Simple translation-invariant concepts are hard to learn:
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Bibliographische Detailangaben
Beteilige Person: Jerrum, Mark 1955- (VerfasserIn)
Format: Buch
Sprache:Englisch
Veröffentlicht: Edinburgh 1991
Schriftenreihe:University <Edinburgh> / Department of Computer Science: CSR 12
Schlagwörter:
Abstract:Abstract: "The concept class TCM of 'translation-closed monomials' was proposed by Maragos and Valiant as a natural starting point for the investigation of the computational complexity of learning translation-invariant concepts. Concepts in TCM are (satisfy assignments to) DNF formulas such as [formula], (over the variables x b0 s, x b1 s, ..., x b4 s) which are generated from a single monomial (conjunction of variables) by cyclically permuting indices, and forming the disjunction of the monomials so formed. Note that concepts in TCM are invariant under cyclic permutations of the variable set. This note investigates the computational complexity of learning TCM concepts within the Valiant (PAC) model
Despite their obvious simplicity, TCM concepts are apparently difficult to learn. Indeed: (i) the concept class TCM is not polynomially learnable unless RP=NP; (ii) TCM is polynomially predictable if the only if the concept class of DNF formulas is polynomially predictable; (iii) TCM is not polynomially predictable from positive examples alone. The second of these results relates the computational complexity of predicting TCM concepts to a well known open problem in computational learning theory.
Umfang:13 S.
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