A sufficiently fast algorithm for finding close to optimal clique trees

Becker, Ann; Geiger, Dan

doi:10.1016/s0004-3702(00)00075-8

Cited by 43 publications

(56 citation statements)

References 15 publications

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“…Computing the optimal elimination order is an NP-hard problem (Arnborg, Corneil, & Proskurowski, 1987) and elimination orders yielding low induced tree width do not exist for some problems. These issues have been confronted successfully for a large variety of practical problems in the Bayesian network community, which has benefited from a large variety of good heuristics which have been developed for the variable elimination ordering problem (Bertele & Brioschi, 1972;Kjaerulff, 1990;Reed, 1992;Becker & Geiger, 2001). …”

Section: Example 42 Assumementioning

confidence: 99%

Efficient Solution Algorithms for Factored MDPs

Guestrin¹,

Koller²,

Parr³

et al. 2003

jair

264

268

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This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This representation often allows an exponential reduction in the representation size of structured MDPs, but the complexity of exact solution algorithms for such MDPs can grow exponentially in the representation size. In this paper, we present two approximate solution algorithms that exploit structure in factored MDPs. Both use an approximate value function represented as a linear combination of basis functions, where each basis function involves only a small subset of the domain variables. A key contribution of this paper is that it shows how the basic operations of both algorithms can be performed efficiently in closed form, by exploiting both additive and context-specific structure in a factored MDP. A central element of our algorithms is a novel linear program decomposition technique, analogous to variable elimination in Bayesian networks, which reduces an exponentially large LP to a provably equivalent, polynomial-sized one. One algorithm uses approximate linear programming, and the second approximate dynamic programming. Our dynamic programming algorithm is novel in that it uses an approximation based on max-norm, a technique that more directly minimizes the terms that appear in error bounds for approximate MDP algorithms. We provide experimental results on problems with over 10 40 states, demonstrating a promising indication of the scalability of our approach, and compare our algorithm to an existing state-of-the-art approach, showing, in some problems, exponential gains in computation time.

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Section: Example 42 Assumementioning

confidence: 99%

Efficient Solution Algorithms for Factored MDPs

Guestrin¹,

Koller²,

Parr³

et al. 2003

jair

264

268

View full text Add to dashboard Cite

show abstract

“…While this algorithm has interesting theoretical properties, it still is only practical for graphs of reduced size. Becker and Geiger [3] present another algorithm that finds close to optimal ordering. However, this algorithm also is restricted only to those graphs whose domain size is small.…”

Section: Related Researchmentioning

confidence: 99%

Exploiting the Probability of Observation for Efficient Bayesian Network Inference

Mousumi

Grant

2012

Advances in Artificial Intelligence

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It is well-known that the observation of a variable in a Bayesian network can affect the effective connectivity of the network, which in turn affects the efficiency of inference.Unfortunately, the observed variables may not be known until runtime, which limits the amount of compile-time optimization that can be done in this regard. This thesis considers how to improve inference when users know the likelihood of a variable being observed. It demonstrates how these probabilities of observation can be exploited to improve existing heuristics for choosing elimination orderings for inference. Empirical tests over a set of benchmark networks using the Variable Elimination algorithm show reductions of up to 50% and 70% in multiplications and summations, as well as runtime reductions of up to 55%. Similarly, tests using the Elimination Tree algorithm show reductions by as much as 64%, 55%, and 50% in recursive calls, total cache size, and runtime, respectively. iv Acknowledgments I take much pleasure to express my profound gratitude to my supervisor Dr. Kevin Grant for his persistent and inspiring supervision and helping me learn the ABC of Bayesian Networks. Without his endless help and continuous reassurance at the most difficult times, this thesis would not have been a reality. I am indebted to him for his support, encouragement, suggestions, generosity, and the invaluable knowledge he shared with me.

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“…A typical example are the algorithms by Amir [2]. (See e.g., also [10].) Other heuristics do not have such a guarantee, but often give tree decompositions with close to optimal width.…”

Section: Upper Boundsmentioning

confidence: 99%