Transcript Lecture 16: Finite-State Introduction

Finite-State Methods
600.465 - Intro to NLP - J. Eisner
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Finite state acceptors (FSAs)
 Things you may
know about FSAs:
c
a
e
Defines the
language a? c*
= {a, ac, acc, accc, …,
e, c, cc, ccc, …}
600.465 - Intro to NLP - J. Eisner
 Equivalence to
regexps
 Union, Kleene *,
concat, intersect,
complement,
reversal
 Determinization,
minimization
 Pumping,
Myhill-Nerode
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n-gram models not good enough
 Want to model grammaticality
 A “training” sentence known to be grammatical:
BOS mouse traps catch mouse traps EOS
trigram model must allow these trigrams
 Resulting trigram model has to overgeneralize:
 allows sentences with 0 verbs
BOS mouse traps EOS
 allows sentences with 2 or more verbs
BOS mouse traps catch mouse traps
catch mouse traps catch mouse traps EOS
 Can’t remember whether it’s in subject or object
(i.e., whether it’s gotten to the verb yet)
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Finite-state models can “get it”
 Want to model grammaticality
BOS mouse traps catch mouse traps EOS
 Finite-state can capture the generalization here:
Noun+ Verb Noun+
Noun
Noun
Noun
Verb
preverbal states
(still need a verb
to reach final state)
600.465 - Intro to NLP - J. Eisner
Noun
postverbal states
(verbs no longer
allowed)
Allows arbitrarily long
NPs (just keep looping
around for another
Noun modifier).
Still, never forgets
whether it’s preverbal
or postverbal!
(Unlike 50-gram model)
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How powerful are regexps / FSAs?
 More powerful than n-gram models
 The hidden state may “remember” arbitrary past context
 With k states, can remember which of k “types” of context it’s in
 Equivalent to HMMs
 In both cases, you observe a sequence and it is “explained” by a
hidden path of states. The FSA states are like HMM tags.
 Appropriate for phonology and morphology
Word =
=
=
=
Syllable+
(Onset Nucleus Coda?)+
(C+ V+ C*)+
( (b|d|f|…)+ (a|e|i|o|u)+ (b|d|f|…)* )+
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How powerful are regexps / FSAs?
 But less powerful than CFGs / pushdown automata
 Can’t do recursive center-embedding
 Hmm, humans have trouble processing those constructions too …
 This is the rat that ate the malt.
 This is the malt that the rat ate.
 This is the cat that bit the rat that ate the malt.
 This is the malt that the rat that the cat bit ate.
finite-state can
handle this pattern
(can you write the
regexp?)
 This is the dog that chased the cat that bit the rat that ate the malt.
 This is the malt that [the rat that [the cat that [the dog chased] bit] ate].
but not this pattern,
which requires a CFG
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How powerful are regexps / FSAs?
 But less powerful than CFGs / pushdown automata
 More important: Less explanatory than CFGs
 An CFG without recursive center-embedding can be converted
into an equivalent FSA – but the FSA will usually be far larger
 Because FSAs can’t reuse the same phrase type in different places
Noun
S=
Noun
Noun
Verb
duplicated
structure
more elegant – using
nonterminals like this
is equivalent to a CFG
Noun
Noun
duplicated
structure
S=
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NP =
NP
Verb
Noun
NP7
Strings vs. String Pairs
 FSA = “finite-state acceptor”
 Describes a language
(which strings are grammatical?)
 FST = “finite-state transducer”
 Describes a relation
(which pairs of strings are related?)
 underlying form  surface form
 sentence  translation
 original  edited
…
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Example: Edit Distance
position in upper string
0
1
2
3
4
5
Cost of best path
relating
these two
strings?
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position in lower string
0
1
2
3
4
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Example: Morphology
VP [head=vouloir,...]
V[head=vouloir, ...
tense=Present,
num=SG, person=P3]
veut
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slide courtesy of L. Karttunen (modified)
Example: Unweighted transducer
VP [head=vouloir,...]
vouloir +Pres +Sing + P3
V[head=vouloir, ...
Finite-state
transducer
tense=Present,
num=SG, person=P3]
veut
veut
canonical form
v
o
u
v
e
u
l
the relevant path
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inflection codes
i
r
+Pres
+Sing
+P3
t
inflected form
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slide courtesy of L. Karttunen
Example: Unweighted transducer
 Bidirectional: generation or analysis
 Compact and fast
 Xerox sells for about 20 languges
including English, German, Dutch,
French, Italian, Spanish,
Portuguese, Finnish, Russian,
Turkish, Japanese, ...
 Research systems for many other
languages, including Arabic, Malay
vouloir +Pres +Sing + P3
Finite-state
transducer
veut
canonical form
v
o
u
v
e
u
l
the relevant path
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inflection codes
i
r
+Pres
+Sing
+P3
t
inflected form
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Regular Relation (of strings)
 Relation: like a function, but multiple outputs ok
 Regular: finite-state
a:e
 Transducer: automaton w/ outputs
b:b
 b  {b}
?
a  ?{}
 aaaaa  {ac,
? aca, acab,
acabc}
 Invertible?
 Closed under composition?
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a:a
a:c
?:c
b:b
b:e
?:b
?:a
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Regular Relation (of strings)
 Can weight the arcs:  vs. 
 b  {b} a  {}
 aaaaa  {ac, aca, acab,
acabc}
a:e
b:b
a:a
 How to find best outputs?
 For aaaaa?
 For all inputs at once?
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a:c
?:c
b:b
b:e
?:b
?:a
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Function from strings to ...
Acceptors (FSAs)
Unweighted
c
{false, true}
a
e
c/.7
a/.5
.3
e/.5
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c:z
strings
a:x
e:y
numbers
Weighted
Transducers (FSTs)
(string, num) pairs c:z/.7
a:x/.5
.3
e:y/.5
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Sample functions
Acceptors (FSAs)
Unweighted
Weighted
Transducers (FSTs)
{false, true}
strings
Grammatical?
Markup
Correction
Translation
numbers
(string, num) pairs
How grammatical?
Better, how likely?
Good markups
Good corrections
Good translations
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Terminology (acceptors)
Regular language
defines
Regexp
recognizes
compiles into
implements
FSA
String
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Terminology (transducers)
Regular relation
defines
Regexp
recognizes
compiles into
implements
String pair
600.465 - Intro to NLP - J. Eisner
FST
?
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Perspectives on a Transducer
 Remember these CFG perspectives:
3 views of a context-free rule



generation (production): S  NP VP (randsent)
parsing (comprehension): S  NP VP (parse)
verification (checking):
S = NP VP
 Similarly, 3 views of a transducer:
 Given 0 strings, generate a new string pair (by picking a path)
 Given one string (upper or lower), transduce it to the other kind
 Given two strings (upper & lower), decide whether to accept the pair
v
o
u
v
e
u
l
o
i
r
+Pres
+Sing
+P3
t
FST just defines the regular relation (mathematical object: set of pairs).
What’s “input” and “output” depends on what one asks about the relation.
The 0, 1, or 2 given string(s) constrain which paths you can use.
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Functions
ab?d
abcd
abcd
f
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g
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Functions
abcd
ab?d
Function composition: f  g
[first f, then g – intuitive notation, but opposite of the traditional math notation]
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From Functions to Relations
f
ab?d
g
3
2
6
abcd
abed
4
2
8
abjd
abcd
abed
abd
...
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From Functions to Relations
ab?d
3
4
2
2
Relation composition: f  g
6
8
abcd
abed
abd
...
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From Functions to Relations
3+4
ab?d
2+2
Relation composition: f  g
6+8
abcd
abed
abd
...
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From Functions to Relations
ab?d
2+2
Pick min-cost or max-prob output
abed
Often in NLP, all of the functions or relations involved
can be described as finite-state machines, and
manipulated using standard algorithms.
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slide courtesy of L. Karttunen (modified)
Building a lexical transducer
c
l
e
e
big | clear | clever | ear | fat | ...
Regular Expression
Lexicon
f
a
t
a
v
h
r
e
Lexicon
FSA
Compiler
Lexical Transducer
(a single FST)
composition
Regular Expressions
for Rules
Composed
Rule FSTs
b
i
g
b
i
g
one path
600.465 - Intro to NLP - J. Eisner
+Adj
g
+Comp
e
r
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slide courtesy of L. Karttunen (modified)
Building a lexical transducer
c
l
e
e
big | clear | clever | ear | fat | ...
Regular Expression
Lexicon
f
a
t
a
v
h
r
e
Lexicon
FSA
 Actually, the lexicon must contain elements like
big +Adj +Comp
 So write it as a more complicated expression:
(big | clear | clever | fat | ...) +Adj (e | +Comp | +Sup)  adjectives
| (ear | father | ...) +Noun (+Sing | +Pl)
 nouns
| ...
 ...
 Q: Why do we need a lexicon at all?
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Inverting Relations
f
ab?d
g
3
4
abcd
abcd
2
2
abed
abed
6
8
abjd
abd
...
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Inverting Relations
f
g-1
-1
ab?d
3
4
abcd
abcd
2
2
abed
abed
6
8
abjd
abd
...
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Inverting Relations
3+4
ab?d
2+2
(f 
g)-1
=
g-1
f
-1
6+8
abcd
abed
abd
...
600.465 - Intro to NLP - J. Eisner
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slide courtesy of L. Karttunen (modified)
Weighted version of transducer:
Assigns a weight to each string pair
être+IndP +SG + P1
suivre+IndP+SG+P1
“upper language”
suivre+IndP+SG+P2
4
19
suivre+Imp+SG + P2
payer+IndP+SG+P1
20
50
12
Weighted French Transducer
3
suis
“lower language”
paie
paye
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Composition Cascades
 You can build fancy noisy-channel models by
composing transducers …
 Examples:
 Phonological/morphological rewrite rules?
 English orthography  English phonology
 Japanese phonology  Japanese orthography
 e.g. ???  goruhubaggu
 Information extraction
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FASTUS – Information Extraction
Appelt et al, 1992-?
Input: Bridgestone Sports Co. said Friday it has set up a joint venture
in Taiwan with a local concern and a Japanese trading house to
produce golf clubs to be shipped to Japan. The joint venture,
Bridgestone Sports Taiwan Co., capitalized at 20 million new Taiwan
dollars, will start production in January 1990 with …
Output:
Relationship:
Entities:
TIE-UP
“Bridgestone Sports Co.”
“A local concern”
“A Japanese trading house”
Joint Venture Company: “Bridgestone Sports Taiwan Co.”
Amount:
NT$20000000
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FASTUS: Successive Markups
(details on subsequent slides)
Tokenization
.o.
Multiwords
.o.
Basic phrases (noun groups, verb groups …)
.o.
Complex phrases
.o.
Semantic Patterns
.o.
Merging different references
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FASTUS: Tokenization




Spaces, hyphens, etc.
wouldn’t  would not
their  them ’s
company.  company .
but
Co.  Co.
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FASTUS: Multiwords
 “set up”
 “joint venture”
 “San Francisco Symphony Orchestra,”
“Canadian Opera Company”
 … use a specialized regexp to match
musical groups.
 ... what kind of regexp would match
company names?
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FASTUS : Basic phrases
Output looks like this (no nested brackets!):
… [NG it] [VG had set_up] [NP a joint_venture] [Prep in] …
Company Name:
Verb Group:
Noun Group:
Noun Group:
Verb Group:
Noun Group:
Preposition:
Location:
Preposition:
Noun Group:
Bridgestone Sports Co.
said
Friday
it
had set up
a joint venture
in
Taiwan
with
a local concern
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FASTUS: Noun Groups
Build FSA to recognize phrases like
approximately 5 kg
more than 30 people
the newly elected president
the largest leftist political force
a government and commercial project
Use the FSA for left-to-right longest-match markup
What does FSA look like? See next slide …
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FASTUS: Noun Groups
Described with a kind of non-recursive CFG …
(a regexp can include names that stand for other regexps)
NG  Pronoun | Time-NP | Date-NP
NG  (Det) (Adjs) HeadNouns
…
Adjs  sequence of adjectives maybe with commas,
conjunctions, adverbs
…
Det  DetNP | DetNonNP
DetNP  detailed expression to match “the only five,
another three, this, many, hers, all, the most …”
…
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FASTUS: Semantic patterns
BusinessRelationship =
NounGroup(Company/ies) VerbGroup(Set-up)
NounGroup(JointVenture) with
NounGroup(Company/ies) | …
ProductionActivity =
VerbGroup(Produce) NounGroup(Product)
NounGroup(Company/ies)  NounGroup & …
is made easy by the processing done at a previous level
Use this for spotting references to put in the database.
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Composition Cascades
 You can build fancy noisy-channel models
by composing transducers …
 … now let’s turn to how you might build
the individual transducers in the cascade.
 We’ll use a variety of operators that combine
simpler transducers and acceptors into more
complex ones.
 Composition is just one example.
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