Corpora and Statistical Methods Lecture 11. Albert Gatt

Transcription

1 Corpora and Statistical Methods Lecture 11 Albert Gatt

2 Part 2 Statistical parsing

3 Preliminary issues How parsers are evaluated

4 Evaluation The issue: what objective criterion are we trying to maximise? i.e. under what objective function can I say that my parser does well (and how well?) need a gold standard Possibilities: strict match of candidate parse against gold standard match of components of candidate parse against gold standard components

5 Evaluation A classic evaluation metric is the PARSEVAL one initiative to compare parsers on the same data not initially concerned with stochastic parsers evaluate parser output piece by piece Main components: compares gold standard tree to parser tree typically, gold standard is the tree in a treebank computes: precision recall crossing brackets

6 PARSEVAL: labeled recall #correct nodes in candidate parse # nodes in treebank parse Correct node = node in candidate parse which: has same node label originally omitted from PARSEVAL to avoid theoretical conflict spans the same words

7 PARSEVAL: labeled precision #correct nodes in candidate parse # nodes in candidate parse The proportion of correctly labelled and correctly spanning nodes in the candidate.

8 Combining Precision and Recall As usual, Precision and recall can be combined into a single F-measure: 1 F 1 1 (1 ) P R

9 PARSEVAL: crossed brackets number of brackets in the candidate parse which cross brackets in the treebank parse e.g. treebank has ((X Y) Z) and candidate has (X (Y Z)) Unlike precision/recall, this is an objective function to minimise

10 Current performance Current parsers achieve: ca. 90% precision >90% recall 1% cross-bracketed constituents

11 Some issues with PARSEVAL 1. These measures evaluate parses at the level of individual decisions (nodes). ignore the difficulty of getting a globally correct solution by carrying out a correct sequence of decisions 2. Success on crossing brackets depends on the kind of parse trees used Penn Treebank has very flat trees (not much embedding), therefore likelihood of crossed brackets decreases. 3. In PARSEVAL, if a constituent is attached lower in a tree than the gold standard, all its daughters are counted wrong.

12 Probabilistic parsing with PCFGs The basic algorithm

13 The basic PCFG parsing algorithm Many statistical parsers use a version of the CYK algorithm. Assumptions: CFG productions are in Chomsky Normal Form. A BC A a Use indices between words: Book the flight through Houston (0) Book (1) the (2) flight (3) through (4) Houston (5) Procedure (bottom-up): Traverse input sentence left-to-right Use a chart to store constituents and their span + their probability.

14 Probabilistic CYK: example PCFG S NP VP [.80] NP Det N [.30] VP V NP [.20] V includes [.05] Det the [.4] Det a [.4] N meal [.01] N flight [.02]

15 Probabilistic CYK: initialisation The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} //syntactic lookup for i = j-2 to 0 do: chart ij := {} for k = i+1 to j-1 do: for each A -> BC do: if B in chart ik & C in chart kj : chart ij := chart ij U {A}

16 Probabilistic CYK: lexical step The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} Det (.4)

17 Probabilistic CYK: lexical step The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} Det (.4) 1 N

18 Probabilistic CYK: syntactic step The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} //syntactic lookup for i = j-2 to 0 do: chart ij := {} for k = i+1 to j-1 do: for each A -> BC do: if B in chart ik & C in chart kj : chart ij := chart ij U {A} Det (.4) NP N

19 Probabilistic CYK: lexical step The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} Det (.4) NP N.02 2 V

20 Probabilistic CYK: lexical step The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} Det (.4) NP N.02 2 V.05 3 Det.4 4 5

21 Probabilistic CYK: syntactic step The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} Det (.4) NP N.02 2 V.05 3 Det.4 4 N.01

22 Probabilistic CYK: syntactic step The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} //syntactic lookup for i = j-2 to 0 do: chart ij := {} for k = i+1 to j-1 do: for each A -> BC do: if B in chart ik & C in chart kj : chart ij := chart ij U {A} Det (.4) NP N.02 2 V.05 3 Det.4 NP N.01

23 Probabilistic CYK: syntactic step The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} //syntactic lookup for i = j-2 to 0 do: chart ij := {} for k = i+1 to j-1 do: for each A -> BC do: if B in chart ik & C in chart kj : chart ij := chart ij U {A} Det (.4) NP N.02 2 V.05 VP Det.4 NP N.01

24 Probabilistic CYK: syntactic step The flight includes a meal. //Lexical lookup: for j = 1 to length(string) do: chart j-1,j := {X : X->word in G} //syntactic lookup for i = j-2 to 0 do: chart ij := {} for k = i+1 to j-1 do: for each A -> BC do: if B in chart ik & C in chart kj : chart ij := chart ij U {A} 0 Det (.4) NP 1 N V.05 3 Det.4 4 N S VP NP

25 Probabilistic CYK: summary Cells in chart hold probabilities Bottom-up procedure computes probability of a parse incrementally. To obtain parse trees, cells need to be augmented with backpointers.

26 Probabilistic parsing with lexicalised PCFGs Main approaches (focus on Collins (1997,1999)) see also: Charniak (1997)

27 Unlexicalised PCFG Estimation Charniak (1996) used Penn Treebank POS and phrasal categories to induce a maximum likelihood PCFG only used relative frequency of local trees as the estimates for rule probabilities did not apply smoothing or any other techniques Works surprisingly well: 80.4% recall; 78.8% precision (crossed brackets not estimated) Suggests that most parsing decisions are mundane and can be handled well by unlexicalized PCFG

28 Probabilistic lexicalised PCFGs Standard format of lexicalised rules: associate head word with non-terminal e.g. dumped sacks into VP(dumped) VBD(dumped) NP(sacks) PP(into) associate head tag with non-terminal VP(dumped,VBD) VBD(dumped,VBD) NP(sacks,NNS) PP(into,IN) Types of rules: lexical rules expand pre-terminals to words: e.g. NNS(sacks,NNS) sacks probability is always 1 internal rules expand non-terminals e.g. VP(dumped,VBD) VBD(dumped,VBD) NP(sacks,NNS) PP(into,IN)

29 Estimating probabilities Non-generative model: take an MLE estimate of the probability of an entire rule Count( VP(dumped, VBD) VBD(dumped, VBD) NP(sacks, NNS) PP(into,IN)) Count( VP(dumped, VBD)) non-generative models suffer from serious data sparseness problems Generative model: estimate the probability of a rule by breaking it up into sub-rules.

30 Collins Model 1 Main idea: represent CFG rules as expansions into Head + left modifiers + right modifiers LHS STOP Ln Ln 1... L1 H R1... Rn 1Rn STOP L i /R i is of the form L/R(word,tag); e.g. NP(sacks,NNS) STOP: special symbol indicating left/right boundary. Parsing: Given the LHS, generate the head of the rule, then the left modifiers (until STOP) and right modifiers (until STOP) inside-out. Each step has a probability.

31 Collins Model 1: example VP(dumped,VBD) VBD(dumped,VBD) NP(sacks,NNS) PP(into,IN) 1. Head H(hw,ht): ( H( hw, ht) Parent, hw, ht) P H P( VBD(dumped, VBD) VP(dumped, VBD))

32 Collins Model 1: example VP(dumped,VBD) VBD(dumped,VBD) NP(sacks,NNS) PP(into,IN) 1. Head H(hw,ht): P H ( H( hw, ht) Parent, hw, ht) 2. Left modifiers: n 1 i 1 P ( L L i ( lw i, lw t ) Parent, H, hw, ht) P( STOP VP(dumped, VBD), VBD(dumped, VBD))

33 Collins Model 1: example VP(dumped,VBD) VBD(dumped,VBD) NP(sacks,NNS) PP(into,IN) 1. Head H(hw,ht): P H ( H( hw, ht) Parent, hw, ht) 2. Left modifiers: 3. Right modifiers: P P P R R R n 1 i 1 n 1 i 1 P R P ( L L ( R i i ( rw ( lw i i, lw, rw t t ) Parent, H, hw, ht) ) Parent, H, hw, ht) ( NP(sacks, NNS) VP(dumped, VBD), VBD(dumped, VBD)) ( PP(into,IN) VP(dumped, VBD), VBD(dumped, VBD)) (STOP VP(dumped, VBD), VBD(dumped, VBD))

34 Collins Model 1: example VP(dumped,VBD) VBD(dumped,VBD) NP(sacks,NNS) PP(into,IN) 1. Head H(hw,ht): 2. Left modifiers: 3. Right modifiers: n 1 i 1 P H ( H( hw, ht) Parent, hw, ht) n 1 i 1 P ( R R P ( L i L i ( rw i ( lw i, rw, lw t t ) Parent, H, hw, ht) ) Parent, H, hw, ht) 4. Total probability: multiplication of (1) (3)

35 Variations on Model 1: distance Collins proposed to extend rules by conditioning on distance of modifiers from the head: P L ( L ( lw, lw ) P, H, hw, ht,distance ( i 1)) i i t PR ( Ri ( rwi, rwt ) P, H, hw, ht,distance R( i 1)) a function of the yield of modifiers seen. L Distance for R 2 probability = words under R 1

36 Using a distance function Simplest kind of distance function is a tuple of binary features: Is the string of length 0? Does the string contain a verb? Example uses: if the string has length 0, P R should be higher: English is right-branching & most right modifiers are adjacent to the head verb if string contains a verb, P R should be higher: accounts for preference to attach dependencies to main verb

37 Further additions Collins Model 2: subcategorisation preferences distinction between complements and adjuncts. Model 3 augmented to deal with long-distance (WH) dependencies.

38 Smoothing and backoff Rules may condition on words that never occur in training data. Collins used 3-level backoff model. Combined using linear interpolation. 1. use head word P ( R ( rw, rw ) Parent, H, hw, ht) R 2. use head tag i i t P ( R ( rw, rw ) Parent, H, ht) R 3. parent only i i t P R ( R ( rw, rw ) Parent ) i i t

39 Other parsing approaches

40 Data-oriented parsing Alternative to grammar-based models does not attempt to derive a grammar from a treebank treebank data is stored as fragments of trees parser uses whichever trees seem to be useful

41 Data-oriented parsing Suppose we want to parse Sue heard Jim. Corpus contains the following potentially useful fragments: Parser can combine these to give a parse

42 Data-oriented Parsing Multiple fundamentally distinct derivations of a single tree. Parse using Monte Carlo simulation methods: randomly produce a large sample of derivations use these to find the most probable parse disadvantage: needs very large samples to make parses accurate, therefore potentially slow

43 Data-oriented parsing vs. PCFGs Possible advantages: using partial trees directly accounts for lexical dependencies also accounts for multi-word expressions and idioms (e.g. take advantage of) while PCFG rules only represent trees of depth 1, DOP fragments can represent trees of arbitrary length Similarities to PCFG: tree fragments could be equivalent to PCFG rules probabilities estimated for grammar rules are exactly the same as for tree fragments

44 History Based Grammars (HBG) General idea: any derivational step can be influenced by any earlier derivational step (Black et al. 1993) the probability of expansion of the current node conditioned on all previous nodes along the path from the root

45 History Based Grammars (HBG) Black et al lexicalise their grammar. every phrasal node inherits 2 words: its lexical head H 1 a secondary head H 2, deemed to be useful e.g. the PP in the bank might have H1=in and H2=bank Every non-terminal is also assigned: a syntactic category (Syn) e.g. PP a semantic category (Sem) e.g with-data Use the index I that indicates what number child of the parent node is being expanded

46 HBG Example (Black et al 1993)

47 History Based Grammars (HBG) Estimation of the probability of a rule R: P( Syn, Sem, R, H, H2 Syn p, Sem p, Rp, I, H1, H2 1 p p ) probability of: the current rule R to be applied its Syn and Sem category its heads H1 and H2 conditioned on: Syn and Sem of parent node the rule that gave rise to the parent the index of this child relative to the parent the heads H1 and H2 of the parent

48 Summary This concludes our overview of statistical parsing We ve looked at three important models Also considered basic search techniques and algorithms