Projective DNF Formulae and Their Revision

Sloan, Robert H.; Szörényi, Balázs; Turán, György

doi:10.1007/978-3-540-45167-9_45

Cited by 4 publications

(4 citation statements)

References 15 publications

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“…Additional results on revising various forms of DNF formulas may be found in our companion paper [30]. Work on revising Valiant's class of projective DNF functions [53] may be found in Sloan et al [49].…”

Section: Discussionmentioning

confidence: 99%

Theory revision with queries: Horn, read-once, and parity formulas

Goldsmith

Sloan

Szörényi

et al. 2004

Artificial Intelligence

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A theory, in this context, is a Boolean formula; it is used to classify instances, or truth assignments. Theories can model real-world phenomena, and can do so more or less correctly. The theory revision, or concept revision, problem is to correct a given, roughly correct concept. This problem is considered here in the model of learning with equivalence and membership queries. A revision algorithm is considered efficient if the number of queries it makes is polynomial in the revision distance between the initial theory and the target theory, and polylogarithmic in the number of variables and the size of the initial theory. The revision distance is the minimal number of syntactic revision operations, such as the deletion or addition of literals, needed to obtain the target theory from the initial theory. Efficient

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Section: Discussionmentioning

confidence: 99%

Theory revision with queries: Horn, read-once, and parity formulas

Goldsmith

Sloan

Szörényi

et al. 2004

Artificial Intelligence

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“…After all it is one of the most successful tools for learning threshold functions. Furthermore, previously it has been successfully used for revision (see, e.g., [18,19]). The answer is simple and somewhat surprising: under our settings, using Winnow as defined in [10] would result in an inefficient revision algorithm.…”

Section: Lower Bounds and An Open Problemmentioning

confidence: 99%

“…The theoretical study of revision algorithms was initiated by Mooney [12] in the PAC framework. We have studied revision algorithms in the model of learning with equivalence and membership queries [5,6] and in the mistake-bound model [19]. Formal definitions for query model learning, that is, learning from equivalence and membership queries [1], are given in Section 2.…”

Section: Introductionmentioning

confidence: 99%

“…We have also given revision algorithms (with both types of revisions) for two other classes that have attribute-efficient learning algorithms: for parity functions in [6] and for projective DNF in [19]. Projective DNF is a class of DNF introduced by Valiant [23], as a special case of his projective learning model, and as part of a framework to formulate expressive and biologically plausible learning models.…”

Section: Introductionmentioning

confidence: 99%

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Revising threshold functions

Sloan

Szörényi

Turán

2007

Theoretical Computer Science

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A revision algorithm is a learning algorithm that identifies the target concept, starting from an initial concept. Such an algorithm is considered efficient if its complexity (in terms of the resource one is interested in) is polynomial in the syntactic distance between the initial and the target concept, but only polylogarithmic in the number of variables in the universe. We give an efficient revision algorithm in the model of learning with equivalence and membership queries for threshold functions, and some negative results showing, for instance, that threshold functions cannot be revised efficiently from either type of query alone. The algorithms work in a general revision model where both deletion and addition type revision operators are allowed.

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