Statistics Seminars: A geometric approach to uncertainty theory
25 November 2008 14:15 in CM221
Uncertainty measures play a major role in fields like artificial intelligence, where problems involving formalized reasoning are common. An extensive battery of different uncertainty theories have indeed been developed in the last century or so, starting from De Finetti's pioneering work. Most of them comprise classical probabilities as a special case, and form a hierarchy of encapsulated formalisms. Uncertainty measures of different nature (probabilities, possibilities, belief functions, random sets) can be represented as points of a Cartesian space and there analyzed. We can study the geometry of the region where different classes of measures live in terms of the notion of structured collections of simplices or "simplicial complexes". Evidence aggregation operators (like for instance Dempster's rule of combination) can also be seen as geometric operators. Fundamental problems can then be solved by geometric means. These include, for instance, the issues of how to approximate a belief function or a random set with a probability, or how to compute distances between different uncertainty measures. Reasoning frameworks for interval probabilities based on a credal interpretation of such intervals can be developed.
Note the unusual location (CM221) and time (Tuesday 2:15)!
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