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R98922004 Yun-Nung Chen 資工碩一 陳縕儂 1 /39

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Non-projective Dependency Parsing using Spanning Tree Algorithms (HLT/EMNLP 2005) Ryan McDonald, Fernando Pereira, Kiril Ribarov, Jan Hajic 2 /39

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Each word depends on exactly one parent Projective Words in linear order, satisfying ▪ Edges without crossing ▪ A word and its descendants form a contiguous substring of the sentence 4 /39

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English Most projective, some non-projective Languages with more flexible word order Most non-projective ▪ German, Dutch, Czech 5 /39

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Related work relation extraction machine translation 6 /39

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Dependency parsing can be formalized as the search for a maximum spanning tree in a directed graph 7 /39

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sentence: x = x 1 … x n the directed graph G x = ( V x, E x ) given by dependency tree for x: y the tree G y = ( V y, E y ) V y = V x E y = {(i, j), there’s a dependency from x i to x j } 9 /39

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scores of edges score of a dependency tree y for sentence x 10 /39

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11 /39 x = John hit the ball with the bat root hit Johnball the with bat the y1y1 root ball Johnhit the with batthe y2y2 root John ball hit the with batthe y3y3

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1) How to decide weight vector w 2) How to find the tree with the maximum score 12 /39

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dependency trees for x = spanning trees for G x the dependency tree with maximum score for x = maximum spanning trees for G x 13 /39

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Input: graph G = (V, E) Output: a maximum spanning tree in G greedily select the incoming edge with highest weight ▪ Tree ▪ Cycle in G contract cycle into a single vertex and recalculate edge weights going into and out the cycle 15 /39

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x = John saw Mary 16 /39 saw root John Mary 9 30 10 20 9 3 30 11 0 GxGx

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For each word, finding highest scoring incoming edge 17 /39 saw root John Mary 9 30 10 20 9 3 30 11 0 GxGx

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If the result includes Tree – terminate and output Cycle – contract and recalculate 18 /39 saw root John Mary 9 30 10 20 9 3 30 11 0 GxGx

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Contract and recalculate ▪ Contract the cycle into a single node ▪ Recalculate edge weights going into and out the cycle 19 /39 saw root John Mary 9 30 10 20 9 3 30 11 0 GxGx

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Outcoming edges for cycle 20 /39 saw root John Mary 9 30 10 9 3 11 0 GxGx 20 30

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Incoming edges for cycle, 21 /39 saw root John Mary 9 30 10 9 11 0 GxGx 20 30

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x = root ▪ s(root, John) – s(a(John), John) + s(C) = 9-30+50=29 ▪ s(root, saw) – s(a(saw), saw) + s(C) = 10-20+50=40 22 /39 saw root John Mary 9 30 10 9 11 0 GxGx 40 29 20 30

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x = Mary ▪ s(Mary, John) – s(a(John), John) + s(C) = 11-30+50=31 ▪ s(Mary, saw) – s(a(saw), saw) + s(C) = 0-20+50=30 23 /39 saw root John Mary 9 30 11 0 GxGx 31 40 30 20 30

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24 /39 saw root John Mary 9 30 GxGx Reserving highest tree in cycle Recursive run the algorithm 31 40 20 30

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25 /39 saw root John Mary 9 30 GxGx Finding incoming edge with highest score Tree: terminate and output 31 40 30

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26 /39 saw root John Mary 30 GxGx Maximum Spanning Tree of G x 30 40 10

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Each recursive call takes O(n 2 ) to find highest incoming edge for each word At most O(n) recursive calls (contracting n times) Total: O(n 3 ) Tarjan gives an efficient implementation of the algorithm with O(n 2 ) for dense graphs 27 /39

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Eisner Algorithm: O(n 3 ) Using bottom-up dynamic programming Maintain the nested structural constraint (non-crossing constraint) 28 /39

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Supervised learning Target: training weight vectors w between two features (PoS tag) Training data: Testing data: x 30 /39

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Margin Infused Relaxed Algorithm (MIRA) dt(x) : the set of possible dependency trees for x 31 /39 keep new vector as close as possible to the old final weight vector is the average of the weight vectors after each iteration

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Using only the single margin constraint 32 /39

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Local constraints correct incoming edge for j other incoming edge for j correct spanning tree incorrect spanning trees More restrictive than original constraints 33 /39 a margin of 1 the number of incorrect edges

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Language: Czech More flexible word order than English ▪ Non-projective dependency Feature: Czech PoS tag standard PoS, case, gender, tense Ratio of non-projective and projective Less than 2% of total edges are non-projective ▪ Czech-A: entire PDT ▪ Czech-B: including only the 23% of sentences with non- projective dependency 35 /39

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COLL1999 The projective lexicalized phrase-structure parser N&N2005 The pseudo-projective parser McD2005 The projective parser using Eisner and 5-best MIRA Single-best MIRA Factored MIRA The non-projective parser using Chu-Liu-Edmonds 36 /39

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Czech-A (23% non-projective) AccuracyComplete 82.8- 80.031.8 83.331.3 84.132.2 84.432.3 37 /39 Czech-B (non-projective) AccuracyComplete -- -- 74.80.0 81.014.9 81.514.3 COLL1999 O(n 5 ) N&N2005 McD2005 O(n 3 ) Single-best MIRA O(n 2 ) Factored MIRA O(n 2 )

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English AccuracyComplete 90.937.5 90.233.2 90.232.3 38 /39 McD2005 O(n 3 ) Single-best MIRA O(n 2 ) Factored MIRA O(n 2 ) English projective dependency trees Eisner algorithm uses the a priori knowledge that all trees are projective

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