical diagnostics, and interactive/collaborative decision processes. The approach is illustrated by developing and applying simple Dirac networks to the following representative problems: (a) cruise missile - target allocation decision aiding; (b) genetic disease carrier identification using ancestral evidential information; (c) combat system control methodology trade-off analysis; (d) finding rotational symmetries in a digital image; and (e) fusing observational error profiles. Optical device implementations of several Dirac network components are also briefly discussed.