Geometric conditioning in belief calculus

Fabio Cuzzolin
STATUS: submitted to Artificial Intelligence Journal, March 2011; to revise Fall 2012

Conditioning is crucial in applied science when inference involving time series is involved. Belief calculus is an effective way of handling such inference in the presence of uncertainty, but different approaches to conditioning in that framework have been proposed in the past, leaving the matter unsettled. We propose here an approach to the conditioning of belief functions based on geometrically projecting them onto the simplex associated with the conditioning event in the space of all belief functions. Two different such simplices can be defined, as each belief function can be represented as either the vector of its basic probability values or the vector of its belief values. We show here that such a geometric approach to conditioning often produces simple results with straightforward interpretations in terms of degrees of belief. The question of whether classical approaches, such as for instance Dempster's conditioning, can also be reduced to some form of distance minimization remains open: the study of families of combination rules generated by (geometric) conditioning rules appears to be the natural prosecution of the presented research.

BibTeX entry

  AUTHOR = "Fabio Cuzzolin", 
  TITLE = "Geometric conditioning in belief calculus",
  JOURNAL = "submitted to Artificial Intelligence", 
  YEAR = "2013"