Grammar and Parsing

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Transcript Grammar and Parsing

Trees, Grammars, and Parsing

Most slides are taken or adapted from slides by Chris Manning Dan 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  a le centre  I wanna go 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 rug put The boy the tortoise on the rug

Classical NLP: Parsing

• 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)

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. Preposition

The puppy tore up the staircase.

• Complement Structure

The tourists objected to the guide that they couldn’t hear.

She knows you like the back of her hand.

• Gerund vs. Participial Adjective

Visiting relatives can be boring.

Changing schedules frequently confused passengers.

Syntactic Ambiguities 2

• Modifier scope within NPs

impractical design requirements plastic cup holder

• Multiple gap constructions

The chicken is ready to eat.

The contractors are rich enough to sue.

• Coordination scope

Small 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.

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





, 

(

  )  1

  

A grammar G generates a language model L.



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

• • •

w 1n = w 1 … w n

= the word sequence from 1 to n (sentence of length n)

w ab N j ab

= the subsequence w = the nonterminal N

j a … w b

dominating w

a … w b N j

• •

w a … w b

We’ll write P(N



ζ j

) to mean P(N



ζ j

| N

We’ll want to calculate max

P(t )  * w

)

The probability of trees and strings

• P(w it.

1n , t) -- The probability of tree is the product of the probabilities of the rules used to generate

(

)  {



 

(

} 

t R

) {



 

w i P

( } 

t R

) • P(w 1n ) -- The probability of the string is the sum of the probabilities of the trees which have that string as their yield P(w

) = Σ

P(w

, t) where t is a parse of w

Example: A Simple PCFG (in Chomsky Normal Form)

S  VP  VP  PP  P  V  NP VP 1.0 V NP 0.7

VP PP 0.3

P NP 1.0

with

1.0

saw

1.0

NP  NP  NP  NP  NP  NP  NP PP 0.4

astronomers 0.1

ears 0.18

saw 0.04

stars 0.18

telescope 0.1

(

1 ) 

Tree and String Probabilities

• • • •

w 15

= astronomers saw stars with ears P(t

) = 1.0 * 0.1 * 0.7 * 1.0 * 0.4 * 0.18 * 1.0 * 1.0 * 0.18

= 0.0009072

P(t

) = 1.0 * 0.1 * 0.3 * 0.7 * 1.0 * 0.18

* 1.0 * 1.0 * 0.18

= 0.0006804 P(w

) = P(t

) + P(t = 0.0015876

) = 0.0009072 + 0.0006804

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

Treebank binarization

N-ary Trees in Treebank TreeAnnotations.annotateTree

Binary Trees Lexicon and Grammar Parsing TODO: CKY parsing

An example: before binarization…

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

ROOT

After binarization..

S NP @S->_NP VP @VP->_V N cats @VP->_V_NP V scratch NP N people P PP @PP->_P with NP N claws

ROOT S NP VP N cats V NP N P scratch people with PP NP N claws Binary rule

NP ROOT S VP 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) N cats V scratch NP N people P PP @PP->_P with NP N claws

ROOT S ternary rule NP VP N cats V scratch NP N people P PP @PP->_P with NP N claws

ROOT S NP N cats VP @VP->_V @VP->_V_NP V scratch NP N people P PP @PP->_P with NP N claws

ROOT NP N cats S @S->_NP VP @VP->_V @VP->_V_NP V scratch NP N people P PP @PP->_P with NP N claws

ROOT NP N cats S @S->_NP VP @VP->_V V NP N @VP->_V_NP P scratch people with PP @PP->_P VP  V NP PP Remembers 2 siblings NP N claws If there’s a rule VP  V NP PP PP , @VP->_V_NP_PP will exist.

Treebank: empties and unaries

TOP S-HLN TOP S NP-SUBJ VP NP VP -NONE VB -NONE VB  Atone  Atone PTB Tree NoFuncTags TOP S VP VB Atone NoEmpties TOP S TOP VB Atone Atone High Low NoUnaries

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

CKY – Basic Idea

Let the input be a string S consisting of n characters: a 1 ... a

. Let the grammar contain r nonterminal symbols R contains the subset R s 1 ... R

. This grammar 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 R k 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.

CKY Algorithm

For each i = 1 to n For each unit production R j set P[i,1,j] = true. -> a i , 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 R A -> R B R C 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 R s ) Then S is member of language Else S is not member of language 50

CKY In Action

http://www.diotavelli.net/people/void/demos/c ky.html

Probabilistic CKY (This version doesn’t handle unaries)

Input: words, grammar.

For each left = 1 to #words

Output: most likely parse, and its probability.

// initialize: all length 1 spans (indiv. words) For each unit production R j -> words left,left+1 , set score[left,1,j] = P(R j -> words left,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 R A -> R B R C 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(R A If score > score[left,span,A] -> R B R C ) score[left,span,A] = score back[left,span,A] = (B, C, mid) Set parent = argmax start symbols RS score[1,#words,R S ] Set score = score[1,#words,parent] Return [score, buildTree(parent,1,#words, back)] 52

buildTree

Input: root, left, span, backpointers

Set tree.symbol = root

Output: tree

If span = 1 // Base case Set tree.child = w left,left+1

Else

// recur Set (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

6 Possible Solutions: score[1][5] 5 score[1][4] score[2][4] 4 score[1][3] Score[2][3] Score[3][3]

Not shown: back pointer entries.

3 score[1][2] score[2][2] Score[3][2] Score[4][2] 2 Preterminals: score[1][1] score[2][1] score[3][1] score[4][1] score[5][1] 1 1 cats 2 scratch 3 walls

Left

4 with 5 claws 6

Initialization

6 5 4 3 Preterminals: 2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

1 1 cats 2 scratch 3 walls

Left

4 with N->claws .1

V->claws .2

5 claws 6

5 4 6

Induction: Span 2

3 Span 2: Preterminals: 2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

1 1 cats 2 scratch 3 walls

Left

4 with N->claws .1

V->claws .2

5 claws 6

5 6 4

Induction: Span 2

Grammar Probabilities

P(S->N V) = .1

P(NP->N N) = .1

P(VP->V N) = .1

P(VP->V V) = .005

P(NP-> N P) = .01

P(VP-> V P) = .02

P(PP-> P N) = .1

Span 2: 3 S->N V .002

NP->N N .001

VP->V N.0001

VP->V V .00001

2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

Preterminals: 1 1 cats 2 scratch 3 walls

Left

4 with N->claws .1

V->claws .2

5 claws 6 Span = 2 Left = 1 Mid = 1

5 6 4

Induction: Span 2

Grammar Probabilities

P(S->N V) = .1

P(NP->N N) = .1

P(VP->V N) = .1

P(VP->V V) = .005

P(NP-> N P) = .01

P(VP-> V P) = .02

P(PP-> P N) = .1

Span 2: 3 S->N V .002

NP->N N .001

VP->V N.0001

S->N V .0001

NP->N N .002

VP->V N.004

VP->V V .00001

2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

Preterminals: 1 1 cats 2 scratch 3 walls

Left

4 with N->claws .1

V->claws .2

5 claws 6 Span = 2 Left = 2 Mid = 1

5 6 4

Induction: Span 2

Grammar Probabilities

P(S->N V) = .1

P(NP->N N) = .1

P(VP->V N) = .1

P(VP->V V) = .005

P(NP-> N P) = .01

P(VP-> V P) = .02

P(PP-> P N) = .1

Span 2: 3 S->N V .002

NP->N N .001

VP->V N.0001

S->N V .002

NP->N N .001

VP->V N.0001

NP->N P .000001

VP->V P .00001

PP->P N .005

2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

Preterminals: 1 1 cats 2 scratch 3 walls

Left

4 with N->claws .1

V->claws .2

5 claws 6

Preterminals: 6

Induction: Span 4

Span 4: 5 … VP > … V @VP_V 6e-6 V NP 4e-6 Span = 4 Left = 2

Mid = 1

4 S->N VP 2e-6 VP->V NP 2e-6 S->N VP 1e-6 VP->V NP 2e-7 NP->N PP 1e-4 VP->V PP 5e-6 @VP_V-> N PP 1e-4 3 S->N V .002

NP->N N .001

VP->V N.0001

S->N V .002

NP->N N .001

VP->V N.0001

NP->N P .000001

VP->V P .00001

PP->P N .005

2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

N->claws .1

V->claws .2

Grammar Probabilities

P(S->N V) = .1

P(S->N VP) = .2

P(NP->N N) = .1

P(NP->N PP) = .1

P(NP-> N P) = .01

P(VP->V N) = .1

P(VP->V NP) = .2

P(VP->V V) = .005

P(VP-> V P) = .02

P(VP->V PP) = .1

P(VP->V @VP_V) = .3

P(VP->VP PP) = .1

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

P(PP-> P N) = .1

1 1 cats 2 scratch walls 3

Left

4 with 5 claws 6

Preterminals: 6

Induction: Span 4

Span 4: 5 4 … S->N VP 2e-6 VP->V NP 2e-6 VP > … V @VP_V 6e-6 V NP 4e-6 VP PP 5e-8 S->N VP 1e-6 VP->V NP 2e-7 Span = 4 Left = 2

Mid = 2

NP->N PP 1e-4 VP->V PP 5e-6 @VP_V-> N PP 1e-4 3 S->N V .002

NP->N N .001

VP->V N.0001

S->N V .002

NP->N N .001

VP->V N.0001

NP->N P .000001

VP->V P .00001

PP->P N .005

2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

N->claws .1

V->claws .2

Grammar Probabilities

P(S->N V) = .1

P(S->N VP) = .2

P(NP->N N) = .1

P(NP->N PP) = .1

P(NP-> N P) = .01

P(VP->V N) = .1

P(VP->V NP) = .2

P(VP->V V) = .005

P(VP-> V P) = .02

P(VP->V PP) = .1

P(VP->V @VP_V) = .3

P(VP->VP PP) = .1

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

P(PP-> P N) = .1

1 1 cats 2 scratch walls 3

Left

4 with 5 claws 6

Preterminals: 6

Induction: Span 4

Span 4: 5 4 … S->N VP 2e-6 VP->V NP 2e-6 VP > … V @VP_V 6e-6 V NP 4e-6 VP PP 5e-8 S->N VP 1e-6 VP->V NP 2e-7 Span = 4 Left = 2

Mid = 3

NP->N PP 1e-4 VP->V PP 5e-6 @VP_V-> N PP 1e-4 3 S->N V .002

NP->N N .001

VP->V N.0001

S->N V .002

NP->N N .001

VP->V N.0001

NP->N P .000001

VP->V P .00001

PP->P N .005

2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

N->claws .1

V->claws .2

Grammar Probabilities

P(S->N V) = .1

P(S->N VP) = .2

P(NP->N N) = .1

P(NP->N PP) = .1

P(NP-> N P) = .01

P(VP->V N) = .1

P(VP->V NP) = .2

P(VP->V V) = .005

P(VP-> V P) = .02

P(VP->V PP) = .1

P(VP->V @VP_V) = .3

P(VP->VP PP) = .1

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

P(PP-> P N) = .1

1 1 cats 2 scratch walls 3

Left

4 with 5 claws 6

Preterminals: 6

Induction: Span 4

Span 4: 5 4 … S->N VP 2e-6 VP->V NP 2e-6 VP > … V @VP_V 6e-6 V NP 4e-6 VP PP 5e-8 S->N VP 1e-6 VP->V NP 2e-7 Span = 4 Left = 2 NP->N PP 1e-4 VP->V PP 5e-6 @VP_V-> N PP 1e-4 3 S->N V .002

NP->N N .001

VP->V N.0001

S->N V .002

NP->N N .001

VP->V N.0001

NP->N P .000001

VP->V P .00001

PP->P N .005

2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

N->claws .1

V->claws .2

Grammar Probabilities

P(S->N V) = .1

P(S->N VP) = .2

P(NP->N N) = .1

P(NP->N PP) = .1

P(NP-> N P) = .01

P(VP->V N) = .1

P(VP->V NP) = .2

P(VP->V V) = .005

P(VP-> V P) = .02

P(VP->V PP) = .1

P(VP->V @VP_V) = .3

P(VP->VP PP) = .1

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

P(PP-> P N) = .1

1 1 cats 2 scratch walls 3

Left

4 with 5 claws 6

Preterminals: 6

Induction: Span 4

Span 4: 5 … 4 S->N VP 2e-6 VP->V NP 2e-6 VP-> V @VP_V 6e-6 Span = 4 Left = 2 back = (left = V, right = @VP_V, mid=1) S->N VP 1e-6 VP->V NP 2e-7 NP->N PP 1e-4 VP->V PP 5e-6 @VP_V-> N PP 1e-4 3 S->N V .002

NP->N N .001

VP->V N.0001

S->N V .002

NP->N N .001

VP->V N.0001

NP->N P .000001

VP->V P .00001

PP->P N .005

2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

N->claws .1

V->claws .2

Grammar Probabilities

P(S->N V) = .1

P(S->N VP) = .2

P(NP->N N) = .1

P(NP->N PP) = .1

P(NP-> N P) = .01

P(VP->V N) = .1

P(VP->V NP) = .2

P(VP->V V) = .005

P(VP-> V P) = .02

P(VP->V PP) = .1

P(VP->V @VP_V) = .3

P(VP->VP PP) = .1

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

P(PP-> P N) = .1

1 1 cats 2 scratch walls 3

Left

4 with 5 claws 6

Final Chart

6 5

S->N VP 1.2e-7

Back = (left=N, right=VP, mid=1) … VP-> V @VP_V 6e-6 4 S->N VP 2e-6 VP->V NP 2e-6 back = (left = V, right = @VP_V, mid=1) S->N VP 1e-6 VP->V NP 2e-7 NP->N PP 1e-4 VP->V PP 5e-6 @VP_V-> N PP 1e-4 3 S->N V .002

NP->N N .001

VP->V N.0001

S->N V .002

NP->N N .001

VP->V N.0001

NP->N P .000001

VP->V P .00001

PP->P N .005

2 N->cats 0.1

V->cats 0.01

N->scratch .1

V->scratch .2

N->walls .2

V->walls .01

P->with .5

N->claws .1

V->claws .2

Grammar Probabilities

P(S->N V) = .1

P(S->N VP) = .2

P(NP->N N) = .1

P(NP->N PP) = .1

P(NP-> N P) = .01

P(VP->V N) = .1

P(VP->V NP) = .2

P(VP->V V) = .005

P(VP-> V P) = .02

P(VP->V PP) = .1

P(VP->V @VP_V) = .3

P(VP->VP PP) = .1

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

P(PP-> P N) = .1

1 1 cats 2 scratch walls 3

Left

4 with 5 claws 6

Corresponding Tree

S V VP N @VP->_V PP P N

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

probability = score = 1.2e-7 cats scratch walls with claws

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!

360 300 240 180 120 60 • 0 0 10 20 30

Sentence Length

Super-cubic in practice! Why?

50 Best Fit Exponent: 3.47

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 frames put 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

walked

Sue

walked

Sue V

walked

into walked

into

store

into DT

the

store 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  p(VP  p(VP  V NP NP) V NP NP | said) V NP NP | gave) = 0.00151

= 0.00001

= 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: S S  NP VP NP  DT NN NP VP NP – – 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.

Michael Collins (2003, COLT)

Non-Independence I

• Independence assumptions are often too strong.

All NPs NPs under S NPs under VP

23% 21% 11% 9% 9% 9% 7% 6% 4% NP PP DT NN PRP NP PP DT NN PRP NP PP DT NN PRP

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

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: Parent annotation [Johnson 98] Marking possesive NPs • What are the most useful features to encode?

Annotations

• • • • Annotations split the grammar categories into sub-categories.

Conditioning on history vs. annotating – – P( NP^S  P( NP-POS PRP  ) is a lot like P( NP  PRP | S ) 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

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

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

74% 73% 72% 71% 70% 0 1 2v 2 inf Horizontal Markov Order 12000 9000 6000 3000 0 0 1 2v 2 inf Horizontal Markov Order

Vertical Markovization

Order 1 • Vertical Markov order: rewrites depend on past

ancestor nodes.

(cf. parent annotation) 79% 78% 77% 76% 75% 74% 73% 72% 1 2v 2 3v Vertical Markov Order 3 Order 2 25000 20000 15000 10000 5000 0 1 2v 2 3v Vertical Markov Order 3

Vertical and Horizontal

•

80% 78% 76% 74% 72% 3 70% 68% 66% 2 Vertical 0 1 2v 2 Horizontal Order

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

inf 1

v=1, h=  v=3, h=2v

Order 25000 20000 15000 10000 5000 0 0 1 2v 2 Horizontal Order inf 3 1 2 Vertical Order

Model Base: v=h=2v F1 77.8

Size 7.5K

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

Unary Splits

 Solution: Mark unary rewrite sites with -U Annotation Base UNARY F1 77.8

78.3

Size 7.5K

8.0K

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 Previous SPLIT-IN F1 78.3

80.3

Size 8.0K

8.1K

Other Tag Splits

• UNARY-DT : mark demonstratives as DT ^U X” vs. “those”) (“the F1 80.4

• UNARY-RB : mark phrasal adverbs as RB ^U (“quickly” vs. “very”) 80.5

• TAG-PA : mark tags with non-canonical parents (“not” is an RB ^VP ) 81.2

• SPLIT-AUX : mark auxiliary verbs with –AUX [cf. Charniak 97] 81.6

81.7

• SPLIT-CC : separate “but” and “&” from other conjunctions • SPLIT-% : “%” gets its own tag.

81.8

Size 8.1K

8.1K

8.5K

9.0K

9.1K

9.3K

Treebank Splits

• The treebank comes with annotations (e.g., -LOC, -SUBJ , etc).

– Whole set together hurt the baseline.

– Some ( -SUBJ effective than our equivalents.

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

) – We marked gapped S nodes as well.

Annotation Previous NP-TMP GAPPED-S F1 81.8

82.2

82.3

Size 9.3K

9.6K

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 Previous POSS-NP SPLIT-VP F1 82.3

83.1

85.7

Size 9.7K

9.8K

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 NP -v VP NP v Annotation Previous BASE-NP DOMINATES-V RIGHT-REC-NP PP F1 85.7

86.0

86.9

87.0

Size 10.5K

11.7K

14.1K

15.2K

A Fully Annotated Tree

Final Test Set Results

Parser Magerman 95 Collins 96 Klein & M 03 Charniak 97 Collins 99 LP 84.9

86.3

86.9

87.4

88.7

LR 84.6

85.8

85.7

87.5

88.6

F1 84.7

86.0

86.3

87.4

88.6

CB 1.26

1.14

1.10

1.00

0.90

0 CB 56.6

59.9

60.3

62.1

67.1

• Beats “first generation” lexicalized parsers.

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):

(

l p

t p

l g

)

(

l p

t p

) • • • 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

Petrov and Klein (2006): Learning Latent Annotations

Outside

Can you automatically find good symbols?

    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.

He was right

Inside

40 35 30 25 20 15 10 5 0

Number of phrasal subcategories

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

 Proper Nouns (NNP): NNP-14 NNP-12 NNP-2 NNP-1 NNP-15 NNP-3 Oct.

John J.

Bush New York Nov.

Robert E.

Noriega San Francisco Sept.

James L.

Peters Wall Street  Personal pronouns (PRP): PRP-0 PRP-1 PRP-2 It it it He he them I they him

The Latest Parsing Results…

Parser

Klein & Manning unlexicalized 2003 Matsuzaki et al. simple EM latent states 2005 Charniak generative (“maxent inspired”) 2000 Petrov and Klein NAACL 2007 Charniak & Johnson discriminative reranker 2005

F1 ≤ 40 words

86.3

86.7

90.1

90.6

92.0

F1 all words

85.7

86.1

89.5

90.1

91.4