TY - JOUR

T1 - Cost-based abduction and MAP explanation

AU - Charniak, Eugene

AU - Shimony, Solomon Eyal

N1 - Funding Information:
This work has been supported in part by the National Science Foundation under grants IST 8416034 and IST 8515005 and Office of Naval Research under grant N00014-79-C-0529. The second named author was funded by a Corinna Borden Keen Fellowship while in residence at Brown University. We wish to thank Robert Goldman for initially pointing out that our best-first cost-based abduction algorithm, together with our semantics, constitutes an MAP computation algorithm.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - Cost-based abduction attempts to find the best explanation for a set of facts by finding a minimal cost proof for the facts. The costs are computed by summing the costs of the assumptions necessary for the proof plus the cost of the rules. We examine existing methods for constructing explanations (proofs), as a minimization problem on a DAG (directed acyclic graph). We then define a probabilistic semantics for the costs, and prove the equivalence of the cost minimization problem to the Bayesian network MAP (maximum a posteriori probability) solution of the system. A simple best-first algorithm for finding least-cost proofs is presented, and possible improvements are suggested. The semantics of cost-based abduction for complete models are then generalized to handle negation. This, in turn, allows us to apply the best-first search algorithm as a novel way of computing MAP assignments to belief networks that can enumerate assignments in order of decreasing probability. An important point is that improvement results for the best-first search algorithm carry over to the computation of MAPs.

AB - Cost-based abduction attempts to find the best explanation for a set of facts by finding a minimal cost proof for the facts. The costs are computed by summing the costs of the assumptions necessary for the proof plus the cost of the rules. We examine existing methods for constructing explanations (proofs), as a minimization problem on a DAG (directed acyclic graph). We then define a probabilistic semantics for the costs, and prove the equivalence of the cost minimization problem to the Bayesian network MAP (maximum a posteriori probability) solution of the system. A simple best-first algorithm for finding least-cost proofs is presented, and possible improvements are suggested. The semantics of cost-based abduction for complete models are then generalized to handle negation. This, in turn, allows us to apply the best-first search algorithm as a novel way of computing MAP assignments to belief networks that can enumerate assignments in order of decreasing probability. An important point is that improvement results for the best-first search algorithm carry over to the computation of MAPs.

UR - http://www.scopus.com/inward/record.url?scp=0028408874&partnerID=8YFLogxK

U2 - 10.1016/0004-3702(94)90030-2

DO - 10.1016/0004-3702(94)90030-2

M3 - Article

AN - SCOPUS:0028408874

SN - 0004-3702

VL - 66

SP - 345

EP - 374

JO - Artificial Intelligence

JF - Artificial Intelligence

IS - 2

ER -