Inference in credal networks using multilinear programming

A credal network is a graphical tool for representation and manipulation of uncertainty, where probability values may be imprecise or indeterminate. A credal network associates a directed acyclic graph with a collection of sets of probability measures; in this context, inference is the computation of tight lower and upper bounds for conditional probabilities. In this paper we present new algorithms for inference in credal networks based on multilinear programming techniques. Experiments indicate that these new algorithms have better performance than existing ones, in the sense that they can produce more accurate results in larger networks.

[1]  Serafín Moral,et al.  An axiomatic framework for propagating uncertainty in directed acyclic networks , 1993, Int. J. Approx. Reason..

[2]  Fabio Gagliardi Cozman,et al.  Robustness Analysis of Bayesian Networks with Local Convex Sets of Distributions , 1997, UAI.

[3]  Fabio Gagliardi Cozman,et al.  Inference in Credal Networks with Branch-and-Bound Algorithms , 2003, ISIPTA.

[4]  AnHai Doan,et al.  Geometric foundations for interval-based probabilities , 1998, Annals of Mathematics and Artificial Intelligence.

[5]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[6]  D. V. Shapot,et al.  Problems in multilinear programming , 2001 .

[7]  Panos M. Pardalos,et al.  Constrained Global Optimization: Algorithms and Applications , 1987, Lecture Notes in Computer Science.

[8]  Andr Es Cano,et al.  Using Probability Trees to Compute Marginals with Imprecise Probabilities , 2002 .

[9]  P. C. Haarhoff,et al.  A New Method for the Optimization of a Nonlinear Function Subject to Nonlinear Constraints , 1970, Comput. J..

[10]  Isaac Levi,et al.  The Enterprise Of Knowledge , 1980 .

[11]  H. Tuy.  Convex analysis and global optimization , 1998 .

[12]  Bjørnar Tessem,et al.  Interval probability propagation , 1992, Int. J. Approx. Reason..

[13]  P. Walley,et al.  A survey of concepts of independence for imprecise probabilities , 2000 .

[14]  D. Avis.  lrs : A Revised Implementation of the Rev rse Search Vertex Enumeration Algorithm , 1998 .

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

[16]  R. Dembo,et al.  Solution of Generalized Geometric Programs , 1975 .

[17]  Gregory F. Cooper,et al.  The ALARM Monitoring System: A Case Study with two Probabilistic Inference Techniques for Belief Networks , 1989, AIME.

[18]  Leon S. Lasdon,et al.  Solving geometric programs using GRG: Results and comparisons , 1978 .

[19]  D. Avis.  A Revised Implementation of the Reverse Search Vertex Enumeration Algorithm , 2000 .

[20]  Fabio Gagliardi Cozman,et al.  Inference in Polytrees with Sets of Probabilities , 2002, UAI.

[21]  X. M. Martens,et al.  Comparison of generalized geometric programming algorithms , 1978 .

[22]  Fabio Gagliardi Cozman,et al.  Propositional and Relational Bayesian Networks Associated with Imprecise and Qualitat , 2004, UAI.

[23]  Hanif D. Sherali,et al.  A global optimization algorithm for polynomial programming problems using a Reformulation-Linearization Technique , 1992, J. Glob. Optim..

[24]  Fabio Gagliardi Cozman,et al.  Random Generation of Bayesian Networks , 2002, SBIA.

[25]  Andrés Cano,et al.  Convex Sets Of Probabilities Propagation By Simulated Annealing , 1994 .

[26]  Andrés Cano,et al.  A Genetic algorithm to approximate convex sets of probabilities , 1996 .

[27]  R. Horst,et al.  Global Optimization: Deterministic Approaches , 1992 .

[28]  F. Cozman,et al.  Generalizing variable elimination in Bayesian networks , 2000 .

[29]  Fabio Gagliardi Cozman,et al.  Credal networks , 2000, Artif. Intell..

[30]  Warren P. Adams,et al.  A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems , 1998 .

[31]  Enrico Fagiuoli,et al.  2U: An Exact Interval Propagation Algorithm for Polytrees with Binary Variables , 1998, Artif. Intell..

[32]  Luis M. de Campos,et al.  Independence Concepts for Convex Sets of Probabilities , 1995, UAI.

[33]  R. Duffin.  Linearizing Geometric Programs , 1970 .

[34]  Steven A. Orszag,et al.  CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS , 1978 .

[35]  Yves Smeers,et al.  A Branch-and-Bound Method for Reversed Geometric Programming , 1979, Oper. Res..

[36]  John N. Hooker,et al.  Bayesian logic , 1994, Decision Support Systems.

[37]  Fabio Gagliardi Cozman,et al.  Inference with Seperately Specified Sets of Probabilities in Credal Networks , 2002, UAI.