Identification and Interpretation of Belief Structure in Dempster-Shafer Theory
This addresses a foundational issue in DST for researchers and practitioners in uncertainty reasoning, enabling data-driven applications, though it is incremental as it builds on existing theory.
The paper tackles the problem of the lack of a frequentist interpretation in Dempster-Shafer Theory (DST), which prevents experimental validation and data-driven model construction, by developing such an interpretation and proposing three algorithms for automatically acquiring DST belief models from data for tree, poly-tree, and general belief network structures.
Mathematical Theory of Evidence called also Dempster-Shafer Theory (DST) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its foundation, many questions remain open. One of the most important open questions seems to be the relationship between frequencies and the Mathematical Theory of Evidence. The theory is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: (1) no experiment may be run to compare the performance of DST-based models of real world processes against real world data, (2) data may not serve as foundation for construction of an appropriate belief model. In this paper we develop a frequentist interpretation of the DST bringing to fall the above argument against DST. An immediate consequence of it is the possibility to develop algorithms acquiring automatically DST belief models from data. We propose three such algorithms for various classes of belief model structures: for tree structured belief networks, for poly-tree belief networks and for general type belief networks.