Towards Schema-Guided XML Query Induction

Transcription

1 Towards Schema-Guided XML Query Induction Jérôme Champavère Rémi Gilleron Aurélien Lemay Joachim Niehren Université de Lille INRIA, France ICML-2007 Workshop on Challenges and Applications of Grammar Induction June 24, 2007 J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 1/36

2 Query on XML Documents Introduction J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 2/36

3 Query on XML Documents Introduction The query is to extract the name-function pair list of this web page. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 2/36

4 Query on XML Documents Introduction Name Function L. Pauling Chemist M. Groening Cartoonist The query is to extract the name-function pair list of this web page. The result can be put in a regular database. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 2/36

5 Tree View for Queries Introduction TABLE TH TH TD TD TD TD Name Function L. Pauling Chemist M. Groening Cartoonist J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 3/36

6 Tree View for Queries Introduction TABLE TH TH TD TD TD TD Name Function L. Pauling Chemist M. Groening Cartoonist J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 3/36

7 Tree View for Queries Introduction TABLE TH TH TD TD TD TD Name Function L. Pauling Chemist M. Groening Cartoonist J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 3/36

8 Introduction Query Induction Representation of Queries Programs: C, Perl,... Ad hoc formalisms: XPath, XQuery,... Other formalisms: relational algebra, MSO formula,... Conception of Queries Hand-made: hard, error-prone, need for expert With visual tools: like Lixto [Gottolb, Koch 2000], still not easy Automatically induced: users just give some examples of wanted information J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 4/36

9 Introduction Query Induction Representation of Queries Programs: C, Perl,... Ad hoc formalisms: XPath, XQuery,... Other formalisms: relational algebra, MSO formula,... Conception of Queries Hand-made: hard, error-prone, need for expert With visual tools: like Lixto [Gottolb, Koch 2000], still not easy Automatically induced: users just give some examples of wanted information Our approach: Queries are represented by tree automata, and inferred by an RPNI-like algorithm. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 4/36

10 Introduction Schema-guided Induction The learning task faces some challenges. Very few examples obtained from users All available information has to be used The schema is such information (DTD, XML Schema, Relax NG,...) We investigate here how this information can be used for query induction. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 5/36

11 Introduction 1 Queries over XML Documents 2 Schema-guided Learning 3 Efficient Inclusion Checking 4 Learning from Partially Annotated Examples J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 6/36

12 Outline Queries over XML Documents 1 Queries over XML Documents 2 Schema-guided Learning 3 Efficient Inclusion Checking 4 Learning from Partially Annotated Examples J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 7/36

13 Queries over XML Documents Query as Tree Language Consider the monadic query extracting names. Two equivalent views: Function from trees to annotated trees Language of correctly annotated trees TABLE TABLE TH TH TD TD TH TH TD TD TD TD TABLE TABLE TH TH TD TD TD TD TD TD TH TH TH TD TD TD This language is functional. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 8/36

14 Queries over XML Documents Node Selecting Tree Transducers (NSTTs) Queries represented by tree automata (regular queries). 4 TABLE TH 3 TD TD+ 2 1 Represented here as string automata In fact, classical tree automata operating on Curried encoding J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 9/36

15 Queries over XML Documents Node Selecting Tree Transducers (NSTTs) Queries represented by tree automata (regular queries). 4 TABLE TABLE TH 3 TD TD+ 2 TH TH TD+ TD TD+ TD 1 Represented here as string automata In fact, classical tree automata operating on Curried encoding J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 9/36

16 Queries over XML Documents Node Selecting Tree Transducers (NSTTs) Queries represented by tree automata (regular queries). 4 TABLE TABLE 5 TH TD TD+ 2 TH 3 TH 3 TD+2 TD 1 TD+2 TD 1 1 Represented here as string automata In fact, classical tree automata operating on Curried encoding J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 9/36

17 Queries over XML Documents Answering Queries Find the proper boolean annotation At most one possible annotation (functionality of queries) TABLE TH TH TD TD TD TD J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 10/36

18 Queries over XML Documents Answering Queries Find the proper boolean annotation At most one possible annotation (functionality of queries) TABLE TH TH TD+ TD TD+ TD Query answering: O( t A ) J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 10/36

19 Queries over XML Documents How To Learn Queries NSTTs are tree automata Can be learned using RPNI [Oncina & García, 1993] One difference: no negative examples, use of functionality instead J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 11/36

20 Query Induction Issues Queries over XML Documents Theoretical results Theoretical characteristic sample: more than 1000 trees Availability: about 3 trees In practice Works on monadic queries with heuristics More complicated for n-ary queries Main difficulty: very few examples, leads to wrong generalizations Generalizations out of the domain Use of domain knowledge allows to avoid them J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 12/36

21 Outline Schema-guided Learning 1 Queries over XML Documents 2 Schema-guided Learning 3 Efficient Inclusion Checking 4 Learning from Partially Annotated Examples J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 13/36

22 Schema-guided Learning Schema: A Domain for Queries Schemas: languages describing valid documents For XML: DTD, XSD, Relax NG HTML has a DTD Subclasses of regular tree languages J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 14/36

23 Schema-guided Learning Schema: A Domain for Queries Schemas: languages describing valid documents For XML: DTD, XSD, Relax NG HTML has a DTD Subclasses of regular tree languages Queries can be encompassed by schemas represented by tree automata. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 14/36

24 Schema-guided Learning Origin of Schemas Schemas can be either given or inferred: Given: DTD of HTML typically Inferred: DTD inference algorithm Advantage: more precise than the DTD of HTML But more difficult to obtain J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 15/36

25 Schema-guided Learning Using Schema Typing bias [Coste et al., 2004] States are typed according to a typing automaton from the domain Only states of the same type are merged Goal: constrain the structure of inferred automata For us, the form of the automaton doesn t matter, whereas language does. Inclusion We use inclusion into schema to prevent wrong generalizations. Inferred automata should satisfy the DTD at each step Domain bias [Coste et al., 2004] Use of complement as negative examples Promising experimental results J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 16/36

26 Schema-guided Learning Learning with Inclusion Checking Schema-guided RPNI Input: Sample and schema Run RPNI as usual and test inclusion at each step Output: NSTT J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 17/36

27 Schema-guided Learning Learning with Inclusion Checking Schema-guided RPNI Input: Sample and schema Run RPNI as usual and test inclusion at each step Output: NSTT Need for an efficient inclusion test. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 17/36

28 Outline Efficient Inclusion Checking 1 Queries over XML Documents 2 Schema-guided Learning 3 Efficient Inclusion Checking 4 Learning from Partially Annotated Examples J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 18/36

29 Inclusion Test Principle Efficient Inclusion Checking Deterministic DTD over Σ Linear transformation into deterministic tree automaton D [Brüggemann-Klein & Wood, 1998] c <!ELEMENT TABLE ( ) > <!ELEMENT (TH,TH TD,TD)> <!ELEMENT TH (#PCDATA)> <!ELEMENT TD (#PCDATA)> TABLE Current hypothesis NSTT over Σ Bool (i.e. annotated) Projection onto Σ: tree automaton A L(A) L(D) t L(A) L(D) C TH TD d b a b a b a c J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 19/36

30 Efficient Inclusion Checking Classical Method Complete D Compute D C Compute A D C Check that A D C has no accessible final state. L(A) L(D) L(A D C ) = J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 20/36

31 Efficient Inclusion Checking Classical Method Complete D Compute D C Compute A D C Check that A D C has no accessible final state. L(A) L(D) L(A D C ) = Time complexity in O( A Σ D 2 ) because of complement of D computation, which needs D to be complete. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 20/36

32 Efficient Inclusion Checking Our Approach for Testing Inclusion Avoid the complement of D computation Accessibility in A D instead of A D C Detection of one inclusion failure: Failure 1: problem with initial rules Failure 2: problem with internal rules Failure 3: problem with final states Proposition: Inclusion L(A) L(D) fails if and only if one of the tree failure conditions occurs. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 21/36

33 Failure 1 Efficient Inclusion Checking No TH in the DTD: automaton A has a rule TH 3 whereas automaton D has no state q such that TH q. 4 TABLE TH TABLE c d b b c TD TD 2 TD b 1 Time complexity in O( states(a) states(d) ). J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 22/36

34 Failure 3 Efficient Inclusion Checking Trees evaluated in (5, d) by A D with 5 final in A but d not final in D. 4 TABLE TH TD TD TABLE TD TH c d b a b a b a c 1 Time complexity in O( A D ), i.e. time to compute accessible states of A D. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 23/36

35 Failure 2 Efficient Inclusion Checking Accessible states (3,c) and (2,a) Rule in A No rule c a X in D (4,X) TD(2,b) TH(1,a) TH TD 2 1 1,2 1,2 3 4 We look for such configurations during computation of accessible states of A D, without enumerating all states of A D. TH TD b a b a c b a d J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 24/36

36 Efficient Inclusion Checking Complexity Considerations Failure 2 Naive approach in O( A 2 D 2 ) Algorithmic trick leads to O( A D ) J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 25/36

37 Efficient Inclusion Checking Complexity Considerations Failure 2 Naive approach in O( A 2 D 2 ) Algorithmic trick leads to O( A D ) Theorem: Inclusion L(A) L(D) can be computed in O( A D ) when D is deterministic. Corollary: Runtime of schema-guided RPNI is O( S 3 D ) where S is a sample of positive examples and D a schema. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 25/36

38 Outline Learning from Partially Annotated Examples 1 Queries over XML Documents 2 Schema-guided Learning 3 Efficient Inclusion Checking 4 Learning from Partially Annotated Examples J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 26/36

39 Learning from Partially Annotated Examples Limitations of Completely Annotated Examples Until now, input: completely annotated documents. Two main problems: Time consuming J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 27/36

40 Learning from Partially Annotated Examples Limitations of Completely Annotated Examples Until now, input: completely annotated documents. Two main problems: Time consuming J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 27/36

41 Learning from Partially Annotated Examples Limitations of Completely Annotated Examples Until now, input: completely annotated documents. Two main problems: Time consuming Whole document considered J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 27/36

42 Learning from Partially Annotated Examples Limitations of Completely Annotated Examples Until now, input: completely annotated documents. Two main problems: Time consuming Whole document considered Solution: pruning trees [Carme et al., 2007] J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 27/36

43 Principle of Pruning Learning from Partially Annotated Examples Input: set of partially annotated trees. TABLE TH TH TD TD TD+ TD TD TD J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 28/36

44 Learning from Partially Annotated Examples Principle of Pruning Input: set of partially annotated trees. Our strategy: We prune subtrees not on a path of selected nodes as they are irrelevant or unannotated. TABLE TD+ J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 28/36

45 Learning from Partially Annotated Examples Principle of Pruning Input: set of partially annotated trees. Our strategy: We prune subtrees not on a path of selected nodes as they are irrelevant or unannotated and annotate negatively the rest. TABLE TD+ J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 28/36

46 Learning from Partially Annotated Examples Principle of Pruning Input: set of partially annotated trees. Our strategy: We prune subtrees not on a path of selected nodes as they are irrelevant or unannotated and annotate negatively the rest. TABLE TD+ We obtain completely annotated pruned trees. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 28/36

47 Learning from Partially Annotated Examples Learning with Pruning Using RPNI: First we prune, then we learn No functionality anymore, but cut-functionality Output: NSTT recognizing completely annotated pruned tree languages J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 29/36

48 Learning from Partially Annotated Examples Answering Queries Using Pruned NSTT TABLE TABLE TD+ TD+ 2 1 TH TH TABLE TD TD TD TD TD TD Find consistent pruned trees can be replaced by any subtree Answer in O( t A ) J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 30/36

49 Learning from Partially Annotated Examples Answering Queries Using Pruned NSTT TABLE TABLE TD+ TD+ 2 1 TH TH TABLE TD TD TD+ TD TD TD Find consistent pruned trees can be replaced by any subtree Answer in O( t A ) J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 30/36

50 Learning from Partially Annotated Examples Answering Queries Using Pruned NSTT TABLE TABLE TD+ TD+ 2 1 TH TH TABLE TD TD TD+ TD TD+ TD Find consistent pruned trees can be replaced by any subtree Answer in O( t A ) J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 30/36

51 Learning from Partially Annotated Examples Answering Queries Using Pruned NSTT TABLE TABLE TD+ TD+ 2 1 TH TH TABLE TD+ TD TD+ TD TD+ TD Find consistent pruned trees can be replaced by any subtree Answer in O( t A ) J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 30/36

52 Learning from Partially Annotated Examples Answering Queries Using Pruned NSTT TABLE TABLE TD+ TD+ 2 1 TH TH TABLE TD+ TD TD+ TD TD+ TD Find consistent pruned trees can be replaced by any subtree Answer in O( t A ) J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 30/36

53 Learning from Partially Annotated Examples Flaws of Pruned NSTT The previous pruning technique cannot be used with schema inclusion This tree for instance can be annotated: TABLE TABLE TH TH TH TD TD TD TD TD TD+ J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 31/36

54 Learning from Partially Annotated Examples Flaws of Pruned NSTT The previous pruning technique cannot be used with schema inclusion This tree for instance can be annotated: TABLE TABLE TH TH TH TD TD TD TD+ TD TD+ J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 31/36

55 Learning from Partially Annotated Examples Flaws of Pruned NSTT The previous pruning technique cannot be used with schema inclusion This tree for instance can be annotated: TABLE TABLE TH TH TH TD TD TD TD+ TD TD+ But it doesn t satisfy the DTD! J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 31/36

56 Schema-guided Pruning Learning from Partially Annotated Examples Trees are pruned using states of the DTD instead of. c TABLE TD d b b a b a c TH a TABLE TH TH TD TD TD+ TD TD TD J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 32/36

57 Schema-guided Pruning Learning from Partially Annotated Examples Trees are pruned using states of the DTD instead of. c TABLE TD d b b a b a c TH a TABLEd c c c c THa THa TDb TDb TD+b TDb TDb TDb J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 32/36

58 Schema-guided Pruning Learning from Partially Annotated Examples Trees are pruned using states of the DTD instead of. c TABLE TD d b b a b a c TH a TABLE c c TD+ a c J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 32/36

59 Schema-guided Pruning Learning from Partially Annotated Examples Trees are pruned using states of the DTD instead of. c TABLE TD d b b a b a c TH a TABLE c c c TD+ a J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 32/36

60 Query Answering with Schema-guided Pruning Learning from Partially Annotated Examples Same as before, except that states are replaced by consistent subtrees. TABLE TABLE c c c TD+ b TH TH TD TD TD+ Match. TD TD TD TABLE TH TH TH TD TD TD TD TD Do not match. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 33/36

61 Learning from Partially Annotated Examples Schema-guided Learning with Pruning Schema-guided RPNI with Pruning Input: Set of partially annotated trees and schema Prune the trees w.r.t. the schema Run RPNI with inclusion test Output: NSTT operating on trees pruned w.r.t. the schema J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 34/36

62 Learning from Partially Annotated Examples Conclusion Summary Use of inclusion test in query induction New efficient inclusion checking algorithm Schema-guided pruning Work in Progress Experiments Adaptation to n-ary queries (especially pruning) J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 35/36

63 References Learning from Partially Annotated Examples Brüggemann-Klein, A., & Wood, D. (1998). One-unambiguous regular languages. Information and Computation, 142, Carme, J., Gilleron, R., Lemay, A., & Niehren, J. (2007). Interactive learning of node selecting tree transducers. Machine Learning, 66, Coste, F., Fredouille, D., Kermovant, C., & de la Higuera, C. (2004). Introducing domain and typing bias in automata inference. Proceedings of the 7th ICGI (pp ). Springer Verlag. Oncina, J., & García, P. (1993). Inference of recognizable tree sets (Technical Report). Departamento de Sistemas Informáticos y Computación, Universidad de Alicante. DSIC-II/47/93. J. Champavère, R. Gilleron, A. Lemay, J. Niehren Towards Schema-Guided XML Query Induction CAGI07 36/36