Simple translation-invariant concepts are hard to learn:
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 formula...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Edinburgh
1991
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| Schriftenreihe: | University <Edinburgh> / Department of Computer Science: CSR
12 |
| Schlagworte: | |
| Zusammenfassung: | 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. |
| Beschreibung: | 13 S. |
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| 490 | 1 | |a University <Edinburgh> / Department of Computer Science: CSR |v 12 | |
| 520 | 3 | |a 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 | |
| 520 | 3 | |a 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. | |
| 650 | 7 | |a Computer software |2 sigle | |
| 650 | 7 | |a Mathematical sciences |2 sigle | |
| 650 | 4 | |a Computational complexity | |
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| author | Jerrum, Mark 1955- |
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| id | DE-604.BV010437307 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:52:32Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006955634 |
| oclc_num | 25310678 |
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| physical | 13 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| record_format | marc |
| series2 | University <Edinburgh> / Department of Computer Science: CSR |
| spelling | Jerrum, Mark 1955- Verfasser (DE-588)12443133X aut Simple translation-invariant concepts are hard to learn Edinburgh 1991 13 S. txt rdacontent n rdamedia nc rdacarrier University <Edinburgh> / Department of Computer Science: CSR 12 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. Computer software sigle Mathematical sciences sigle Computational complexity Department of Computer Science: CSR University <Edinburgh> 12 (DE-604)BV008906637 12 |
| spellingShingle | Jerrum, Mark 1955- Simple translation-invariant concepts are hard to learn Computer software sigle Mathematical sciences sigle Computational complexity |
| title | Simple translation-invariant concepts are hard to learn |
| title_auth | Simple translation-invariant concepts are hard to learn |
| title_exact_search | Simple translation-invariant concepts are hard to learn |
| title_full | Simple translation-invariant concepts are hard to learn |
| title_fullStr | Simple translation-invariant concepts are hard to learn |
| title_full_unstemmed | Simple translation-invariant concepts are hard to learn |
| title_short | Simple translation-invariant concepts are hard to learn |
| title_sort | simple translation invariant concepts are hard to learn |
| topic | Computer software sigle Mathematical sciences sigle Computational complexity |
| topic_facet | Computer software Mathematical sciences Computational complexity |
| volume_link | (DE-604)BV008906637 |
| work_keys_str_mv | AT jerrummark simpletranslationinvariantconceptsarehardtolearn |