Ordered valuation algebras: a generic framework for approximating inference

The paper presents a generic approach of approximating inference. The method is based on the concept of valuation algebras with its wide range of possible applications in many different domains. We present convenient resource-bounded anytime algorithms, where the maximal time of computation is determined by the user.

[1]  Serafín Moral,et al.  Penniless propagation in join trees , 2000, Int. J. Intell. Syst..

[2]  R. Dechter,et al.  Efficient reasoning in graphical models , 1999 .

[3]  Augustine Kong,et al.  Optimality Issues in Constructing a Markov Tree from Graphical Models , 2006 .

[4]  Jane W.-S. Liu,et al.  An object-oriented query processor that produces monotonically improving approximate answers , 1991, [1991] Proceedings. Seventh International Conference on Data Engineering.

[5]  Serafín Moral,et al.  Heuristic Algorithms for the Triangulation of Graphs , 1994, IPMU.

[6]  Alessandro Saffiotti,et al.  The Transferable Belief Model , 1991, ECSQARU.

[7]  David Harmanec,et al.  Faithful Approximations of Belief Functions , 1999, UAI.

[8]  Glenn Shafer,et al.  Probabilistic expert systems , 1996, CBMS-NSF regional conference series in applied mathematics.

[9]  Shlomo Zilberstein,et al.  Using Anytime Algorithms in Intelligent Systems , 1996, AI Mag..

[10]  Prakash P. Shenoy,et al.  Binary join trees for computing marginals in the Shenoy-Shafer architecture , 1997, Int. J. Approx. Reason..

[11]  John D. Lowrance,et al.  A Framework for Evidential-Reasoning Systems , 1990, AAAI.

[12]  Bjørnar Tessem,et al.  Approximations for Efficient Computation in the Theory of Evidence , 1993, Artif. Intell..

[13]  Jürg Kohlas.  Information algebras - generic structures for inference , 2003, Discrete mathematics and theoretical computer science.

[14]  Thierry Denoeux,et al.  Inner and Outer Approximation of Belief Structures Using a Hierarchical Clustering Approach , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[15]  Shlomo Zilberstein,et al.  Anytime Sensing Planning and Action: A Practical Model for Robot Control , 1993, IJCAI.

[16]  R. Haenni,et al.  Belief Function Propagation Based on Shenoy ’ s Fusion Algorithm ∗ , 2000 .

[17]  Prakash P. Shenoy,et al.  Probability propagation , 1990, Annals of Mathematics and Artificial Intelligence.

[18]  Rolf Haenni.  A Query-Driven Anytime Algorithm for Argumentative and Abductive Reasoning , 2002, Soft-Ware.

[19]  Michael I. Jordan,et al.  Probabilistic Networks and Expert Systems , 1999 .

[20]  Rolf Haenni,et al.  Resource bounded and anytime approximation of belief function computations , 2002, Int. J. Approx. Reason..

[21]  Rina Dechter,et al.  Mini-buckets: a general scheme for approximating inference , 2002 .

[22]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[23]  Didier Dubois,et al.  Consonant approximations of belief functions , 1990, Int. J. Approx. Reason..

[24]  Frank van Harmelen,et al.  Anytime Diagnostic Reasoning using Approximate Boolean Constraint Propagation , 2000, KR.

[25]  Shlomo Zilberstein,et al.  Approximate Reasoning Using Anytime Algorithms , 1995 .

[26]  Swaminathan Natarajan.  Imprecise and Approximate Computation , 1995 .

[27]  Khaled Mellouli,et al.  Propagating belief functions in qualitative Markov trees , 1987, Int. J. Approx. Reason..

[28]  Rina Dechter.  Bucket Elimination: a Unifying Framework for Processing Hard and Soft Constraints , 2004, Constraints.

[29]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[30]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[31]  Norbert Lehmann,et al.  Argumentation systems and belief functions , 2001 .

[32]  Michael P. Wellman,et al.  State-Space Abstraction for Anytime Evaluation of Probabilistic Networks , 1994, UAI.

[33]  Khaled Mellouli,et al.  Propagation of belief functions: a distributed approach , 1986, UAI.

[34]  Detlef D. Nauck.  Fuzzy data analysis with NEFCLASS , 2003, Int. J. Approx. Reason..

[35]  Jürg Kohlas,et al.  Handbook of Defeasible Reasoning and Uncertainty Management Systems , 2000 .

[36]  Prakash P. Shenoy,et al.  Some Improvements to the Shenoy-Shafer and Hugin Architectures for Computing Marginals , 1998, Artif. Intell..

[38]  L. Zadeh,et al.  Fuzzy Logic for the Management of Uncertainty , 1992 .

[39]  Steffen L. Lauritzen,et al.  Bayesian updating in causal probabilistic networks by local computations , 1990 .

[40]  Rina Dechter,et al.  Bucket Elimination: A Unifying Framework for Reasoning , 1999, Artif. Intell..

[41]  Rina Dechter,et al.  Mini-Buckets: A General Scheme for Generating Approximations in Automated Reasoning , 1997, IJCAI.

[42]  Glenn Shafer,et al.  Readings in Uncertain Reasoning , 1990 .

[43]  Prakash P. Shenoy,et al.  Binary Join Trees , 1996, UAI.

[44]  Mathias Bauer,et al.  Approximation algorithms and decision making in the Dempster-Shafer theory of evidence - An empirical study , 1997, Int. J. Approx. Reason..

[45]  J. Kohlas,et al.  Information Algebras and Information Systems , 1996 .

[46]  Eugene C. Freuder,et al.  Anytime algorithms for constraint satisfaction and SAT problems , 1996, SGAR.

[47]  Jürg Kohlas,et al.  A Mathematical Theory of Hints , 1995 .

[48]  Eric Horvitz,et al.  Bounded Conditioning: Flexible Inference for Decisions under Scarce Resources , 2013, UAI 1989.

[49]  Rina Dechter,et al.  Bucket elimination: A unifying framework for probabilistic inference , 1996, UAI.

[50]  Frans Voorbraak,et al.  A Computationally Efficient Approximation of Dempster-Shafer Theory , 1988, Int. J. Man Mach. Stud..

[51]  UpdatingRobert Mateescu,et al.  Partition-based Anytime Approximation for Belief , 2001 .

[52]  Khaled Mellouli,et al.  3 Min-Based Possibilistic Graphs , 2002 .

[53]  Prakash P. Shenoy,et al.  A valuation-based language for expert systems , 1989, Int. J. Approx. Reason..

[54]  Thierry Denœux,et al.  Inner and outer approximation of belief structures using a hierarchical clustering approach , 2001 .

[55]  Jürg Kohlas,et al.  Propositional Information Systems , 1999, J. Log. Comput..

[56]  Russell G. Almond.  Graphical belief modeling , 1995 .

[57]  Rolf Haenni.  Anytime argumentative and abductive reasoning , 2003, Soft Comput..

[58]  Andrew P. Sage,et al.  Uncertainty in Artificial Intelligence , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[59]  Prakash P. Shenoy,et al.  Computation in Valuation Algebras , 2000 .

[60]  Prakash P. Shenoy,et al.  Valuation-based systems: a framework for managing uncertainty in expert systems , 1992 .