Generating logical expressions from positive and negative examples via a branch-and-bound approach

Evangelos Triantaphyllou, Allen L. Soyster, Soundar Rajan Tirupatikumara

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Consider a logical system with N entities which assume binary values of either TRUE (1) or FALSE (0). There are 2N vectors, each with N components, of this type. Even when a modest value of N, e.g. N = 50, the number of such vectors exceeds one quadrillion. We assume that an 'expert' exists which can ascertain whether a particular vector (observation) such as (1, 1, 0, 0, 1, 0, ..., 1) is allowable or not. This expert can be a human expert or an unknown system whose rules have to be inferred. Further, we assume that a sampling of m observations has resulted in M1 instances which the expert has classified as allowable and M2 = m - M1 instances which are not allowable. We call these instances positive and negative examples, respectively. The objective of this research is to infer a set of logical rules for the entire system based upon the m, and possibly, additional sample observations. The proposed algorithm in this paper is based on an highly efficient branch-and-bound formulation. This algorithm configures a sequence of logical clauses in conjunctive normal form (CNF), that when are taken together, accept all the positive examples and reject all the negative examples. Some computational results indicate that the proposed approach can process problems that involve hundreds of positive and negative examples in a few CPU seconds and with small memory requirements.

Original languageEnglish (US)
Pages (from-to)185-197
Number of pages13
JournalComputers and Operations Research
Volume21
Issue number2
DOIs
StatePublished - Jan 1 1994

Fingerprint

Branch-and-bound
expert
Conjunctive Normal Form
Program processors
Sampling
Computational Results
Data storage equipment
Values
Exceed
Entire
Binary
Unknown
Logic
Formulation
Requirements
Observation

All Science Journal Classification (ASJC) codes

  • Information Systems and Management
  • Management Science and Operations Research
  • Applied Mathematics
  • Modeling and Simulation
  • Transportation

Cite this

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title = "Generating logical expressions from positive and negative examples via a branch-and-bound approach",
abstract = "Consider a logical system with N entities which assume binary values of either TRUE (1) or FALSE (0). There are 2N vectors, each with N components, of this type. Even when a modest value of N, e.g. N = 50, the number of such vectors exceeds one quadrillion. We assume that an 'expert' exists which can ascertain whether a particular vector (observation) such as (1, 1, 0, 0, 1, 0, ..., 1) is allowable or not. This expert can be a human expert or an unknown system whose rules have to be inferred. Further, we assume that a sampling of m observations has resulted in M1 instances which the expert has classified as allowable and M2 = m - M1 instances which are not allowable. We call these instances positive and negative examples, respectively. The objective of this research is to infer a set of logical rules for the entire system based upon the m, and possibly, additional sample observations. The proposed algorithm in this paper is based on an highly efficient branch-and-bound formulation. This algorithm configures a sequence of logical clauses in conjunctive normal form (CNF), that when are taken together, accept all the positive examples and reject all the negative examples. Some computational results indicate that the proposed approach can process problems that involve hundreds of positive and negative examples in a few CPU seconds and with small memory requirements.",
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Generating logical expressions from positive and negative examples via a branch-and-bound approach. / Triantaphyllou, Evangelos; Soyster, Allen L.; Tirupatikumara, Soundar Rajan.

In: Computers and Operations Research, Vol. 21, No. 2, 01.01.1994, p. 185-197.

Research output: Contribution to journalArticle

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