Minimizing the Average Query Complexity of Learning Monotone Boolean Functions

This paper addresses the problem of completely reconstructing deterministic monotone Boolean functions via membership queries. The minimum average query complexity is guaranteed via recursion, where partially ordered sets (posets) make up the overlapping subproblems. For problems with up to 4 variab...

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Bibliographic Details
Published in:INFORMS journal on computing Vol. 14; no. 2; pp. 144 - 174
Main Authors: Torvik, Vetle I, Triantaphyllou, Evangelos
Format: Journal Article
Language:English
Published: Linthicum INFORMS 22.03.2002
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
Artificial Intelligence
Boolean
Breast cancer
Codes
Computational mathematics
Integer programming
Interactive learning
Medical diagnosis
Networks-Graphs: Matchings
Programming: Integer: Algorithms: Branch and Bound
Queries
Rheumatology
Software
Statistics: Sampling
Web browsers
ISSN:1091-9856, 1526-5528, 1091-9856
Online Access:Get full text
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Summary:This paper addresses the problem of completely reconstructing deterministic monotone Boolean functions via membership queries. The minimum average query complexity is guaranteed via recursion, where partially ordered sets (posets) make up the overlapping subproblems. For problems with up to 4 variables, the posets' optimality conditions are summarized in the form of an evaluative criterion. The evaluative criterion extends then computational feasibility to problems involving up to about 20 variables. A frameworkfor unbiased average case comparison of monotone Boolean function inference algorithms is developed using unequal probability sampling. The unbiased empirical results show that an implementation of the subroutine considered as a standard in the literature performs almost twice as many queries as the evaluative criterion on the average. It should also be noted that the first algorithm ever designed for this problem performed consistently within two percentage points of the evaluative criterion. As such, it prevails, by far, as the most efficient of the many preexisting algorithms.
Bibliography:SourceType-Scholarly Journals-1
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content type line 14
ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.14.2.144.117