TY - JOUR

T1 - The role of relevance in explanation II

T2 - Disjunctive assignments and approximate independence

AU - Shimony, Solomon Eyal

N1 - Funding Information:
I wish to thank Eugene Charniak for supporting this research, both financially and with solid advice. This work has been supported in part by the National Science Foundation under grants IST 8416034 and IST 8515005, and the Office of Naval Research under grant N00014-79-C-0529. The author was also funded by a Corinna Borden Keen Fellowship while at Brown University.

PY - 1995/1/1

Y1 - 1995/1/1

N2 - Relevance-based explanation is a scheme in which partial assignments to Bayes network variables are explanations (abductive conclusions). We allow variables to remain unassigned in explanations as long as they are irrelevant to the explanation, where irrelevance is defined in terms of statistical independence. Equating irrelevance with exact independence leads to problems when events are almost statistically independent (but still intuitively irrelevant). Approximate independence alleviates the problem. Interesting properties of approximate independence are discussed, as well as an algorithm based on these properties. Another issue is multiple-valued variables: their existence in the system, especially when subsets of values correspond to natural types of events, causes the overspecification problem to resurface. Generalizing the notion of assignments to allow disjunctive assignments is a solution to this problem. We define generalized independence-based explanations as maximum-posterior-probability independence-based generalized assignments (GIB MAPs). GIB assignments are shown to have certain properties that ease the design of algorithms for computing GIB MAPs. One such algorithm is discussed here, as well as suggestions for how other algorithms may be adapted to compute GIB MAPs. Additionally, both approximate independence and GIB explanations are useful constructs for algorithms that approximate marginal distributions by enumeration of high-probability explanations.

AB - Relevance-based explanation is a scheme in which partial assignments to Bayes network variables are explanations (abductive conclusions). We allow variables to remain unassigned in explanations as long as they are irrelevant to the explanation, where irrelevance is defined in terms of statistical independence. Equating irrelevance with exact independence leads to problems when events are almost statistically independent (but still intuitively irrelevant). Approximate independence alleviates the problem. Interesting properties of approximate independence are discussed, as well as an algorithm based on these properties. Another issue is multiple-valued variables: their existence in the system, especially when subsets of values correspond to natural types of events, causes the overspecification problem to resurface. Generalizing the notion of assignments to allow disjunctive assignments is a solution to this problem. We define generalized independence-based explanations as maximum-posterior-probability independence-based generalized assignments (GIB MAPs). GIB assignments are shown to have certain properties that ease the design of algorithms for computing GIB MAPs. One such algorithm is discussed here, as well as suggestions for how other algorithms may be adapted to compute GIB MAPs. Additionally, both approximate independence and GIB explanations are useful constructs for algorithms that approximate marginal distributions by enumeration of high-probability explanations.

KW - abductive and probabilistic reasoning

KW - explanation

KW - relevance

UR - http://www.scopus.com/inward/record.url?scp=0342895946&partnerID=8YFLogxK

U2 - 10.1016/0888-613X(94)00019-Y

DO - 10.1016/0888-613X(94)00019-Y

M3 - Article

AN - SCOPUS:0342895946

VL - 13

SP - 27

EP - 60

JO - International Journal of Approximate Reasoning

JF - International Journal of Approximate Reasoning

SN - 0888-613X

IS - 1

ER -