Simple translation-invariant concepts are hard to learn:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Edinburgh
1991
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| Series: | University <Edinburgh> / Department of Computer Science: CSR
12 |
| Subjects: | |
| 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. |
| Physical Description: | 13 S. |
Staff View
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| 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. | |
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Record in the Search Index
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| id | DE-604.BV010437307 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:54:09Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006955634 |
| oclc_num | 25310678 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 13 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| record_format | marc |
| series2 | University <Edinburgh> / Department of Computer Science: CSR |
| 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 |
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Branch Library Mathematics & Informatics, Reports
| Call Number: |
0111 2001 B 6032-12
Floor plan |
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| Copy 1 | Available for loan On Shelf |