On the non-efficient PAC learnability of conjunctive queries
This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting...
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Elsevier B.V
01.01.2024
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| Abstract | This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of acyclicity; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.
•Conjunctive Queries (CQs) are known to be not efficiently PAC learnable. We give a self-contained exposition.•Acyclic CQs are not efficiently PAC learnable, even for very restrictive notions of acyclicity.•Conjunctive Queries (CQs), and Unions of Conjunctive Queries (UCQs), are efficiently PAC learnable with membership queries. |
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| AbstractList | This note serves three purposes: (i) we provide a self-contained exposition of the fact that conjunctive queries are not efficiently learnable in the Probably-Approximately-Correct (PAC) model, paying clear attention to the complicating fact that this concept class lacks the polynomial-size fitting property, a property that is tacitly assumed in much of the computational learning theory literature; (ii) we establish a strong negative PAC learnability result that applies to many restricted classes of conjunctive queries (CQs), including acyclic CQs for a wide range of notions of acyclicity; (iii) we show that CQs (and UCQs) are efficiently PAC learnable with membership queries.
•Conjunctive Queries (CQs) are known to be not efficiently PAC learnable. We give a self-contained exposition.•Acyclic CQs are not efficiently PAC learnable, even for very restrictive notions of acyclicity.•Conjunctive Queries (CQs), and Unions of Conjunctive Queries (UCQs), are efficiently PAC learnable with membership queries. |
| ArticleNumber | 106431 |
| Author | ten Cate, Balder Funk, Maurice Jung, Jean Christoph Lutz, Carsten |
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| Keywords | Computational learning theory Databases Inductive logic programming Conjunctive queries |
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