Approximate Factoring for A* Search

Aria Haghighi, John DeNero, and Dan Klein

Computer Science Division

University of California Berkeley

Inference for NLP Tasks

A* Search

Inference as Search

ya1

a2

a3

PartialHypothesis

a2

VP

S

NP

Bitext Parsing as Search

translation is hard , la traducción es dificil

Weighted Synchronous Grammar

Parsing O(n6)

Modified CKY over bi-spans (X[i,j],X’[i’,j’])

Source Target

VP

S

NP

S S’

A* Search

Completion ScoreScore So Far

y

A* Search

Heuristic Design Tight

small Admissible

Efficient to compute

This way hypothesis!

A* Heuristic ManOptimal Result

A* Example: Bitext Search

Viterbi Inside Score

Cost So Far

Bi-Span

A* Bitext Search

Viterbi Outside Score

Completion Score

O(n6)Ideal Heuristic

Of Stately Projections ¼

S S’

S SVP

S

NP

S S’

S S’

VP

S

NP VP’

S’

NP’

VP’

S’

NP’

A* Bitext Search

Suppose,Then,

VP

S

NP

S S’

VPVP

S

NP

S

NP

VP’

S’

NP’

Projection Heuristic

O(n3) O(n3) O(n6)

Klein and Manning [2003]

When models don’t factorize

When models don’t factorize

Pointwise Admissibility

y

c(a)

x

¼s(y)

Ás(a)

¼s(x) ¼t(y)

Át(a)

¼t(x)

When models don’t factorize

Admissibility

¼s(y) ¼t(y)

y

Finding Factored Costs

Pointwise Gap

How to find Ás and Át?

Finding Factored Costs

Small gaps

Finding Factored Costs

PointwiseAdmissibility

Finding Factored Costs

Bitext Experiments

Synchronous Tree-to-Tree Transducer Trained on 40k sentences of English-Spanish Europarl [Galley et. al, 2004] Rare words replaced with POS tags Tested on 1,200 sent. max length 5-15

Optimization Problem Solved only once per grammar 206K Variables 160K Constraints 29 minutes

Bitext Experiments

Bitext Experiments

Bitext Experiments

Zhang and Gildea (2006)

Bitext Experiments

Zhang and Gildea (2006)

Lexicalized Parsing

NP-(translation,NN)

S-(is,VBZ)

VP-(is,VBZ)

(is,VBZ)

(translation, NN)NP

S

VP

Klein and Manning [2003]

Lexicalized Parsing

Lexicalized Parsing

Too many constraints to efficiently solve!

Over 64e13

possiblelexicalized

rules

Lexicalized Parsing

Lexicalized Parsing

Lexicalized Parsing

Lexicalized Parsing

Lexicalized Model Experiments

Standard Setup Train on section 2-21 of the treebank Test on section 23 (length · 40)

Models Tested Factored model [Klein and Manning, 2003]

Non-Factored Model

Lexicalized Parsing

Factored Model [Klein and Manning, 2003]

Lexicalized Parsing

Non-Factored Model

Conclusions

General technique for generating A* estimates

Can explicitly control admissibility tightness trade-off

Future Work: Explore different objectives and applications

Thanks

http://nlp.cs.berkeley.edu