Combination calculi for uncertainty reasoning: representing uncertainty using distributions
Annals of Mathematics and Artificial Intelligence
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IN THIS PAPER WE DESCRIBE THE MATHEMATICAL FOUNDATIONS OF A KNOWLEDGE REPRESENTATION AND EVIDENCE COMBINATION FRAMEWORK AND RELATE IT TO THE THEORY OF EVIDENTIAL REASONING AS DEVELOPED BY DEMPSTER AND SHAFER. ALTHOUGH OUR DISCUSSION TAKES PLACE IN THE CONTEXT OF COMPUTER VISION, THE RESULTS ARE APPLICABLE TO PROBLEMS IN KNOWLEDGE REPRESENTATION AND DATA INTERPRETATION. OUR REPRESENTATION, CALLED PL-FUNCTIONS, AND A SIMPLE MULTIPLICATIVE COMBINATION RULE IS SHOWN TO BE EQUIVALENT TO A SUB-CLASS OF THE FAMILY OF MASS-FUNCTIONS AS DESCRIBED BY SHAFER WITH DEMPSTER''S RULE AS THE COMBINATION FUNCTION. HOWEVER, THE SIMPLER COMBINATION RULE HAS A COMPLEXITY WHICH IS LINEAR WITH RESPECT TO THE NUMBER OF ELEMENTS IN THE FRAME OF DISCERNMENT. THIS IS A TREMENDOUS COMPUTATIONAL ADVANTAGE OVER THE GENERAL THEORY WHICH PROVIDES A COMBINATION RULE EXPONENTIAL WITH RESPECT TO THE NUMBER OF OBJECTS OVER WHICH WE ARE REASONING. WE ALSO DIS- CUSS A METHOD WHICH ALLOWS OUR REPRESENTATION TO BE AUTOMATICALLY GENERATED FROM STATISTICAL DATA.