Probabilistic inference algorithms for finding the most probable explanation, the maximum aposteriori hypothesis, and the maximum expected utility and for updating belief are reformulated as an elimination--type algorithm called bucket elimination. This emphasizes the principle common to many of the algorithms appearing in that literature and clarifies their relationship to nonserial dynamic programming algorithms. We also present a general way of combining conditioning and elimination within this framework. Bounds on complexity are given for all the algorithms as a function of the problem's structure.
|
4388
|
Probabilistic Reasoning in Intelligent Systems
– Pearl
- 1988
|
|
904
|
Local computations with probabilities on graphical structures and their applications to expert systems
– Lauritzen, Spiegelhalter
- 1988
|
|
778
|
A computing procedure for quantification theory
– Davis, Putnam
- 1960
|
|
739
|
Constraint Networks
– Dechter
- 1992
|
|
354
|
Networks of constraints: Fundamental properties and applications to picture processing
– Montanari
- 1974
|
|
275
|
Evaluating influence diagrams
– Shachter
- 1986
|
|
243
|
Constraint Satisfaction
– Mackworth
- 1987
|
|
239
|
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
– Dechter
- 1990
|
|
220
|
Bayesian updating in causal probabilistic networks by local computations
– Jensen, Lauritzen, et al.
- 1990
|
|
217
|
A sufficient condition for backtrack-free search
– Freuder
- 1982
|
|
213
|
Tree clustering for constraint networks
– Dechter, Pearl
- 1989
|
|
188
|
Efficient algorithms for combinatorial problems on graphs with bounded decomposability
– Arnborg
- 1985
|
|
176
|
Context-specific independence in bayesian networks
– Boutilier, Friedman, et al.
- 1996
|
|
150
|
Nonserial Dynamic Programming
– Bertele, Brioschi
- 1972
|
|
116
|
Linear time algorithms for NP-hard problems on graphs embedded in k-trees
– Arnborg, Proskurowski
- 1989
|
|
91
|
Valuation-based systems for Bayesian decision analysis
– Shenoy
- 1992
|
|
88
|
From Influence Diagrams to Junction Trees
– JENSEN, JENSEN, et al.
- 1994
|
|
86
|
Probabilistic inference and influence diagrams
– Shachter
- 1988
|
|
83
|
Directional resolution: The Davis-Putnam procedure, revisited
– Dechter, Rish
- 1994
|
|
77
|
Identifying independence in Bayesian networks
– Geiger, Verma, et al.
- 1990
|
|
71
|
Graphical models for preference and utility
– Bacchus, Grove
- 1995
|
|
68
|
Dynamic Variable Ordering in CSPs
– Bacchus, Run
- 1995
|
|
65
|
Dynamic programming and influence diagrams
– Tatman, Shachter
- 1990
|
|
56
|
A computational scheme for reasoning in dynamic probabilistic networks
– Kjaerulff
- 1992
|
|
55
|
A sufficiently fast algorithm for finding close to optimal junction trees
– Becker, Geiger
- 1996
|
|
53
|
Local and global relational consistency
– Dechter, Beek
- 1997
|
|
50
|
A su cient condition for backtrack-free search
– Freuder
|
|
48
|
Decision making using probabilistic inference methods
– Shachter, Peot
- 1992
|
|
45
|
Symbolic probabilistic inference in belief networks," Automated Reasoning
– Shachter, D'Ambrosio, et al.
- 1990
|
|
42
|
Fattah. Topological Parameters for Time-Space Tradeoff
– Dechter, El
|
|
39
|
Global conditioning for probabilistic inference in belief networks
– Shachter, Andersen, et al.
- 1994
|
|
37
|
On the generation of alternative explanations with implications for belief revision
– Santos
- 1991
|
|
36
|
A New Algorithm for Finding MAP Assignments to Belief Networks
– Shimony, Charniack
- 1991
|
|
36
|
Probabilistic reasoning in predictive expert systems
– Spiegelhalter
- 1986
|
|
30
|
A connectionist model for diagnostic problem solving
– Peng, Reggia
- 1989
|
|
29
|
Constraint networks. Encyclopedia of Artificial Intelligence
– Dechter
- 1992
|
|
29
|
Mini-buckets: A general scheme for generating approximations in automated reasoning
– Dechter
- 1997
|
|
28
|
Probability functions on complex pedigrees
– Cannings, Thompson, et al.
- 1978
|
|
26
|
A computing procedure for quanti cation theory
– Davis, Putnam
- 1960
|
|
23
|
Gaussian in uence diagrams
– Shachter, Kenley
- 1989
|
|
20
|
An Ordered Examination of Influence Diagrams
– Shachter
- 1990
|
|
15
|
An evaluation of structural parameters for probabilistic reasoning: Results on benchmark circuits
– Fattah, Dechter
- 1996
|
|
13
|
Reggia \Plausability of diagnostic hypothesis
– Peng, A
- 1986
|
|
12
|
Topological parameters for time-space trade-o
– Dechter
- 1996
|
|
8
|
A computer-based medical diagnosis aid that integrates causal and probabilistic knowledge
– Nestor
- 1984
|
|
8
|
To guess or to think? hybrid algorithms for sat
– Rish, Dechter
- 1996
|
|
8
|
A new algorithm for nding map assignments to belief networks
– Shimony, Charniak
- 1991
|
|
8
|
Dynamic programming and in uence diagrams
– Tatman, Shachter
- 1990
|
|
7
|
Probabilistic inference and in uence diagrams
– Shachter
- 1988
|
|
6
|
NESTOR: A Computer-Based Medical Diagnosis that Integrates Causal and Probabilistic Knowledge
– Cooper
- 1984
|
|
