Independence, Decomposability and functions which take values into an Abelian Group

Adrian Silvescu, Vasant Honavar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Decomposition is an important property that we exploit in order to render problems more tractable. The decomposability of a problem implies the existence of some "independences" between relevant variables of the problem under consideration. In this paper we investigate the decomposability of functions which take values into an Abelian Group. Examples of such functions include: probability distributions, energy functions, value functions, fitness functions, and relations. For such problems we define a notion of conditional independence between subsets of the problem's variables. We prove a decomposition theorem that relates independences between subsets of the problem's variables with a factorization property of the respective function. As particular cases of this theorem we retrieve the Hammersley-Clifford theorem for probability distributions; an Additive Decomposition theorem for energy functions, value functions, fitness functions; and a relational algebra decomposition theorem.

Original languageEnglish (US)
Title of host publication9th International Symposium on Artificial Intelligence and Mathematics, ISAIM 2006
StatePublished - 2006
Event9th International Symposium on Artificial Intelligence and Mathematics, ISAIM 2006 - Fort Lauderdale, FL, United States
Duration: Jan 4 2006Jan 6 2006

Other

Other9th International Symposium on Artificial Intelligence and Mathematics, ISAIM 2006
CountryUnited States
CityFort Lauderdale, FL
Period1/4/061/6/06

Fingerprint

Decomposability
Abelian group
Decomposition Theorem
Fitness Function
Energy Function
Value Function
Decomposition
Clifford's theorems
Relational Algebra
Probability distributions
Subset
Conditional Independence
Probability Distribution Function
Independence
Factorization
Probability Distribution
Set theory
Imply
Decompose
Algebra

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Applied Mathematics

Cite this

Silvescu, A., & Honavar, V. (2006). Independence, Decomposability and functions which take values into an Abelian Group. In 9th International Symposium on Artificial Intelligence and Mathematics, ISAIM 2006
Silvescu, Adrian ; Honavar, Vasant. / Independence, Decomposability and functions which take values into an Abelian Group. 9th International Symposium on Artificial Intelligence and Mathematics, ISAIM 2006. 2006.
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Silvescu, A & Honavar, V 2006, Independence, Decomposability and functions which take values into an Abelian Group. in 9th International Symposium on Artificial Intelligence and Mathematics, ISAIM 2006. 9th International Symposium on Artificial Intelligence and Mathematics, ISAIM 2006, Fort Lauderdale, FL, United States, 1/4/06.

Independence, Decomposability and functions which take values into an Abelian Group. / Silvescu, Adrian; Honavar, Vasant.

9th International Symposium on Artificial Intelligence and Mathematics, ISAIM 2006. 2006.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Silvescu A, Honavar V. Independence, Decomposability and functions which take values into an Abelian Group. In 9th International Symposium on Artificial Intelligence and Mathematics, ISAIM 2006. 2006