Identification and Interpretation of Belief Structure in Dempster-Shafer Theory

TL;DR

This paper develops a frequentist interpretation of Dempster-Shafer Theory, enabling automatic construction of belief models from data and proposing algorithms for different belief network structures.

Contribution

It introduces a frequentist interpretation of DST and presents three algorithms for automatic belief model construction from data across various network types.

Findings

Established a frequentist interpretation of DST.

Developed algorithms for belief model construction from data.

Applied algorithms to different belief network structures.

Abstract

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.