✬ ✩ Introduction to Natural Language Processing PARSING: Earley, Bottom-Up Chart Parsing Jean-C´ edric Chappelier Jean-Cedric.Chappelier@epfl.ch Artificial Intelligence Laboratory ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 1/20 I&C J.-C. Chappelier
✬ ✩ Objectives of this lecture ➥ After CYK algorithm, present two other algorithms used for syntactic parsing ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 2/20 I&C J.-C. Chappelier
✬ ✩ Earley Parsing Bottom-up = inference Top-down algorithm(predictive) Top-down = search 3 advantages: ✌ best known worst-case complexity (as CYK) ✌ adaptive complexity for least complex languages (e.g. regular languages) ✌ No need for a special form of the CF grammar 2 drawbacks : ➷ No way to correct/reconstruct non-parsable sentences (”early error detection”) ➷ not very intuitive ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 3/20 I&C J.-C. Chappelier
✬ ✩ Earley Parsing (2) Idea: on-line (i.e during parsing) binarization of the grammar ☞ doted rules and ”Earley items” doted rules: X → X 1 ...X k • X k +1 ...X m with X → X 1 ...X m a rule of the grammar Earley item: one doted rule with one integer i ( 0 ≤ i ≤ n , n : size of the input string) ☞ the part before the dot ( • ) represents the subpart of the rule that derives a substring of the input string starting at position i + 1 Example: ( VP → V • NP, 2) is an Earley item for input string the cat ate a mouse 1 2 3 4 5 ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 4/20 I&C J.-C. Chappelier
✬ ✩ Earley Parsing (3) Principle: Starting from all possible ( S → • X 1 ... X m , 0) , parallel construction of all the dotted rules deriving (larger and larger) substrings of the input string, up to a point where the whole input sentence is derived ☞ construction of sets of items ( E j ) such that: ( X → α • β, i ) ∈ E j ⇐ ⇒ ∃ γ, δ : S ⇒ ∗ γ X δ γ ⇒ ∗ w 1 ... w i α ⇒ ∗ w i +1 ... w j and and Example: in the former example ( VP → V • NP, 2) ∈ E 3 The input string (length n ) is syntactically correct (accepted) iff at least one ( S → X 1 ... X m • , 0) is in E n ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 5/20 I&C J.-C. Chappelier
✬ ✩ Earley Parsing (4) ➊ Initialization: construction of E 0 1. For each rule S → X 1 ... X m in the grammar: add ( S → • X 1 ... X m , 0) to E 0 2. For each ( X → • Y β, 0) in E 0 and every rule Y → γ , add ( Y → • γ, 0) to E 0 3. Iterate (2) until convergence of E 0 ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 6/20 I&C J.-C. Chappelier
✬ ✩ Earley Parsing: Interpretation ➋ Iterations: building of derivations of w 1 ...w j ( E j ) 1. Linking with words : Introduce word w j whenever a derivation of w 1 ...w j − 1 can ”eat” w j (i.e. ” there is a • before w j ”) 2. Stepping in the derivation : Whenever non-terminal X can derive a subsequence starting at w i +1 and if there exists one subderivation ending in w i which can ”eat” X , do it! 3. Prediction (of useful items): If at some place Y could be ”eaten” by some rule, then introduce all the rules that might (later on) produce Y ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 7/20 I&C J.-C. Chappelier
✬ ✩ Earley Parsing (next) ➋ Iterations: construction of the E j sets ( 1 ≤ j ≤ n ) 1. for all ( X → α • w j β, i ) in E j − 1 , add ( X → α w j • β, i ) to E j 2. For all ( X → γ • , i ) of E j , for all ( Y → α • Xβ, k ) of E i , add ( Y → α X • β, k ) to E j 3. For all ( Y → α • Xβ, i ) in E j and for each rule X → γ , add ( X → • γ, j ) to E j 4. Repeat to (2) while E j keeps changing ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 8/20 I&C J.-C. Chappelier
✬ ✩ Earley Parsing: Full Example Example for ” I think ”, and the grammar: S → NP VP Pron → I NP → Pron V → think NP → Det N VP → V VP → V S VP → V NP ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 9/20 I&C J.-C. Chappelier
✬ ✩ E 0 : ( S → • NP VP, 0) ( NP → • Pron, 0) ( NP → • Det N, 0) ( Pron → • I , 0) E 1 : ( Pron → I • , 0) ( NP → Pron • , 0) ( S → NP • VP, 0) ( VP → • V, 1) ( VP → • V P, 1) ( VP → • V NP, 1) ( V → • think , 1) E 2 : ( V → think • , 1) ( VP → V • , 1) ( VP → V • S, 1) ( VP → V • NP, 1) ( S → NP VP • , 0) ( S → • NP VP, 2) ( NP → • Pron, 2) ( NP → • Det N, 2) ( Pron → • I , 2) ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 10/20 I&C J.-C. Chappelier
✬ ✩ Link between CYK and Earley ( X → α • β, i ) ∈ E j ⇐ ⇒ ( X → α • β ) ∈ cell j − i, i +1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( S → NP VP • , 0) ( S → NP • VP, 0) ( VP → V • S, 1) ( VP → V • NP, 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( NP → Pron • , 0) ( VP → V • , 1) ( Pron → I • , 0) ( V → think • , 1) ( S → • NP VP, 0) ( VP → • V, 1) ( S → • NP VP, 2) ( NP → • Pron, 0) ( VP → • V S, 1) ( NP → • N, 2) ( NP → • Det N, 0) ( VP → • V NP, 1) ( NP → • Det N, 2) ( Pron → • I , 0) ( V → • think , 1) ( Pron → • I , 2) I think ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 11/20 I&C J.-C. Chappelier
✬ ✩ Bottom-up Chart Parsing Idea: keep the best of both CYK and Earley ☞ on-line binarization ”` a la” Earley (and even better) within a bottom-up CYK-like algorithm Mainly: • no need for indices in items: cell position is enough • factorize (with respect to α ) all the X → α • β α • ... ☞ This is possible when processing bottom-up • replace all the X → α • simply by X • supression of X → • α This is possible when processing bottom-up (and without lookahead) ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 12/20 I&C J.-C. Chappelier
✬ ✩ Bottom-up Chart Parsing: Example S S VP ... ... NP NP �� �� �� �� NP NP ... �� �� ... ... Det V Det �� �� � � Det N V VP Det N The crocodile ate the cat ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 13/20 I&C J.-C. Chappelier
✬ ✩ Bottom-up Chart Parsing (3) More formally, a CYK algorithm in which: If cell contents are denoted by [ α • ..., i, j ] and [ X, i, j ] respectively Then initialization is w ij ⇒ [ X, i, j ] for X → w ij ∈ R and the completion phase becomes: (association of two cells) [ α X • ..., i + k, j ] if Y → α Xβ ∈ R [ α • ..., i, j ] ⊕ [ X, k, j + i ] ⇒ if Y → α X ∈ R [ Y, i + k, j ] (”self-filling”) [ X • ..., i, j ] if Y → Xβ ∈ R [ X, i, j ] ⇒ if Y → X ∈ R [ Y, i, j ] ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 14/20 I&C J.-C. Chappelier
✬ ✩ Bottom-up Chart Parsing: Example Det N V Det N dog The hate the cat Initialization: ... ... ... Det Det V Det N V VP Det N dog The hate the cat k �� �� �� �� �� �� Completion: �� �� �� �� �� �� k ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 15/20 I&C J.-C. Chappelier
✬ ✩ S S VP � � � � ... ... NP NP � � � � NP NP ... �� �� �� �� ... ... Det V Det �� �� �� �� �� �� Det N V NP Det N The crocodile ate the cat ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 16/20 I&C J.-C. Chappelier
✬ ✩ Dealing with compounds Example on how to deal with compouds during initialization phase: N N V N credit card ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 17/20 I&C J.-C. Chappelier
✬ ✩ Complexity still in O ( n 3 ) What coefficient for n 3 ? (with respect to grammar parameters) m ( R ′ ) · |NT | · n 3 where m ( R ′ ) the number of internal nodes of the trie of the right-hand sides of the non-lexical grammar rules NT : the set of non-terminals R ′ : the set of non-lexical grammar rules ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 18/20 I&C J.-C. Chappelier
✬ ✩ Keypoints ➟ The way algorithms work (Earley items, linking, stepping, prediction, link CYK-Earley) ➟ worst-case complexity O ( n 3 ) ➟ Advantages and drawbacks of algorithms ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 19/20 I&C J.-C. Chappelier
✬ ✩ References [1] D. Jurafsky & J. H. Martin, Speech and Language Processing , pp. 377-385, Prentice Hall, 2000. [2] R. Dale, H. Moisi, H. Somers, Handbook of Natural Language Processing , pp. 69-73, Dekker, 2000. ✫ ✪ M. Rajman LIA Introduction to Natural Language Processing (CS-431) 20/20 I&C J.-C. Chappelier
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