Implementing and Approximating DempsterShafer Theory

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Implementing and ApproximatingDempster-Shafer
Theory
Rolf Haenni Computer Science Department University
of California, Los Angeles
Contents
1. Introduction 2. Implementing DS-Theory 3.
Incomplete Belief Potentials 4. Resource-Bounded
Approximation 5. Conclusion
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1. Introduction
R. Haenni, N. Lehmann. Implementing Belief
Function Computations. Submitted to
International Journal of Intelligent Systems.
2002.
R. Haenni, N. Lehmann. Resource-Bounded and
Anytime Approximation of Belief Function
Computations. Submitted to Int. Journal of
Approx. Reasoning. 2002.
R. Haenni. Ordered Valuation Algebras a Generic
Framework for Approximating Inference. Submitted
to Artificial Intelligence. 2002.
R. Haenni, N. Lehmann. Probabilistic
Argumentation Systems a New Perspective on
Dempster- Shafer Theory. Submitted to Int.
Journal of Intelligent Systems. 2002.
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2. Implementing DS-Theory
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Representing Focal Sets
1) List of vectors ? beyond practical
applicability
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Bit String Representation
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Regrouping
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Quasi-Projection
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3. Incomplete Belief Potentials
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4. Resource-Bounded Approximation
Example

• computation often infeasible
• effective running time is not predictable

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Resource-bounded combination
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Problem choose parameters t during propagation
(if the total time is restricted to T
milliseconds)
Solution share T equally among the nodes of the
join tree and redistribute unused portions
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Inward propagation
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Remarks

• the procedure stops after at most T milliseconds

• method relies on the assumption that the time for
  marginalization is neglectable

• the same idea can be used for the outward
  propagation phase

• a refining procedure exists for cases where the
  accuracy of the results is not satisfactory (this
  leads to convenient anytime algorithms)

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5. Conclusion

• Important tools for implementing Dempster-Shafer
  theory are bit strings, hash tables,
  quasi-projection, fusion, and memoizing

• Incomplete belief potentials allow to approximate
  belief and plausibility by lower and upper bounds
  

• The resource-bounded combination operator allows
  to define inward and outward propagation as a
  resource-bounded procedure

• Refining leads to convenient anytime algorithms

• Idea can be generalized for valuation algebras
  (axioms)

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