Probabilistic and Lexicalized Parsing

CS 4705

Probabilistic CFGs: PCFGs

• Weighted CFGs– Attach weights to rules of CFG– Compute weights of derivations– Use weights to choose preferred parses

• Utility: Pruning and ordering the search space, disambiguate, Language Model for ASR

• Parsing with weighted grammars: find the parse T’ which maximizes the weights of the derivations in the parse tree for all the possible parses of S

• T’(S) = argmaxT∈τ(S) W(T,S)

• Probabilistic CFGs are one form of weighted CFGs

Rule Probability

• Attach probabilities to grammar rules• Expansions for a given non-terminal sum to 1

R1: VP V .55

R2: VP V NP .40

R3: VP V NP NP .05• Estimate probabilities from annotated corpora

– E.g. Penn Treebank– P(R1)=counts(R1)/counts(VP)

Derivation Probability

• For a derivation T= {R1…Rn}:

– Probability of the derivation: • Product of probabilities of rules expanded in tree

– Most likely probable parse: – Probability of a sentence:

• Sum over all possible derivations for the sentence

• Note the independence assumption: Parse probability does not change based on where the rule is expanded.

)(maxarg* TPTT

n

iiRPTP

1

)()(

T

STPSP )|()(

One Approach: CYK Parser

• Bottom-up parsing via dynamic programming– Assign probabilities to constituents as they

are completed and placed in a table– Use the maximum probability for each

constituent type going up the tree to S• The Intuition:

– We know probabilities for constituents lower in the tree, so as we construct higher level constituents we don’t need to recompute these

CYK (Cocke-Younger-Kasami) Parser

• Bottom-up parser with top-down filtering• Uses dynamic programming to store intermediate results

(cf. Earley algorithm for top-down case)• Input: PCFG in Chomsky Normal Form

– Rules of form Aw or ABC; no ε• Chart: array [i,j,A] to hold probability that non-terminal A

spans input i-j

– Start State(s): (i,i+1,A) for each Awi+1

– End State: (1,n,S) where n is the input size– Next State Rules: (i,k,B) (k,j,C) (i,j,A) if ABC

• Maintain back-pointers to recover the parse

Structural Ambiguity

• S NP VP• VP V NP• NP NP PP• VP VP PP• PP P NP

• NP John | Mary | Denver• V -> called• P -> from

John called Mary from Denver

S

VP PP

NP VP

V NP NPP

John called Mary from Denver

S

NP

NP VP

V NP PP

PJohn called Mary

from Denver

NP

Example

John called Mary from Denver

Base Case: Aw

NP

P Denver

NP from

V Mary

NP called

John

Recursive Cases: ABC

NP

P Denver

NP from

X V Mary

NP called

John

NP

P Denver

VP NP from

X V Mary

NP called

John

NP

X P Denver

VP NP from

X V Mary

NP called

John

PP NP

X P Denver

VP NP from

X V Mary

NP called

John

PP NP

X P Denver

S VP NP from

V Mary

NP called

John

PP NP

X X P Denver

S VP NP from

X V Mary

NP called

John

NP PP NP

X P Denver

S VP NP from

X V Mary

NP called

John

NP PP NP

X X X P Denver

S VP NP from

X V Mary

NP called

John

VP NP PP NP

X X X P Denver

S VP NP from

X V Mary

NP called

John

VP NP PP NP

X X X P Denver

S VP NP from

X V Mary

NP called

John

VP1

VP2

NP PP NP

X X X P Denver

S VP NP from

X V Mary

NP called

John

S VP1

VP2

NP PP NP

X X X P Denver

S VP NP from

X V Mary

NP called

John

S VP NP PP NP

X X X P Denver

S VP NP from

X V Mary

NP called

John

Problems with PCFGs• Probability model just based on rules in the derivation.• Lexical insensitivity:

– Doesn’t use words in any real way– But structural disambiguation is lexically driven

• PP attachment often depends on the verb, its object, and the preposition

• I ate pickles with a fork. • I ate pickles with relish.

• Context insensitivity of the derivation– Doesn’t take into account where in the derivation a rule is used

• Pronouns more often subjects than objects • She hates Mary. • Mary hates her.

• Solution: Lexicalization– Add lexical information to each rule– I.e. Condition the rule probabilities on the actual words

An example: Phrasal Heads

• Phrasal heads can ‘take the place of’ whole phrases, defining most important characteristics of the phrase

• Phrases generally identified by their heads– Head of an NP is a noun, of a VP is the main verb, of a

PP is preposition

• Each PFCG rule’s LHS shares a lexical item with a non-terminal in its RHS

Increase in Size of Rule Set in Lexicalized CFG

• If R is the number of binary branching rules in CFG and ∑ is the lexicon, O(2*|∑|*|R|)

• For unary rules: O(|∑|*|R|)

Example (correct parse)

Attribute grammar

Example (less preferred)

Computing Lexicalized Rule Probabilities

• We started with rule probabilities as before– VP V NP PP P(rule|VP)

• E.g., count of this rule divided by the number of VPs in a treebank

• Now we want lexicalized probabilities– VP(dumped) V(dumped) NP(sacks)

PP(into)• i.e., P(rule|VP ^ dumped is the verb ^ sacks is the

head of the NP ^ into is the head of the PP)

– Not likely to have significant counts in any treebank

Exploit the Data You Have

• So, exploit the independence assumption and collect the statistics you can…

• Focus on capturing– Verb subcategorization

• Particular verbs have affinities for particular VPs

– Objects’ affinity for their predicates• Mostly their mothers and grandmothers• Some objects fit better with some predicates than

others

Verb Subcategorization

• Condition particular VP rules on their heads– E.g. for a rule r VP -> V NP PP

• P(r|VP) becomes P(r ^ V=dumped | VP ^ dumped)

– How do you get the probability?• How many times was rule r used with dumped,

divided by the number of VPs that dumped appears in, in total

• How predictive of r is the verb dumped?

– Captures affinity between VP heads (verbs) and VP rules

Example (correct parse)

Example (less preferred)

Affinity of Phrasal Heads for Other Heads: PP Attachment

• Verbs with preps vs. Nouns with preps• E.g. dumped with into vs. sacks with into

– How often is dumped the head of a VP which includes a PP daughter with into as its head relative to other PP heads or… what’s P(into|PP,dumped is mother VP’s head))

– Vs…how often is sacks the head of an NP with a PP daughter whose head is into relative to other PP heads or… P(into|PP,sacks is mother’s head))

But Other Relationships do Not Involve Heads (Hindle & Rooth ’91)

• Affinity of gusto for eat is greater than for spaghetti; and affinity of marinara for spaghetti is greater than for ate

Vp (ate) Vp(ate)

Vp(ate) Pp(with)

Pp(with)

Np(spag)

npvvAte spaghetti with marinaraAte spaghetti with gusto

np

Log-linear models for Parsing

• Why restrict to the conditioning to the elements of a rule?– Use even larger context…word sequence, word

types, sub-tree context etc.

• Compute P(y|x); where fi(x,y) tests properties of context and i is weight of feature

• Use as scores in CKY algorithm to find best parse

Yy

yxf

yxf

ii

ii

e

exyP

),(*

),(*

)|(

Supertagging: Almost parsing

Poachers now control the underground trade

NP

N

poachers

N

NN

tradeS

NP

VP

V

NP

N

poachers

::

S

SAdv

now

VP

VPAdv

now

VP

AdvVP

now

::

S

S

VP

V

NP

control

S

NP

VP

V

NP

control

S

NP

VP

V

NP

control

S

NP

NPDet

the

NP

NP

N

trade

N

NN

poachers

S

NP

VP

V

NP

N

trade

N

NAdj

underground

S

NP

VP

V

NP

Adj

underground

S

NP

VP

V

NP

Adj

underground

S

NP

:

Summary

• Parsing context-free grammars– Top-down and Bottom-up parsers– Mixed approaches (CKY, Earley parsers)

• Preferences over parses using probabilities– Parsing with PCFG and PCKY algorithms

• Enriching the probability model– Lexicalization– Log-linear models for parsing– Super-tagging