Dependency Parsing Parsing Algorithms Peng.Huang

Outline  Introduction  Phrase Structure Grammar  Dependency Grammar  Comparison and Conve rsion  Dependency Parsing  Formal definition  Parsing Algorithms  Introduction  Dynamic programming  Constraint satisfaction  Deterministic search 2

Introduction  Syntactic Parsing  finding the correct syntactic structure of that sentence in a given formalism/grammar  Two Formalism  Dependency Parsing (DG)  Phrase Structure Grammar (PSG) 3

Phrase Structure Grammar (PSG)  Breaks sentence into constituents (phrases)  Which are then broken into smaller constituents  Describes phrase structure, clause structure  E.g.. NP, PP, VP etc..  Structures often recursive  The clever tall blue-eyed old … man 4

Tree Structure 5

Dependency Grammar  Syntactic structure consists of lexical items, linked by binary asymmetric relations called dependencies  Interested in grammatical relations between individual words (governing & dependent words)  Does not propose a recursive structure  Rather a network of relations  These relations can also have labels 6

Comparison Dependency structures explicitly represent –Head-dependent relations (directed arcs) –Functional categories (arc labels) –Possibly some structural categories (parts-of-speech) Phrase structure explicitly represent –Phrases (non-terminal nodes) –Structural categories (non-terminal labels) –Possibly some functional categories (grammatical functions) 7

Conversion … PSG to DG  Head of a phrase governs/dominates all the siblings  Heads are calculated using heuristics  Dependency relations are established between the head of each phrase as the parent and its siblings as children  The tree thus formed is the unlabeled dependency tree 8

PSG to DG 9

Conversion … DG to PSG  Each head together with its dependents (and their dependents) forms a constituent of the sentence  Difficult to assign the structural categories (NP, VP, S, PP etc…) to these derived constituents  Every projective dependency grammar has a strongly equivalent context-free grammar, but not vice versa [Gaifman 1965] 10

Outline  Introduction  Phrase Structure Grammar  Dependency Grammar  Comparison and Conve rsion  Dependency Parsing  Formal definition  Parsing Algorithms  Introduction  Dynamic programming  Constraint satisfaction  Deterministic search 11

Dependency Tree  Formal definition –An input word sequence w 1 …w n –Dependency graph D = (W,E) where  W is the set of nodes i.e. word tokens in the input seq  E is the set of unlabeled tree edges (w i, w j ) (w i, w j є W)  (w i, w j ) indicates an edge from w i (parent) to w j (child)  Formal definition Task of mapping an input string to a dependency graph satisfying certain conditions is called dependency parsing 12

Well-formedness  A dependency graph is well-formed iff  Single head: Each word has only one head  Acyclic: The graph should be acyclic  Connected: The graph should be a single tree with all the words in the sentence Projective: If word A depends on word B, then all words between A and B are also subordinate to B (i.e. dominated by B) 13

14 Non-projective dependency tree Ram saw a dog yesterday which was a Yorkshire Terrier * Crossing lines English has very few non-projective cases.

Outline  Introduction  Phrase Structure Grammar  Dependency Grammar  Comparison and Conve rsion  Dependency Parsing  Formal definition  Parsing Algorithms  Introduction  Dynamic programming  Constraint satisfaction  Deterministic search 15

Dependency Parsing (P. Mannem)16 Dependency Parsing Dependency based parsers can be broadly categorized into –Grammar driven approaches Parsing done using grammars. –Data driven approaches Parsing by training on annotated/un-annotated data. May 28, 2008

Well-formedness  A dependency graph is well-formed iff  Single head: Each word has only one head  Acyclic: The graph should be acyclic  Connected: The graph should be a single tree with all the words in the sentence Projective: If word A depends on word B, then all words between A and B are also subordinate to B (i.e. dominated by B) 17

18 Parsing Methods Three main traditions –Dynamic programming CYK, Eisner, McDonald –Constraint satisfaction Maruyama, Foth et al., Duchier –Deterministic search Covington, Yamada and Matsumuto, Nivre

Dynamic Programming  Basic Idea: Treat dependencies as constituents  Use, e.g., CYK parser (with minor modifications) 19

Eisner 1996  Two novel aspects:  Modified parsing algorithm  Probabilistic dependency parsing  Time requirement: O(n 3 )  Modification: Instead of storing subtrees, store spans  Span: Substring such that no interior word links to any word outside the span  Idea: In a span, only the boundary words are active, i.e. still need a head or a child 20

21 Re d figure s onon th e scree n indicat ed fallin g stocks_ROO T_ Example

22 Red figuresonthescreenindicatedfallingstocks_ROOT_ Example indicatedfallingstocks Red figures Spans:

23 Red figuresonthescreenindicatedfallingstocks_ROOT_ Assembly of correct parse Red figures Start by combining adjacent words to minimal spans figureson the

24 Red figuresonthescreenindicatedfallingstocks_ROOT _ Assembly of correct parse Combine spans which overlap in one word; this word must be governed by a word in the left or right span. onthe screen +→ onthescreen

25 Red figuresonthescreenindicatedfallingstocks_ROOT _ Assembly of correct parse Combine spans which overlap in one word; this word must be governed by a word in the left or right span. figure s on +→ thescreenfiguresonthescreen

26 Red figuresonthescreenindicatedfallingstocks_ROOT _ Assembly of correct parse Combine spans which overlap in one word; this word must be governed by a word in the left or right span. Invalid span Red figuresonthescreen

McDonald’s Maximum Spanning Trees  Score of a dependency tree = sum of scores of dependencies  Scores are independent of other dependencies  If scores are available, parsing can be formulated as maximum spanning tree problem  Uses online learning for determining weight vector w 27

McDonald’s Algorithm Score entire dependency tree Online Learning 28

29 Parsing Methods Three main traditions –Dynamic programming CYK, Eisner, McDonald –Constraint satisfaction Maruyama, Foth et al., Duchier –Deterministic search Covington, Yamada and Matsumuto, Nivre

Dependency Parsing (P. Mannem)30 Constraint Satisfaction Uses Constraint Dependency Grammar Grammar consists of a set of boolean constraints, i.e. logical formulas that describe well-formed trees A constraint is a logical formula with variables that range over a set of predefined values Parsing is defined as a constraint satisfaction problem Constraint satisfaction removes values that contradict constraints May 28, 2008

31 Parsing Methods Three main traditions –Dynamic programming CYK, Eisner, McDonald –Constraint satisfaction Maruyama, Foth et al., Duchier –Deterministic search Covington, Yamada and Matsumuto, Nivre

Deterministic Parsing  Basic idea –Derive a single syntactic representation (dependency graph) through a deterministic sequence of elementary parsing actions – Sometimes combined with backtracking or repair 32

Shift-Reduce Type Algorithms Data structures: –Stack [...,w i ]S of partially processed tokens –Queue [w j,...]Q of remaining input tokens Parsing actions built from atomic actions: –Adding arcs (w i → w j, w i ← w j ) –Stack and queue operations Left-to-right parsing 33

34 Yamada’s Algorithm  Three parsing actions:  Shift [...]S [w i,...]Q  [..., w i ]S [...]Q  Left[..., w i, w j ]S [...]Q  [..., w i ]S [...]Q w i → w j  Right[..., w i, w j ]S [...]Q  [..., w j ]S [...]Q w i ← w j  Multiple passes over the input give time complexity O(n 2 )

35 Yamada and Matsumoto Parsing in several rounds: deterministic bottom-up O(n 2 ) Looks at pairs of words 3 actions: shift, left, right Shift: shifts focus to next word pair

36 Yamada and Matsumoto Right: decides that the right word depends on the left word  Left: decides that the left word depends on the right one

37 Nivre’s Algorithm Four parsing actions: Shift[...]S [w i,...]Q [..., w i ]S [...]Q Reduce[..., w i ]S [...]Q Эw k : w k → w i [...]S [...]Q Left-Arc[..., w i ]S [w j,...]Q ¬Эw k : w k → w i [...]S [w j,...]Q w i ← w j Right-Arc [...,w i ]S [w j,...]Q ¬Эw k : w k → w j [..., w i, w j ]S [...]Q w i → w j

Dependency Parsing (P. Mannem)38 Nivre’s Algorithm Characteristics: –Arc-eager processing of right-dependents –Single pass over the input gives time worst case complexity O(2n) May 28, 2008

39 Red figuresonthescreenindicatedfallingstocks_ROOT_ Example SQ

40 Red figuresonthescreenindicatedfallingstocks_ROOT _ Example SQ Shift

41 Red figuresonthescreenindicatedfallingstocks_ROOT _ Example SQ Left-arc

42 Red figuresonthescreenindicatedfallingstocks_ROOT _ Example SQ Shift

43 Red figuresonthescreenindicatedfallingstocks_ROOT _ Example SQ Right-arc

44 Red figuresonthescreenindicatedfallingstocks_ROOT _ Example SQ Shift

45 Red figureson the screenindicatedfallingstocks_ROOT _ Example SQ Left-arc

46 Red figureson the screenindicatedfallingstocks_ROOT _ Example SQ Right-arc

47 Red figureson thescreen indicatedfallingstocks_ROOT _ Example SQ Reduce

48 Red figures onthescreen indicatedfallingstocks_ROOT _ Example SQ Reduce

49 Red figuresonthescreen indicatedfallingstocks_ROOT _ Example SQ Left-arc

50 Red figure s onthescreen indicatedfallingstocks_ROOT _ Example SQ Right-arc

51 Red figure s onthescreen indicatedfallingstocks_ROOT _ Example SQ Shift

52 Red figuresonthescreen indicated falling stocks_ROOT _ Example SQ Left-arc

53 Red figuresonthescreen indicated falling stocks_ROOT _ Example SQ Right-arc

54 Red figuresonthescreen indicated fallingstocks _ROOT _ Example SQ Reduce

55 Red figuresonthescreenindicate d fallingstocks _ROOT _ Example SQ Reduce

The End QAQA 56