trees, grammars, and parsing

Trees, Grammars, and Parsing

Most slides are taken or adapted from slides by

Chris ManningDan Klein

Parse Trees

From latent state sequences to latent tree structures (edges and nodes)

Types of Trees

There are several ways to add tree structures to sentences. We will consider 2:- Phrase structure (constituency) trees- Dependency trees

1. Phrase structure• Phrase structure trees organize

sentences into constituents or brackets.

• Each constituent gets a label.

• The constituents are nested in a tree form.

• Linguists can and do argue about the details.

• Lots of ambiguity …

Constituency Tests• How do we know what nodes go in the tree?

• Classic constituency tests:– Substitution by proform– Question answers– Semantic grounds

• Coherence• Reference• Idioms

– Dislocation– Conjunction

• Cross-linguistic arguments

Conflicting Tests

Constituency isn’t always clear.

• Phonological Reduction:– I will go I’ll go– I want to go I wanna go– a le centre au centre

• Coordination– He went to and came from the store.

2. Dependency structure

• Dependency structure shows which words depend on (modify or are arguments of) which other words.

The boy put the tortoise on the rugrug

the

the

ontortoise

put

boy

The

• Write symbolic or logical rules:

• Use deduction systems to prove parses from words– Minimal grammar on “Fed” sentence: 36 parses– Simple, 10-rule grammar: 592 parses– Real-size grammar: many millions of parses– With hand-built grammar, ~30% of sentences have no parse

• This scales very badly.– Hard to produce enough rules for every variation of language (coverage)– Many, many parses for each valid sentence (disambiguation)

Classical NLP: Parsing

Ambiguity examples

The bad effects of V/N ambiguities

Ambiguities: PP Attachment

Attachments

• I cleaned the dishes from dinner.

• I cleaned the dishes with detergent.

• I cleaned the dishes in my pajamas.

• I cleaned the dishes in the sink.

Syntactic Ambiguities 1• Prepositional Phrases

They cooked the beans in the pot on the stove with handles.

• Particle vs. PrepositionThe puppy tore up the staircase.

• Complement StructureThe tourists objected to the guide that they couldn’t hear.She knows you like the back of her hand.

• Gerund vs. Participial AdjectiveVisiting relatives can be boring.Changing schedules frequently confused passengers.

Syntactic Ambiguities 2• Modifier scope within NPs

impractical design requirementsplastic cup holder

• Multiple gap constructionsThe chicken is ready to eat.The contractors are rich enough to sue.

• Coordination scopeSmall rats and mice can squeeze into holes or cracks in

the wall.

Classical NLP Parsing:The problem and its solution

• Very constrained grammars attempt to limit unlikely/weird parses for sentences– But the attempt makes the grammars not robust: many

sentences have no parse

• A less constrained grammar can parse more sentences– But simple sentences end up with ever more parses

• Solution: We need mechanisms that allow us to find the most likely parse(s)– Statistical parsing lets us work with very loose grammars that

admit millions of parses for sentences but to still quickly find the best parse(s)

Polynomial-time Parsing with Context Free Grammars

Parsing

Computational task:Given a set of grammar rules and a sentence, find a

valid parse of the sentence (efficiently)

Naively, you could try all possible trees until you get to a parse tree that conforms to the grammar rules, that has “S” at the root, and that has the right words at the leaves.

But that takes exponential time in the number of words.

17

Aspects of parsing• Running a grammar backwards to find possible structures for a sentence

• Parsing can be viewed as a search problem

• Parsing is a hidden data problem

• For the moment, we want to examine all structures for a string of words

• We can do this bottom-up or top-down– This distinction is independent of depth-first or breadth-first search –

we can do either both ways– We search by building a search tree which his distinct from the parse

tree

Human parsing

• Humans often do ambiguity maintenance– Have the police … eaten their supper?– come in and look around.– taken out and shot.

• But humans also commit early and are “garden pathed”:– The man who hunts ducks out on weekends.– The cotton shirts are made from grows in Mississippi.– The horse raced past the barn fell.

A phrase structure grammar

• S NP VP N cats• VP V NP N claws• VP V NP PP N people• NP NP PP N scratch• NP N V scratch• NP e P with• NP N N• PP P NP

• By convention, S is the start symbol, but in the PTB, we have an extra node at the top (ROOT, TOP)

Phrase structure grammars = context-free grammars

• G = (T, N, S, R)– T is set of terminals– N is set of nonterminals

• For NLP, we usually distinguish out a set P N of preterminals, which always rewrite as terminals

• S is the start symbol (one of the nonterminals)• R is rules/productions of the form X , where X is a

nonterminal and is a sequence of terminals and nonterminals (possibly an empty sequence)

• A grammar G generates a language L.

Probabilistic or stochastic context-free grammars (PCFGs)

• G = (T, N, S, R, P)– T is set of terminals– N is set of nonterminals

• For NLP, we usually distinguish out a set P N of preterminals, which always rewrite as terminals

• S is the start symbol (one of the nonterminals)• R is rules/productions of the form X , where X is a

nonterminal and is a sequence of terminals and nonterminals (possibly an empty sequence)

• P(R) gives the probability of each rule.

• A grammar G generates a language model L.

X N, P(X )1X R

Soundness and completeness

• A parser is sound if every parse it returns is valid/correct

• A parser terminates if it is guaranteed to not go off into an infinite loop

• A parser is complete if for any given grammar and sentence, it is sound, produces every valid parse for that sentence, and terminates

• (For many purposes, we settle for sound but incomplete parsers: e.g., probabilistic parsers that return a k-best list.)

Top-down parsing• Top-down parsing is goal directed

• A top-down parser starts with a list of constituents to be built. The top-down parser rewrites the goals in the goal list by matching one against the LHS of the grammar rules, and expanding it with the RHS, attempting to match the sentence to be derived.

• If a goal can be rewritten in several ways, then there is a choice of which rule to apply (search problem)

• Can use depth-first or breadth-first search, and goal ordering.

Top-down parsing

Problems with top-down parsing• Left recursive rules

• A top-down parser will do badly if there are many different rules for the same LHS. Consider if there are 600 rules for S, 599 of which start with NP, but one of which starts with V, and the sentence starts with V.

• Useless work: expands things that are possible top-down but not there

• Top-down parsers do well if there is useful grammar-driven control: search is directed by the grammar

• Top-down is hopeless for rewriting parts of speech (preterminals) with words (terminals). In practice that is always done bottom-up as lexical lookup.

• Repeated work: anywhere there is common substructure

Repeated work…

Bottom-up parsing• Bottom-up parsing is data directed

• The initial goal list of a bottom-up parser is the string to be parsed. If a sequence in the goal list matches the RHS of a rule, then this sequence may be replaced by the LHS of the rule.

• Parsing is finished when the goal list contains just the start category.

• If the RHS of several rules match the goal list, then there is a choice of which rule to apply (search problem)

• Can use depth-first or breadth-first search, and goal ordering.

• The standard presentation is as shift-reduce parsing.

Problems with bottom-up parsing• Unable to deal with empty categories: termination

problem, unless rewriting empties as constituents is somehow restricted (but then it's generally incomplete)

• Useless work: locally possible, but globally impossible.

• Inefficient when there is great lexical ambiguity (grammar-driven control might help here)

• Conversely, it is data-directed: it attempts to parse the words that are there.

• Repeated work: anywhere there is common substructure

PCFGs – Notation• w1n = w1 … wn = the word sequence from 1 to n

(sentence of length n) • wab = the subsequence wa … wb • Nj

ab = the nonterminal Nj dominating wa … wb

Nj

wa … wb

• We’ll write P(Ni ζj) to mean P(Ni ζj | Ni )• We’ll want to calculate maxt P(t * wab)

The probability of trees and strings

• P(w1n, t) -- The probability of tree is the product of the probabilities of the rules used to generate it.

• P(w1n) -- The probability of the string is the sum of the probabilities of the trees which have that string as their yield

P(w1n) = Σt P(w1n, t) where t is a parse of w1n

twXRtABXR

n

i

RPRPtwP}{}{

1 )()(),(

Example: A Simple PCFG (in Chomsky Normal Form)

S NP VP 1.0 VP V NP 0.7VP VP PP 0.3PP P NP 1.0P with 1.0V saw 1.0

NP NP PP 0.4 NP astronomers 0.1 NP ears 0.18 NP saw 0.04 NP stars 0.18 NP telescope 0.1

)( 1tP

Tree and String Probabilities• w15 = astronomers saw stars with ears• P(t1) = 1.0 * 0.1 * 0.7 * 1.0 * 0.4 * 0.18 * 1.0 * 1.0 * 0.18 = 0.0009072• P(t2) = 1.0 * 0.1 * 0.3 * 0.7 * 1.0 * 0.18 * 1.0 * 1.0 * 0.18 = 0.0006804 • P(w15) = P(t1) + P(t2)

= 0.0009072 + 0.0006804 = 0.0015876

Chomsky Normal Form

• All rules are of the form X Y Z or X w.• A transformation to this form doesn’t change the

weak generative capacity of CFGs.– With some extra book-keeping in symbol names, you

can even reconstruct the same trees with a detransform

– Unaries/empties are removed recursively– N-ary rules introduce new nonterminals:

• VP V NP PP becomes VP V @VP-V and @VP-V NP PP

• In practice it’s a pain– Reconstructing n-aries is easy– Reconstructing unaries can be trickier

• But it makes parsing easier/more efficient

N-ary Trees in Treebank

Lexicon and Grammar

Binary Trees

TreeAnnotations.annotateTree

Parsing

TODO:CKY parsing

Treebank binarization

ROOT

S

NP VP

N

cats

V NP PP

P NP

clawswithpeoplescratch

NN

An example: before binarization…

P

NP

claws

N

@PP->_P

with

NP

N

cats peoplescratch

N

VP

V NP PP

@VP->_V

@VP->_V_NP

ROOT

S

@S->_NP

After binarization..

ROOT

S

NP VP

N

cats

V NP PP

P NP

clawswithpeoplescratch

NN

Binary rule

PP

P

NP

claws

N

@PP->_P

with

ROOT

S

NP VP

N

cats

V NP

peoplescratch

N

Seems redundant? (the rule was already binary)Reason: easier to see how to make finite-order horizontal markovizations – it’s like a finite automaton (explained later)

PP

P

NP

claws

N

@PP->_P

with

ROOT

S

NP VP

N

cats

V NP

peoplescratch

N

ternary rule

P

NP

claws

N

@PP->_P

with

ROOT

S

NP

N

cats peoplescratch

N

VP

V NP PP

@VP->_V

@VP->_V_NP

P

NP

claws

N

@PP->_P

with

NP

N

cats peoplescratch

N

VP

V NP PP

@VP->_V

@VP->_V_NP

ROOT

S

@S->_NP

P

NP

claws

N

@PP->_P

with

NP

N

cats peoplescratch

N

VP

V NP PP

@VP->_V

@VP->_V_NP

ROOT

S

@S->_NP

VPV NP PPRemembers 2 siblings

If there’s a ruleVP V NP PP PP,@VP->_V_NP_PP will exist.

Treebank: empties and unaries

TOP

S-HLN

NP-SUBJ VP

VB-NONE-

Atone

PTB Tree

TOP

S

NP VP

VB-NONE-

Atone

NoFuncTags

TOP

S

VP

VB

Atone

NoEmpties

TOP

S

Atone

NoUnaries

TOP

VB

Atone

High

Low

CKY Parsing (aka, CYK)

Cocke–Younger–Kasami (CYK or CKY) parsing is a dynamic programming solution to identifying a valid parse for a sentence.

Dynamic programming: simplifying a complicated problem by breaking it down into simpler subproblems in a recursive manner

48

CKY – Basic IdeaLet the input be a string S consisting of n characters: a1 ... an.

Let the grammar contain r nonterminal symbols R1 ... Rr. This grammar contains the subset Rs which is the set of start symbols.

Let P[n,n,r] be an array of booleans. Initialize all elements of P to false.

At each step, the algorithm sets P[i,j,k] to be true if the subsequence of words (span) starting from i of length j can be generated from Rk

We will start with spans of length 1 (individual words), and then proceed to increasingly larger spans, and determining which ones are valid given the smaller spans that have already been processed.

49

CKY AlgorithmFor each i = 1 to n

For each unit production Rj -> ai, set P[i,1,j] = true.

For each i = 2 to n -- Length of span For each j = 1 to n-i+1 -- Start of span

For each k = 1 to i-1 -- Partition of span For each production RA -> RB RC

If P[j,k,B] and P[j+k,i-k,C] then set P[j,i,A] = true

If any of P[1,n,x] is true (x is iterated over the set s, where s are all the indices for Rs)

Then S is member of language Else S is not member of language

50

CKY In Action

http://www.diotavelli.net/people/void/demos/cky.html

51



Probabilistic CKY (This version doesn’t handle unaries)

Input: words, grammar. Output: most likely parse, and its probability.For each left = 1 to #words // initialize: all length 1 spans (indiv. words)

For each unit production Rj -> wordsleft,left+1, set score[left,1,j] = P(Rj -> wordsleft,left+1).

For each span = 2 to #words -- Length of span // induction: increasing span For each left = 1 to #words-span+1 -- Start of span

For each mid = 1 to span-1 -- Partition of span For each production RA -> RB RC If score[left,mid,B]>0 and score[left+mid,span-mid,C]>0

score = score[left,mid,B] * score[left+mid,span-mid,C] * P(RA -> RB RC)If score > score[left,span,A] score[left,span,A] = score back[left,span,A] = (B, C, mid)

Set parent = argmaxstart symbols RS score[1,#words,RS]Set score = score[1,#words,parent]Return [score, buildTree(parent,1,#words, back)]

52

buildTree Input: root, left, span, backpointers Output: tree

Set tree.symbol = root

If span = 1 // Base caseSet tree.child = wleft,left+1

Else // recurSet (B, C, mid) = backpointers[left, span, root]Set tree.leftChild = buildTree(B, left, mid, backpointers)Set tree.rightRight = buildTree(C, left+mid, span-mid, backpointers)

Return tree

53

score[1][1]

score[1][2]

score[1][3]

score[1][4]

score[1][5]

score[2][1]

score[2][2]

Score[2][3]

score[2][4]

score[3][1]

Score[3][2]

Score[3][3]

score[4][1]

Score[4][2]

score[5][1]

1

2

3

4

5

1 2 3 4 5cats scratch walls with claws 6

6

Left

Preterminals:

Possible Solutions:Not shown: back pointer entries.

N->cats 0.1V->cats 0.01

N->scratch .1V->scratch .2

N->walls .2V->walls .01

P->with .5 N->claws .1V->claws .2

1

2

3

4

5


6

Left

Preterminals:

Initialization





1

2

3

4

5


6

Left

Preterminals:

Induction: Span 2

Span 2:


S->N V .002NP->N N .001VP->V N.0001VP->V V.00001




1

2

3

4

5


6

Left

Preterminals:

Induction: Span 2

Span 2:

Span = 2Left = 1Mid = 1

Grammar ProbabilitiesP(S->N V) = .1P(NP->N N) = .1P(VP->V N) = .1P(VP->V V) = .005P(NP-> N P) = .01P(VP-> V P) = .02P(PP-> P N) = .1


S->N V .002NP->N N .001VP->V N.0001


S->N V .0001NP->N N .002VP->V N.004VP->V V.00001



1

2

3

4

5


6

Left

Preterminals:

Induction: Span 2

Span 2:

Span = 2Left = 2Mid = 1



S->N V .002NP->N N .001VP->V N.0001


S->N V .002NP->N N .001VP->V N.0001


NP->N P .000001VP->V P .00001

P->with .5

PP->P N .005

N->claws .1V->claws .2

1

2

3

4

5


6

Left

Preterminals:

Induction: Span 2

Span 2:



S->N V .002NP->N N .001VP->V N.0001

S->N VP 2e-6VP->V NP 2e-6

…


S->N V .002NP->N N .001VP->V N.0001

S->N VP 1e-6VP->V NP2e-7

VP-> …V @VP_V 6e-6V NP 4e-6


NP->N P .000001VP->V P .00001

NP->N PP 1e-4VP->V PP 5e-6@VP_V->N PP 1e-4

P->with .5

PP->P N .005


1

2

3

4

5


6

Left

Preterminals:

Induction: Span 4

Span 4:Span = 4Left = 2Mid = 1

Grammar ProbabilitiesP(S->N V) = .1P(S->N VP) = .2

P(NP->N N) = .1P(NP->N PP) = .1P(NP-> N P) = .01

P(VP->V N) = .1P(VP->V NP) = .2P(VP->V V) = .005P(VP-> V P) = .02P(VP->V PP) = .1P(VP->V @VP_V) = .3P(VP->VP PP) = .1

P(@VP_V -> N PP) = .1

P(PP-> P N) = .1


S->N V .002NP->N N .001VP->V N.0001


…


S->N V .002NP->N N .001VP->V N.0001


VP-> …V @VP_V 6e-6V NP 4e-6VP PP5e-8


NP->N P .000001VP->V P .00001


P->with .5

PP->P N .005


1

2

3

4

5


6

Left

Preterminals:

Induction: Span 4





P(@VP_V -> N PP) = .1

P(PP-> P N) = .1


S->N V .002NP->N N .001VP->V N.0001


…


S->N V .002NP->N N .001VP->V N.0001




NP->N P .000001VP->V P .00001


P->with .5

PP->P N .005


1

2

3

4

5


6

Left

Preterminals:

Induction: Span 4





P(@VP_V -> N PP) = .1

P(PP-> P N) = .1


S->N V .002NP->N N .001VP->V N.0001


…


S->N V .002NP->N N .001VP->V N.0001




NP->N P .000001VP->V P .00001


P->with .5

PP->P N .005


1

2

3

4

5


6

Left

Preterminals:

Induction: Span 4

Span 4:Span = 4Left = 2




P(@VP_V -> N PP) = .1

P(PP-> P N) = .1


S->N V .002NP->N N .001VP->V N.0001


…


S->N V .002NP->N N .001VP->V N.0001


VP-> V @VP_V 6e-6

back = (left = V, right = @VP_V, mid=1)


NP->N P .000001VP->V P .00001


P->with .5

PP->P N .005


1

2

3

4

5


6

Left

Preterminals:

Induction: Span 4

Span 4:Span = 4Left = 2




P(@VP_V -> N PP) = .1

P(PP-> P N) = .1


S->N V .002NP->N N .001VP->V N.0001


…

S->N VP1.2e-7Back =(left=N,right=VP,mid=1)


S->N V .002NP->N N .001VP->V N.0001


VP-> V @VP_V 6e-6

back = (left = V, right = @VP_V, mid=1)


NP->N P .000001VP->V P .00001


P->with .5

PP->P N .005


1

2

3

4

5


6

Left

Final ChartGrammar ProbabilitiesP(S->N V) = .1P(S->N VP) = .2



P(@VP_V -> N PP) = .1

P(PP-> P N) = .1

P

claws

N

with

S

N

cats wallsscratch

N

VP

V PP

@VP->_V

Corresponding Tree

(This is different from tree I showed before because this one doesn’t include unaries.)

probability = score = 1.2e-7

Extended CKY parsing

• Unaries can be incorporated into the algorithm– Messy, but doesn’t increase algorithmic complexity

• Empties can be incorporated– Use fenceposts– Doesn’t increase complexity; essentially like unaries

• Binarization is vital– Without binarization, you don’t get parsing cubic in the

length of the sentence• Binarization may be an explicit transformation or implicit in how

the parser works (Early-style dotted rules), but it’s always there.

Efficient CKY parsing• CKY parsing can be made very fast (!), partly due to the

simplicity of the structures used.– But that means a lot of the speed comes from engineering

details– And a little from cleverer filtering

– Store chart as (ragged) 3 dimensional array of float (log probabilities)

• score[start][end][category]– For treebank grammars the load is high enough that you don’t really gain

from lists of things that were possible– 50wds: (50x50)/2x(1000 to 20000)x4 bytes = 5–100MB for parse triangle.

Large (can move to beam for span[i][j]).

– Use int to represent categories/words (Index)

Efficient CKY parsing

• Provide efficient grammar/lexicon accessors:– E.g., return list of rules with this left child category– Iterate over left child, check for zero (Neg. inf.) prob

of X:[i,j] (abort loop), otherwise get rules with X on left

– Some X:[i,j] can be filtered based on the input string• Not enough space to complete a long flat rule?• No word in the string can be a CC?

– Using a lexicon of possible POS for words gives a lot of constraint rather than allowing all POS for words

• Cf. later discussion of figures-of-merit/A* heuristics

Runtime in practice: super-cubic!

• Super-cubic in practice! Why?

Best Fit Exponent:

3.47

0

60

120

180

240

300

360

0 10 20 30 40 50Sentence Length

Tim

e (s

ec)

How good are PCFGs?• Robust (usually admit everything, but with low probability)

• Partial solution for grammar ambiguity: a PCFG gives some idea of the plausibility of a sentence

• But not so good because the independence assumptions are too strong

• Give a probabilistic language model – But in a simple case it performs worse than a trigram model

• The problem seems to be it lacks the lexicalization of a trigram model

Parser Evaluation

Evaluating Parsing Accuracy

• Most sentences are not given a completely correct parse by any currently existing parsers.

• Standardly for Penn Treebank parsing, evaluation is done in terms of the percentage of correct constituents (labeled spans).

• [ label, start, finish ]

• A constituent is a triple, all of which must be in the true parse for the constituent to be marked correct.

Evaluating Constituent Accuracy: LP/LR measure

• Let C be the number of correct constituents produced by the parser over the test set, M be the total number of constituents produced, and N be the total in the correct version [microaveraged]

• Precision = C/M• Recall = C/N

• It is possible to artificially inflate either one.• Thus people typically give the F-measure (harmonic mean) of the two.

Not a big issue here; like average.

• This isn’t necessarily a great measure … me and many other people think dependency accuracy would be better.

Extensions to basic PCFG Parsing

Many, many possibilities

• Tree Annotations– Lexicalization– Grandparent, sibling, etc. annotations– Manual label splitting– Latent label splitting

• Horizontal and Vertical Markovization• Discriminative Reranking

Putting words into PCFGs• A PCFG uses the actual words only to determine the probability of

parts-of-speech (the preterminals)• In many cases we need to know about words to choose a parse• The head word of a phrase gives a good representation of the

phrase’s structure and meaning

– Attachment ambiguities The astronomer saw the moon with the telescope

– Coordination the dogs in the house and the cats

– Subcategorization framesput versus like

(Head) Lexicalization• put takes both an NP and a VP

– Sue put [ the book ]NP [ on the table ]PP

– * Sue put [ the book ]NP

– * Sue put [ on the table ]PP

• like usually takes an NP and not a PP– Sue likes [ the book ]NP

– * Sue likes [ on the table ]PP

• We can’t tell this if we just have a VP with a verb, but we can if we know which verb it is

(Head) Lexicalization

• Collins 1997, Charniak 1997• Puts the properties of words into a PCFG

Swalked

NPSue VPwalked

Sue Vwalked PPinto

walked Pinto NPstore

into DTthe NPstore

the store

Lexicalized Parsing was seen as the breakthrough of the late 90s

• Eugene Charniak, 2000 JHU workshop: “To do better, it is necessary to condition probabilities on the actual words of the sentence. This makes the probabilities much tighter:– p(VP V NP NP) = 0.00151– p(VP V NP NP | said) = 0.00001– p(VP V NP NP | gave) = 0.01980 ”

• Michael Collins, 2003 COLT tutorial: “Lexicalized Probabilistic Context-Free Grammars … perform vastly better than PCFGs (88% vs. 73% accuracy)”

Michael Collins (2003, COLT)

Klein and Manning --Accurate Unlexicalized Parsing:

PCFGs and Independence• The symbols in a PCFG define independence

assumptions:

– At any node, the material inside that node is independent of the material outside that node, given the label of that node.

– Any information that statistically connects behavior inside and outside a node must flow through that node.

NP

S

VP

S NP VP

NP DT NNNP

Michael Collins (2003, COLT)

Non-Independence I

• Independence assumptions are often too strong.

• Example: the expansion of an NP is highly dependent on the parent of the NP (i.e., subjects vs. objects).

11%9%

6%

NP PP DT NN PRP

9% 9%

21%

NP PP DT NN PRP

7%4%

23%

NP PP DT NN PRP

All NPs NPs under S NPs under VP

Non-Independence II

• Who cares?– NB, HMMs, all make false assumptions!– For generation, consequences would be obvious.– For parsing, does it impact accuracy?

• Symptoms of overly strong assumptions:– Rewrites get used where they don’t belong.– Rewrites get used too often or too rarely.

In the PTB, this construction is for possesives

Breaking Up the Symbols

• We can relax independence assumptions by encoding dependencies into the PCFG symbols:

• What are the most useful features to encode?

Parent annotation[Johnson 98]

Marking possesive NPs

Annotations

• Annotations split the grammar categories into sub-categories.

• Conditioning on history vs. annotating– P(NP^S PRP) is a lot like P(NP PRP | S)– P(NP-POS NNP POS) isn’t history conditioning.

• Feature grammars vs. annotation– Can think of a symbol like NP^NP-POS as

NP [parent:NP, +POS]

• After parsing with an annotated grammar, the annotations are then stripped for evaluation.

Lexicalization

• Lexical heads are important for certain classes of ambiguities (e.g., PP attachment):

• Lexicalizing grammar creates a much larger grammar.– Sophisticated smoothing needed– Smarter parsing algorithms needed– More data needed

• How necessary is lexicalization?– Bilexical vs. monolexical selection– Closed vs. open class lexicalization

Experimental Setup

• Corpus: Penn Treebank, WSJ

• Accuracy – F1: harmonic mean of per-node labeled precision and recall.

• Size – number of symbols in grammar.– Passive / complete symbols: NP, NP^S– Active / incomplete symbols: NP NP CC

Training: sections 02-21Development: section 22 (first 20 files)Test: section 23

Experimental Process

• We’ll take a highly conservative approach:– Annotate as sparingly as possible– Highest accuracy with fewest symbols– Error-driven, manual hill-climb, adding one

annotation type at a time

Unlexicalized PCFGs

• What do we mean by an “unlexicalized” PCFG?– Grammar rules are not systematically specified down to

the level of lexical items• NP-stocks is not allowed• NP^S-CC is fine

– Closed vs. open class words (NP^S-the)• Long tradition in linguistics of using function words as features

or markers for selection• Contrary to the bilexical idea of semantic heads• Open-class selection really a proxy for semantics

• Honesty checks:– Number of symbols: keep the grammar very small– No smoothing: over-annotating is a real danger

Horizontal Markovization

• Horizontal Markovization: Merges States

70%

71%

72%

73%

74%

0 1 2v 2 inf

Horizontal Markov Order

0

3000

6000

9000

12000

0 1 2v 2 inf

Horizontal Markov Order

Sym

bo

ls

Merged

Vertical Markovization

• Vertical Markov order: rewrites depend on past k ancestor nodes.(cf. parent annotation)

Order 1 Order 2

72%73%74%75%76%77%78%79%

1 2v 2 3v 3

Vertical Markov Order

0

5000

10000

15000

20000

25000

1 2v 2 3v 3

Vertical Markov Order

Sym

bo

ls

Vertical and Horizontal

• Examples:– Raw treebank: v=1, h=– Johnson 98: v=2, h=– Collins 99: v=2, h=2– Best F1: v=3, h=2v

0 1 2v 2 inf1

2

3

66%68%70%72%74%76%78%80%

Horizontal Order

Vertical Order 0 1 2v 2 inf

1

2

3

0

5000

10000

15000

20000

25000

Sym

bo

lsHorizontal Order

Vertical Order

Model F1 Size

Base: v=h=2v 77.8 7.5K

Unary Splits

• Problem: unary rewrites used to transmute categories so a high-probability rule can be used.

Annotation F1 Size

Base 77.8 7.5K

UNARY 78.3 8.0K

Solution: Mark unary rewrite sites with -U

Tag Splits

• Problem: Treebank tags are too coarse.

• Example: Sentential, PP, and other prepositions are all marked IN.

• Partial Solution:– Subdivide the IN tag.

Annotation F1 Size

Previous 78.3 8.0K

SPLIT-IN 80.3 8.1K

Other Tag Splits• UNARY-DT: mark demonstratives as DT^U (“the X”

vs. “those”)

• UNARY-RB: mark phrasal adverbs as RB^U (“quickly” vs. “very”)

• TAG-PA: mark tags with non-canonical parents (“not” is an RB^VP)

• SPLIT-AUX: mark auxiliary verbs with –AUX [cf. Charniak 97]

• SPLIT-CC: separate “but” and “&” from other conjunctions

• SPLIT-%: “%” gets its own tag.

F1 Size

80.4 8.1K

80.5 8.1K

81.2 8.5K

81.6 9.0K

81.7 9.1K

81.8 9.3K

Treebank Splits

• The treebank comes with annotations (e.g., -LOC, -SUBJ, etc).– Whole set together hurt

the baseline.– Some (-SUBJ) were less

effective than our equivalents.

– One in particular was very useful (NP-TMP) when pushed down to the head tag.

– We marked gapped S nodes as well.

Annotation F1 Size

Previous 81.8 9.3K

NP-TMP 82.2 9.6K

GAPPED-S 82.3 9.7K

Yield Splits

• Problem: sometimes the behavior of a category depends on something inside its future yield.

• Examples:– Possessive NPs– Finite vs. infinite VPs– Lexical heads!

• Solution: annotate future elements into nodes.

Annotation F1 Size

Previous 82.3 9.7K

POSS-NP 83.1 9.8K

SPLIT-VP 85.7 10.5K

Distance / Recursion Splits

• Problem: vanilla PCFGs cannot distinguish attachment heights.

• Solution: mark a property of higher or lower sites:– Contains a verb.– Is (non)-recursive.

• Base NPs [cf. Collins 99]• Right-recursive NPs

Annotation F1 Size

Previous 85.7 10.5K

BASE-NP 86.0 11.7K

DOMINATES-V 86.9 14.1K

RIGHT-REC-NP 87.0 15.2K

NP

VP

PP

NP

v

-v

A Fully Annotated Tree

Final Test Set Results

• Beats “first generation” lexicalized parsers.

Parser LP LR F1 CB 0 CB

Magerman 95 84.9 84.6 84.7 1.26 56.6

Collins 96 86.3 85.8 86.0 1.14 59.9

Klein & M 03 86.9 85.7 86.3 1.10 60.3

Charniak 97 87.4 87.5 87.4 1.00 62.1

Collins 99 88.7 88.6 88.6 0.90 67.1

Bilexical statistics are used often [Bikel 2004]

• The 1.49% use of bilexical dependencies suggests they don’t play much of a role in parsing

• But the parser pursues many (very) incorrect theories• So, instead of asking how often the decoder can use bigram probability on

average, ask how often while pursuing its top-scoring theory • Answering question by having parser constrain-parse its own output

– train as normal on §§02–21– parse §00– feed parse trees as constraints

• Percentage of time parser made use of bigram statistics shot up to 28.8%• So, used often, but use barely affect overall parsing accuracy• Exploratory Data Analysis suggests explanation

– distributions that include head words are usually sufficiently similar to those that do not as to make almost no difference in terms of accuracy

Charniak (2000) NAACL: A Maximum-Entropy-Inspired Parser

• There was nothing maximum entropy about it. It was a cleverly smoothed generative model

• Smoothes estimates by smoothing ratio of conditional terms (which are a bit like maxent features):

• Biggest improvement is actually that generative model predicts head tag first and then does P(w|t,…)– Like Collins (1999)

• Markovizes rules similarly to Collins (1999)• Gets 90.1% LP/LR F score on sentences ≤ 40 wds

),,|(

),,,|(

pp

gpp

tlltP

ltlltP

Outside

Petrov and Klein (2006):Learning Latent Annotations

Can you automatically find good symbols?

X1

X2X7X4

X5 X6X3

He was right

.

Brackets are known Base categories are known Induce subcategories Clever split/merge category refinement

EM algorithm, like Forward-Backward for HMMs, but constrained by tree.

Inside

0

5

10

15

20

25

30

35

40

NP

VP PP

AD

VP S

AD

JP

SB

AR QP

WH

NP

PR

N

NX

SIN

V

PR

T

WH

PP

SQ

CO

NJP

FR

AG

NA

C

UC

P

WH

AD

VP

INT

J

SB

AR

Q

RR

C

WH

AD

JP X

RO

OT

LST

Number of phrasal subcategories

Proper Nouns (NNP):

Personal pronouns (PRP):

NNP-14 Oct. Nov. Sept.

NNP-12 John Robert James

NNP-2 J. E. L.

NNP-1 Bush Noriega Peters

NNP-15 New San Wall

NNP-3 York Francisco Street

PRP-0 It He I

PRP-1 it he they

PRP-2 it them him

POS tag splits, commonest words: effectively a class-based model

F1≤ 40 words

F1all words

Parser

Klein & Manning unlexicalized 2003

86.3 85.7

Matsuzaki et al. simple EM latent states 2005

86.7 86.1

Charniak generative (“maxent inspired”) 2000

90.1 89.5

Petrov and Klein NAACL 2007 90.6 90.1

Charniak & Johnson discriminative reranker 2005

92.0 91.4

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