1 computational lexicology, morphology and syntax course 5 diana trandab ă ț academic year:...

1

Computational Lexicology, Morphology and Syntax

Course 5

Diana TrandabățAcademic year: 2014-2015

Word Classes

• Words that somehow ‘behave’ alike:–Appear in similar contexts–Perform similar functions in sentences–Undergo similar transformations

• ~9 traditional word classes of parts of speech (POS)–Noun, verb, adjective, preposition, adverb, article,

interjection, pronoun, conjunction

2

Some Examples

• N noun chair, bandwidth, pacing

• V verb study, debate, munch• ADJ adjective purple, tall, ridiculous• ADV adverb unfortunately, slowly• P preposition of, by, to• PRO pronoun I, me, mine• DET determiner the, a, that, those

3

Defining POS Tagging

• The process of assigning a part-of-speech or lexical class marker to each word in a corpus:

4

thekoalaputthekeysonthetable

WORDSTAGS

NVPDET

Applications for POS Tagging• Speech synthesis pronunciation

– Lead Lead– INsult inSULT– OBject obJECT– OVERflow overFLOW– DIScount disCOUNT– CONtent conTENT

• Word Sense Disambiguation: e.g. Time flies like an arrow– Is flies an N or V?

• Word prediction in speech recognition – Possessive pronouns (my, your, her) are likely to be followed by

nouns– Personal pronouns (I, you, he) are likely to be followed by verbs

• Machine Translation5

Closed vs. Open class of words

• Closed class categories are composed of a small, fixed set of grammatical words for a given language.– Prepositions: of, in, by, …– Auxiliary verbs: may, can, will, had, been, …– Pronouns: I, you, she, mine, his, them, …– Usually function words (short common words which play a

role in grammar)• Open class categories have large number of words and

new ones are easily invented.– English has 4 categories: Nouns, Verbs, Adjectives, Adverbs– Nouns: Googler– Verbs: Google– Adjectives: geeky

6

Ambiguity in POS Tagging

• “Like” can be a verb or a preposition– I like/VBP candy.– Time flies like/IN an arrow.

• “Around” can be a preposition, particle, or adverb– I bought it at the shop around/IN the corner.– I never got around/RP to getting a car.– A new Prius costs around/RB $25K.

7

Open Class Words

• Nouns–Proper nouns

• Columbia University, New York City, Arthi Ramachandran, Metropolitan Transit Center

• English (and Romanian, and many other languages) capitalizes these

• Many have abbreviations

–Common nouns• All the rest

8

– Count nouns vs. mass nouns• Count: Have plurals, countable: goat/goats, one goat, two goats• Mass: Not countable (fish, salt, communism) (?two fishes)

• Adjectives: identify properties or qualities of nouns– Color, size, age, …– Adjective ordering restrictions in English:

• Old blue book, not Blue old book– In Korean, adjectives are realized as verbs

• Adverbs: also modify things (verbs, adjectives, adverbs)– The very happy man walked home extremely slowly

yesterday.

9

– Directional/locative adverbs (here, home, downhill)

– Degree adverbs (extremely, very, somewhat)– Manner adverbs (slowly, silkily, delicately)– Temporal adverbs (Monday, tomorrow)

• Verbs:– In most languages take morphological affixes

(eat/eats/eaten)– Represent actions (walk, ate), processes (provide,

see), and states (be, seem)– Many subclasses, e.g.

• eats/V eat/VB, eat/VBP, eats/VBZ, ate/VBD, eaten/VBN, eating/VBG, ...

• Reflect morphological form & syntactic function

How Do We Assign Words to Open or Closed?

• Nouns denote people, places and things and can be preceded by articles. But…

My typing is very bad.*The Mary loves John.

• Verbs are used to refer to actions, processes, states–But some are closed class and some are openI will have emailed everyone by noon.

• Adverbs modify actions– Is Monday a temporal adverbial or a noun?

11

Closed Class Words

• Closed class words (Prep, Det, Pron, Conj, Aux, Part, Num) are generally easy to process, since we can enumerate them…. but– Is it a Particles or a Preposition?

• George eats up his dinner/George eats his dinner up.• George eats up the street/*George eats the street up.

–Articles come in 2 flavors: definite (the) and indefinite (a, an)• What is this in ‘this guy…’?

12

Choosing a POS Tagset

• To do POS tagging, first need to choose a set of tags

• Could pick very coarse (small) tagsets–N, V, Adj, Adv.

• More commonly used: Brown Corpus (Francis & Kucera ‘82), 1M words, 87 tags – more informative but more difficult to tag

• Most commonly used: Penn Treebank: hand-annotated corpus of Wall Street Journal, 1M words, 45 tags

13

http://www.cis.upenn.edu/~treebank/

English Parts of Speech• Noun (person, place or thing)

– Singular (NN): dog, fork– Plural (NNS): dogs, forks– Proper (NNP, NNPS): John, Springfields

• Pronouns– Personal pronoun (PRP): I, you, he, she, it– Wh-pronoun (WP): who, what

• Verb (actions and processes)– Base, infinitive (VB): eat– Past tense (VBD): ate– Gerund (VBG): eating– Past participle (VBN): eaten– Non 3rd person singular present tense (VBP): eat– 3rd person singular present tense: (VBZ): eats– Modal (MD): should, can– To (TO): to (to eat) 14

English Parts of Speech (cont.)• Adjective (modify nouns)

– Basic (JJ): red, tall– Comparative (JJR): redder, taller– Superlative (JJS): reddest, tallest

• Adverb (modify verbs)– Basic (RB): quickly– Comparative (RBR): quicker– Superlative (RBS): quickest

• Preposition (IN): on, in, by, to, with• Determiner:

– Basic (DT) a, an, the– WH-determiner (WDT): which, that

• Coordinating Conjunction (CC): and, but, or,• Particle (RP): off (took off), up (put up)

15

Penn Treebank Tagset

16

Part of Speech (POS) Tagging• Lowest level of syntactic analysis.

17

John saw the saw and decided to take it to the table.NNP VBD DT NN CC VBD TO VB PRP IN DT NN

POS Tagging Process• Usually assume a separate initial tokenization process that

separates and/or disambiguates punctuation, including detecting sentence boundaries.

• Degree of ambiguity in English (based on Brown corpus)– 11.5% of word types are ambiguous.– 40% of word tokens are ambiguous.

• Average POS tagging disagreement amongst expert human judges for the Penn treebank was 3.5%– Based on correcting the output of an initial automated tagger, which

was deemed to be more accurate than tagging from scratch.• Baseline: Picking the most frequent tag for each specific word

type gives about 90% accuracy– 93.7% if use model for unknown words for Penn Treebank tagset.

18

POS Tagging Approaches• Rule-Based: Human crafted rules based on lexical

and other linguistic knowledge.• Learning-Based: Trained on human annotated

corpora like the Penn Treebank.– Statistical models: Hidden Markov Model (HMM),

Maximum Entropy Markov Model (MEMM), Conditional Random Field (CRF)

– Rule learning: Transformation Based Learning (TBL)• Generally, learning-based approaches have been

found to be more effective overall, taking into account the total amount of human expertise and effort involved.

19

20/24

Simple taggers• Default tagger has one tag per word, and assigns it on the

basis of dictionary lookup– Tags may indicate ambiguity but not resolve it, e.g. NVB for noun-or-

verb• Words may be assigned different tags with associated

probabilities – Tagger will assign most probable tag unless – there is some way to identify when a less probable tag is in fact

correct• Tag sequences may be defined by regular expressions, and

assigned probabilities (including 0 for illegal sequences – negative rules)

21/24

Rule-based taggers

• Earliest type of tagging: two stages• Stage 1: look up word in lexicon to give list of

potential POSs• Stage 2: Apply rules which certify or disallow

tag sequences• Rules originally handwritten; more recently

Machine Learning methods can be used

Start with a POS Dictionary

• she: PRP• promised: VBN,VBD• to: TO• back: VB, JJ, RB, NN• the: DT• bill: NN, VB• Etc… for the ~100,000 words of English

22

Assign All Possible POS to Each Word

NNRB

VBN JJ VBPRP VBD TO VB DT NNShe promised to back the bill

23

Apply Rules Eliminating Some POS

E.g., Eliminate VBN if VBD is an option when VBN|VBD follows “<start> PRP”

NNRB

VBN JJ VBPRP VBD TO VB DT NNShe promised to back the bill

24

Apply Rules Eliminating Some POS

E.g., Eliminate VBN if VBD is an option when VBN|VBD follows “<start> PRP”

NNRB

JJ VBPRP VBD TO VB DT NNShe promised to back the bill

25

EngCG ENGTWOL Tagger

• Richer dictionary includes morphological and syntactic features (e.g. subcategorization frames) as well as possible POS

• Uses two-level morphological analysis on input and returns all possible POS

• Apply negative constraints (> 3744) to rule out incorrect POS

Sample ENGTWOL Dictionary

27

ENGTWOL Tagging: Stage 1• First Stage: Run words through FST morphological analyzer

to get POS info from morph• E.g.: Pavlov had shown that salivation …

Pavlov PAVLOV N NOM SG PROPERhad HAVE V PAST VFIN SVO

HAVE PCP2 SVOshown SHOW PCP2 SVOO SVO SVthat ADV

PRON DEM SGDET CENTRAL DEM SGCS

salivation N NOM SG

28

ENGTWOL Tagging: Stage 2

• Second Stage: Apply NEGATIVE constraints• E.g., Adverbial that rule

–Eliminate all readings of that except the one in It isn’t that odd.

Given input: thatIf

(+1 A/ADV/QUANT) ; if next word is adj/adv/quantifier(+2 SENT-LIM) ; followed by E-O-S(NOT -1 SVOC/A) ; and the previous word is not a verb like

consider which allows adjective complements (e.g. I consider

that odd)Then eliminate non-ADV tagsElse eliminate ADV

29

30/24

How do they work?

• Tagger must be “trained”

• Many different techniques, but typically …

• Small “training corpus” hand-tagged

• Tagging rules learned automatically

• Rules define most likely sequence of tags

• Rules based on – Internal evidence (morphology)– External evidence (context)– Probabilities

31/24

What probabilities do we have to learn?

(a) Individual word probabilities:Probability that a given tag t is appropriate for

a given word w– Easy (in principle): learn from training corpus:

– Problem of “sparse data”:• Add a small amount to each calculation, so we get

no zeros

)(

),()|(

wf

wtfwtP run occurs 4800 times in the

training corpus: 3600 times as averb, 1200 times as a noun:P(verb|run) = 0.75

32/24

(b) Tag sequence probability:

Probability that a given tag sequence t1,t2,…,tn is appropriate for a given word sequence w1,w2,…,wn

– P(t1,t2,…,tn | w1,w2,…,wn ) = ??? – Too hard to calculate for entire sequence:P(t1,t2 ,t3 ,t4 ,...) = P(t2|t1 ) P(t3|t1,t2 ) P(t4|t1,t2 ,t3 ) …

– Subsequence is more tractable– Sequence of 2 or 3 should be enough:

Bigram model: P(t1,t2) = P(t2|t1 )

Trigram model: P(t1,t2 ,t3) = P(t2|t1 ) P(t3|t2 ) N-gram model:

ni

iin ttPttP,1

11 )|(),...,(

33/24

More complex taggers

• Bigram taggers assign tags on the basis of sequences of two words (usually assigning tag to wordn on the basis of wordn-1)

• An nth-order tagger assigns tags on the basis of sequences of n words

• As the value of n increases, so does the complexity of the statistical calculation involved in comparing probability combinations.

34/24

Stochastic taggers

• Nowadays, pretty much all taggers are statistics-based and have been since 1980s (or even earlier ... Some primitive algorithms were already published in 60s and 70s)

• Most common is based on Hidden Markov Models (also found in speech processing, etc.)

35/24

(Hidden) Markov Models• Probability calculations imply Markov models: we assume that

P(t|w) is dependent only on the (or, a sequence of) previous word(s)

• (Informally) Markov models are the class of probabilistic models that assume we can predict the future without taking into account too much of the past

• Markov chains can be modelled by finite state automata: the next state in a Markov chain is always dependent on some finite history of previous states

• Model is “hidden” if it is actually a succession of Markov models, whose intermediate states are of no interest

36/24

Supervised vs unsupervised training

• Learning tagging rules from a marked-up corpus (supervised learning) gives very good results (98% accuracy)– Though assigning most probable tag, and “proper noun” to

unknowns will give 90%• But it depends on having a corpus already marked up

to a high quality• If this is not available, we have to try something else:

– “forward-backward” algorithm– A kind of “bootstrapping” approach

37/24

Forward-backward (Baum-Welch) algorithm

• Start with initial probabilities– If nothing known, assume all Ps equal

• Adjust the individual probabilities so as to increase the overall probability.

• Re-estimate the probabilities on the basis of the last iteration

• Continue until convergence– i.e. there is no improvement, or improvement is below a

threshold• All this can be done automatically

38/24

Transformation-based tagging

• Eric Brill (1993)• Start from an initial tagging, and apply a series

of transformations• Transformations are learned as well, from the

training data• Captures the tagging data in much fewer

parameters than stochastic models• The transformations learned (often) have

linguistic “reality”

39/24

Transformation-based tagging

• Three stages:– Lexical look-up– Lexical rule application for unknown words– Contextual rule application to correct mis-tags

40/24

Transformation-based learning

• Change tag a to b when:– Internal evidence (morphology)– Contextual evidence

• One or more of the preceding/following words has a specific tag• One or more of the preceding/following words is a specific word• One or more of the preceding/following words has a certain form

• Order of rules is important– Rules can change a correct tag into an incorrect tag, so

another rule might correct that “mistake”

41/24

Transformation-based tagging: examples

• if a word is currently tagged NN, and has a suffix of length 1 which consists of the letter 's', change its tag to NNS

• if a word has a suffix of length 2 consisting of the letter sequence 'ly', change its tag to RB (regardless of the initial tag)

• change VBN to VBD if previous word is tagged as NN• Change VBD to VBN if previous word is ‘by’

42/24

Transformation-based tagging: example

Booth/NP killed/VBN Abraham/NP Lincoln/NPAbraham/NP Lincoln/NP was/BEDZ shot/VBD by/BY Booth/NPHe/PPS witnessed/VBD Lincoln/NP killed/VBN by/BY Booth/NP

Example after lexical lookup

Booth/NP killed/VBD Abraham/NP Lincoln/NPAbraham/NP Lincoln/NP was/BEDZ shot/VBN by/BY Booth/NPHe/PPS witnessed/VBD Lincoln/NP killed/VBN by/BY Booth/NP

Example after application of contextual rule ’vbd vbn NEXTWORD by’

Booth/NP killed/VBD Abraham/NP Lincoln/NPAbraham/NP Lincoln/NP was/BEDZ shot/VBD by/BY Booth/NPHe/PPS witnessed/VBD Lincoln/NP killed/VBD by/BY Booth/NP

Example after application of contextual rule ’vbn vbd PREVTAG np’

04/19/23 43

Templates for TBL

04/19/23 44

Sample TBL Rule Application

• Labels every word with its most-likely tag– E.g. race occurences in the Brown corpus:

• P(NN|race) = .98• P(VB|race)= .02• is/VBZ expected/VBN to/TO race/NN tomorrow/NN

• Then TBL applies the following rule– “Change NN to VB when previous tag is TO”

… is/VBZ expected/VBN to/TO race/NN tomorrow/NNbecomes… is/VBZ expected/VBN to/TO race/VB tomorrow/NN

04/19/23 45

TBL Tagging Algorithm• Step 1: Label every word with most likely tag (from

dictionary)• Step 2: Check every possible transformation & select one

which most improves tag accuracy (cf Gold)• Step 3: Re-tag corpus applying this rule, and add rule to end

of rule set• Repeat 2-3 until some stopping criterion is reached, e.g., X

% correct with respect to training corpus• RESULT: Ordered set of transformation rules to use on new

data tagged only with most likely POS tags

04/19/23 46

TBL Issues

• Problem: Could keep applying (new) transformations ad infinitum

• Problem: Rules are learned in ordered sequence

• Problem: Rules may interact• But: Rules are compact and can be

inspected by humans

Evaluating Tagging Approaches• For any NLP problem, we need to know

how to evaluate our solutions• Possible Gold Standards -- ceiling:

– Annotated naturally occurring corpus– Human task performance (96-7%)

• How well do humans agree?• Kappa statistic: avg pairwise agreement

corrected for chance agreement– Can be hard to obtain for some tasks:

sometimes humans don’t agree

• Baseline: how well does simple method do? – For tagging, most common tag for each word

(90%)– How much improvement do we get over

baseline?

Methodology: Error Analysis• Confusion matrix:

– E.g. which tags did we most often confuse with which other tags?

– How much of the overall error does each confusion account for?

VB TO NN

VB

TO

NN

More Complex Issues

• Tag indeterminacy: when ‘truth’ isn’t clearCaribbean cooking, child seat

• Tagging multipart wordswouldn’t --> would/MD n’t/RB

• How to handle unknown words– Assume all tags equally likely– Assume same tag distribution as all other

singletons in corpus– Use morphology, word length,….

Classification Learning

• Typical machine learning addresses the problem of classifying a feature-vector description into a fixed number of classes.

• There are many standard learning methods for this task:– Decision Trees and Rule Learning– Naïve Bayes and Bayesian Networks– Logistic Regression / Maximum Entropy (MaxEnt)– Perceptron and Neural Networks– Support Vector Machines (SVMs)– Nearest-Neighbor / Instance-Based

51

Beyond Classification Learning

• Standard classification problem assumes individual cases are disconnected and independent (i.i.d.: independently and identically distributed).

• Many NLP problems do not satisfy this assumption and involve making many connected decisions, each resolving a different ambiguity, but which are mutually dependent.

• More sophisticated learning and inference techniques are needed to handle such situations in general.

52

Sequence Labeling Problem• Many NLP problems can viewed as sequence

labeling.• Each token in a sequence is assigned a label.• Labels of tokens are dependent on the labels of

other tokens in the sequence, particularly their neighbors (not i.i.d).

53

foo bar blam zonk zonk bar blam

Information Extraction• Identify phrases in language that refer to specific types of

entities and relations in text.• Named entity recognition is task of identifying names of

people, places, organizations, etc. in text. people organizations places

– Michael Dell is the CEO of Dell Computer Corporation and lives in Austin Texas.

• Extract pieces of information relevant to a specific application, e.g. used car ads:

make model year mileage price– For sale, 2002 Toyota Prius, 20,000 mi, $15K or best offer.

Available starting July 30, 2006.

54

Semantic Role Labeling

• For each clause, determine the semantic role played by each noun phrase that is an argument to the verb.agent patient source destination instrument– John drove Mary from Austin to Dallas in his

Toyota Prius.– The hammer broke the window.

• Also referred to a “case role analysis,” “thematic analysis,” and “shallow semantic parsing”

55

Bioinformatics

• Sequence labeling also valuable in labeling genetic sequences in genome analysis.extron intron– AGCTAACGTTCGATACGGATTACAGCCT

56

Sequence Labeling as Classification

• Classify each token independently but use as input features, information about the surrounding tokens (sliding window).

57

John saw the saw and decided to take it to the table.

classifier

NNP



58


classifier

VBD



59


classifier

DT



60


classifier

NN



61


classifier

CC



62


classifier

VBD



63


classifier

TO



64


classifier

VB



65


classifier

PRP



66


classifier

IN



67


classifier

DT



68


classifier

NN

Sequence Labeling as ClassificationUsing Outputs as Inputs

• Better input features are usually the categories of the surrounding tokens, but these are not available yet.

• Can use category of either the preceding or succeeding tokens by going forward or back and using previous output.

69

Forward Classification

70


classifier

NNP


71

NNPJohn saw the saw and decided to take it to the table.

classifier

VBD


72

NNP VBDJohn saw the saw and decided to take it to the table.

classifier

DT


73

NNP VBD DTJohn saw the saw and decided to take it to the table.

classifier

NN


74

NNP VBD DT NNJohn saw the saw and decided to take it to the table.

classifier

CC


75

NNP VBD DT NN CCJohn saw the saw and decided to take it to the table.

classifier

VBD


76

NNP VBD DT NN CC VBDJohn saw the saw and decided to take it to the table.

classifier

TO


77

NNP VBD DT NN CC VBD TOJohn saw the saw and decided to take it to the table.

classifier

VB


78

NNP VBD DT NN CC VBD TO VBJohn saw the saw and decided to take it to the table.

classifier

PRP


79

NNP VBD DT NN CC VBD TO VB PRPJohn saw the saw and decided to take it to the table.

classifier

IN


80

NNP VBD DT NN CC VBD TO VB PRP INJohn saw the saw and decided to take it to the table.

classifier

DT


81

NNP VBD DT NN CC VBD TO VB PRP IN DTJohn saw the saw and decided to take it to the table.

classifier

NN

Backward Classification

• Disambiguating “to” in this case would be even easier backward.

82


classifier

NN



83

NNJohn saw the saw and decided to take it to the table.

classifier

DT



84

DT NNJohn saw the saw and decided to take it to the table.

classifier

IN



85

IN DT NNJohn saw the saw and decided to take it to the table.

classifier

PRP



86

PRP IN DT NNJohn saw the saw and decided to take it to the table.

classifier

VB



87

VB PRP IN DT NNJohn saw the saw and decided to take it to the table.

classifier

TO



88

TO VB PRP IN DT NN John saw the saw and decided to take it to the table.

classifier

VBD



89

VBD TO VB PRP IN DT NN John saw the saw and decided to take it to the table.

classifier

CC

Backward Classification• Disambiguating “to” in this case would be

even easier backward.

90

CC VBD TO VB PRP IN DT NN John saw the saw and decided to take it to the table.

classifier

NN



91

VBD CC VBD TO VB PRP IN DT NNJohn saw the saw and decided to take it to the table.

classifier

DT



92

DT VBD CC VBD TO VB PRP IN DT NNJohn saw the saw and decided to take it to the table.

classifier

VBD



93

VBD DT VBD CC VBD TO VB PRP IN DT NN John saw the saw and decided to take it to the table.

classifier

NNP

Problems with Sequence Labeling as Classification

• Not easy to integrate information from category of tokens on both sides.

• Difficult to propagate uncertainty between decisions and “collectively” determine the most likely joint assignment of categories to all of the tokens in a sequence.

94

Probabilistic Sequence Models

• Probabilistic sequence models allow integrating uncertainty over multiple, interdependent classifications and collectively determine the most likely global assignment.

• Two standard models– Hidden Markov Model (HMM)– Conditional Random Field (CRF)

95

Markov Model / Markov Chain

• A finite state machine with probabilistic state transitions.

• Makes Markov assumption that next state only depends on the current state and independent of previous history.

96

Sample Markov Model for POS

97

0.95

0.05

0.9

0.05stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

start0.1

0.5

0.4

Det Noun

PropNoun

Verb

Sample Markov Model for POS

98

0.95

0.05

0.9

0.05stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

start0.1

0.5

0.4

Det Noun

PropNoun

Verb

P(PropNoun Verb Det Noun) = 0.4*0.8*0.25*0.95*0.1=0.0076

Hidden Markov Model• Probabilistic generative model for sequences.• Assume an underlying set of hidden (unobserved)

states in which the model can be (e.g. parts of speech).

• Assume probabilistic transitions between states over time (e.g. transition from POS to another POS as sequence is generated).

• Assume a probabilistic generation of tokens from states (e.g. words generated for each POS).

99

Sample HMM for POS

100

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

start0.1

0.5

0.4

Sample HMM Generation

101

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

start0.1

0.5

0.4


102

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.10.25

start0.1

0.5

0.4


103

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

John start0.1

0.5

0.4


104

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

John start0.1

0.5

0.4


105

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

John bit start0.1

0.5

0.4


106

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

John bit start0.1

0.5

0.4


107

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

John bit thestart0.1

0.5

0.4


108

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

John bit thestart0.1

0.5

0.4


109

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

John bit the applestart0.1

0.5

0.4


110

PropNoun

JohnMaryAlice

Jerry

Tom

Noun

catdog

carpen

bedapple

Det

a thethe

the

that

a thea

Verb

bit

ate sawplayed

hit

0.95

0.05

0.9

gave0.05

stop

0.5

0.1

0.8

0.1

0.1

0.25

0.25

John bit the applestart0.1

0.5

0.4

Formal Definition of an HMM• A set of N +2 states S={s0,s1,s2, … sN, sF}

– Distinguished start state: s0

– Distinguished final state: sF

• A set of M possible observations V={v1,v2…vM}• A state transition probability distribution A={aij}

• Observation probability distribution for each state j B={bj(k)}

• Total parameter set λ={A,B}

FjiNjisqsqPa itjtij ,0 and ,1 )|( 1

111

Mk1 1 )|at ()( NjsqtvPkb jtkj

Niaa iF

N

jij

011

HMM Generation Procedure

• To generate a sequence of T observations: O = o1 o2 … oT

112

Set initial state q1=s0

For t = 1 to T Transit to another state qt+1=sj based on transition distribution aij for state qt

Pick an observation ot=vk based on being in state qt using distribution bqt(k)

Three Useful HMM Tasks• Observation Likelihood: To classify and order

sequences.• Most likely state sequence (Decoding): To

tag each token in a sequence with a label.• Maximum likelihood training (Learning): To

train models to fit empirical training data.

113

HMM: Observation Likelihood• Given a sequence of observations, O, and a model

with a set of parameters, λ, what is the probability that this observation was generated by this model: P(O| λ) ?

• Allows HMM to be used as a language model: A formal probabilistic model of a language that assigns a probability to each string saying how likely that string was to have been generated by the language.

• Useful for two tasks:– Sequence Classification– Most Likely Sequence

114

Sequence Classification• Assume an HMM is available for each category

(i.e. language).• What is the most likely category for a given

observation sequence, i.e. which category’s HMM is most likely to have generated it?

• Used in speech recognition to find most likely word model to have generate a given sound or phoneme sequence.

115Austin Boston

? ?

P(O | Austin) > P(O | Boston) ?

ah s t e n

O

Most Likely Sequence• Of two or more possible sequences, which

one was most likely generated by a given model?

• Used to score alternative word sequence interpretations in speech recognition.

116

Ordinary English

dice precedent core

vice president Gore

O1

O2

?

?

P(O2 | OrdEnglish) > P(O1 | OrdEnglish) ?

HMM: Observation LikelihoodNaïve Solution

• Consider all possible state sequences, Q, of length T that the model could have traversed in generating the given observation sequence.

• Compute the probability of a given state sequence from A, and multiply it by the probabilities of generating each of given observations in each of the corresponding states in this sequence to get P(O,Q| λ) = P(O| Q, λ) P(Q| λ) .

• Sum this over all possible state sequences to get P(O| λ).

• Computationally complex: O(TNT).

117

HMM: Observation LikelihoodEfficient Solution

• Due to the Markov assumption, the probability of being in any state at any given time t only relies on the probability of being in each of the possible states at time t−1.

• Forward Algorithm: Uses dynamic programming to exploit this fact to efficiently compute observation likelihood in O(TN2) time.– Compute a forward trellis that compactly and implicitly

encodes information about all possible state paths.

118

Forward Probabilities

• Let t(j) be the probability of being in state j after seeing the first t observations (by summing over all initial paths leading to j).

119

)| ,,...,()( 21 jttt sqoooPj

Forward Step• Consider all possible ways of

getting to sj at time t by coming from all possible states si and determine probability of each.

• Sum these to get the total probability of being in state sj at time t while accounting for the first t −1 observations.

• Then multiply by the probability of actually observing ot in sj.

120

s1

s2

sN

sj

t-1(i) t(i)

a1j

a2j

aNj

a2j

Forward Trellis

• Continue forward in time until reaching final time point and sum probability of ending in final state.

121

s1

s2

sN

s0sF

t1 t2 t3 tT-1 tT

Computing the Forward Probabilities

• Initialization

• Recursion

• Termination

122

Njobaj jj 1)()( 101

TtNjobaij tj

N

iijtt

1 ,1)()()(

11

N

iiFTFT aisOP

11 )()()|(

Forward Computational Complexity

• Requires only O(TN2) time to compute the probability of an observed sequence given a model.

• Exploits the fact that all state sequences must merge into one of the N possible states at any point in time and the Markov assumption that only the last state effects the next one.

123

Most Likely State Sequence (Decoding)• Given an observation sequence, O, and a model, λ,

what is the most likely state sequence,Q=q1,q2,…qT, that generated this sequence from this model?

• Used for sequence labeling, assuming each state corresponds to a tag, it determines the globally best assignment of tags to all tokens in a sequence using a principled approach grounded in probability theory.

124

John gave the dog an apple.

Most Likely State Sequence• Given an observation sequence, O, and a model, λ,



125


Det Noun PropNoun Verb




126






127






128






129






130



HMM: Most Likely State SequenceEfficient Solution

• Obviously, could use naïve algorithm based on examining every possible state sequence of length T.

• Dynamic Programming can also be used to exploit the Markov assumption and efficiently determine the most likely state sequence for a given observation and model.

• Standard procedure is called the Viterbi algorithm (Viterbi, 1967) and also has O(N2T) time complexity.

131

Viterbi Scores• Recursively compute the probability of the most

likely subsequence of states that accounts for the first t observations and ends in state sj.

132

)| ,,..., ,,...,,(max)( 11110,...,, 110

jtttqqq

t sqooqqqPjvt

• Also record “backpointers” that subsequently allow backtracing the most probable state sequence. btt(j) stores the state at time t-1 that maximizes the

probability that system was in state sj at time t (given the observed sequence).

Computing the Viterbi Scores

• Initialization

• Recursion

• Termination

133

Njobajv jj 1)()( 101

TtNjobaivjv tjijt

N

it

1 ,1)()(max)( 11

iFT

N

iFT aivsvP )( max)(*

11

Analogous to Forward algorithm except take max instead of sum

Computing the Viterbi Backpointers

• Initialization

• Recursion

• Termination

134

Njsjbt 1)( 01

TtNjobaivjbt tjijt

N

it

1 ,1)()(argmax)( 1

1

iFT

N

iFTT aivsbtq )( argmax)(*

11

Final state in the most probable state sequence. Follow backpointers to initial state to construct full sequence.

Viterbi Backpointers

135

s1

s2

sN

s0sF

t1 t2 t3 tT-1 tT

Viterbi Backtrace

136

s1

s2

sN

s0sF

t1 t2 t3 tT-1 tT

Most likely Sequence: s0 sN s1 s2 …s2 sF

HMM Learning

• Supervised Learning: All training sequences are completely labeled (tagged).

• Unsupervised Learning: All training sequences are unlabelled (but generally know the number of tags, i.e. states).

• Semisupervised Learning: Some training sequences are labeled, most are unlabeled.

137

Supervised HMM Training• If training sequences are labeled (tagged) with the

underlying state sequences that generated them, then the parameters, λ={A,B} can all be estimated directly.

138

SupervisedHMM

Training

John ate the appleA dog bit MaryMary hit the dogJohn gave Mary the cat.

.

.

.

Training Sequences


Supervised Parameter Estimation• Estimate state transition probabilities based on tag

bigram and unigram statistics in the labeled data.

• Estimate the observation probabilities based on tag/word co-occurrence statistics in the labeled data.

• Use appropriate smoothing if training data is sparse.

139

)(

)q ,( 1t

it

jitij sqC

ssqCa

)(

),()(

ji

kijij sqC

vosqCkb

Learning and Using HMM Taggers

• Use a corpus of labeled sequence data to easily construct an HMM using supervised training.

• Given a novel unlabeled test sequence to tag, use the Viterbi algorithm to predict the most likely (globally optimal) tag sequence.

140

Evaluating Taggers

• Train on training set of labeled sequences.• Possibly tune parameters based on performance on a

development set.• Measure accuracy on a disjoint test set.• Generally measure tagging accuracy, i.e. the

percentage of tokens tagged correctly.• Accuracy of most modern POS taggers, including

HMMs is 96−97% (for Penn tagset trained on about 800K words) .– Generally matching human agreement level.

141

Unsupervised Maximum Likelihood Training

142

ah s t e na s t i noh s t u neh z t en

.

.

.

Training Sequences

HMMTraining

Austin

Maximum Likelihood Training

• Given an observation sequence, O, what set of parameters, λ, for a given model maximizes the probability that this data was generated from this model (P(O| λ))?

• Used to train an HMM model and properly induce its parameters from a set of training data.

• Only need to have an unannotated observation sequence (or set of sequences) generated from the model. Does not need to know the correct state sequence(s) for the observation sequence(s). In this sense, it is unsupervised.

143

Maximum Likelihood vs. Maximum A Posteriori (MAP)

• The MAP parameter estimate is the most likely given the observed data, O.

)(

)()|(argmax)|(argmax

OP

POPOPMAP

)()|(argmax

POP

• If all parameterizations are assumed to be equally likely a priori, then MLE and MAP are the same.

• If parameters are given priors (e.g. Gaussian or Lapacian with zero mean), then MAP is a principled way to perform smoothing or regularization.

HMM: Maximum Likelihood TrainingEfficient Solution

• There is no known efficient algorithm for finding the parameters, λ, that truly maximizes P(O| λ).

• However, using iterative re-estimation, the Baum-Welch algorithm (a.k.a. forward-backward) , a version of a standard statistical procedure called Expectation Maximization (EM), is able to locally maximize P(O| λ).

• In practice, EM is able to find a good set of parameters that provide a good fit to the training data in many cases.

146

Sketch of Baum-Welch (EM) Algorithm for Training HMMs

147

Assume an HMM with N states.Randomly set its parameters λ=(A,B) (making sure they represent legal distributions)Until converge (i.e. λ no longer changes) do: E Step: Use the forward/backward procedure to determine the probability of various possible state sequences for generating the training data M Step: Use these probability estimates to re-estimate values for all of the parameters λ

Backward Probabilities

• Let t(i) be the probability of observing the final set of observations from time t+1 to T given that one is in state i at time t.

148

) |,...,()( ,21 itTttt sqoooPi

Computing the Backward Probabilities• Initialization

• Recursion

• Termination

149

Niai iFT 1)(

TtNijobai ttj

N

jijt

1 ,1)()()( 11

1

)()()()()|( 111

001 jobassOP j

N

jjFT

Estimating Probability of State Transitions

• Let t(i,j) be the probability of being in state i at time t and state j at time t + 1

),|,(),( 1 OsqsqPji jtitt

)|(

)()()(

)|(

)|,,(),( 111

OP

jobai

OP

OsqsqPji ttjijtjtit

t

s1

s2

sN

si

a1i

a2i

aNi

a3i

s1

s2

sN

sj

aj1

aj2

ajN

aj3

t-1 t t+1 t+2

)(it )(1 jt

)( 1tjij oba

Re-estimating A

i

jiaij state from ns transitioofnumber expected

to state from ns transitioofnumber expectedˆ

1

1 1

1

1

),(

),(ˆ

T

tt

N

j

T

tt

ij

ji

jia

Estimating Observation Probabilities • Let t(i) be the probability of being in state i at time

t given the observations and the model.

)|(

)()(

)|(

)|,(),|()(

OP

jj

OP

OsqPOsqPj ttjt

jtt

Re-estimating B

j

vjvb k

kj statein timesofnumber expected

observing statein timesofnumber expected)(ˆ

T

tt

T

vt

kj

j

j

vb k

1

o s.t. 1,t

)(

)(

)(ˆ t

154

Pseudocode for Baum-Welch (EM) Algorithm for Training HMMs

Assume an HMM with N states.Randomly set its parameters λ=(A,B) (making sure they represent legal distributions)Until converge (i.e. λ no longer changes) do: E Step: Compute values for t(j) and t(i,j) using current values for parameters A and B. M Step: Re-estimate parameters:

ijij aa ˆ)(ˆ)( kjkj vbvb

EM Properties• Each iteration changes the parameters in a

way that is guaranteed to increase the likelihood of the data: P(O|).

• Anytime algorithm: Can stop at any time prior to convergence to get approximate solution.

• Converges to a local maximum.

Semi-Supervised Learning• EM algorithms can be trained with a mix of

labeled and unlabeled data.• EM basically predicts a probabilistic (soft) labeling

of the instances and then iteratively retrains using supervised learning on these predicted labels (“self training”).

• EM can also exploit supervised data: – 1) Use supervised learning on labeled data to initialize

the parameters (instead of initializing them randomly).– 2) Use known labels for supervised data instead of

predicting soft labels for these examples during retraining iterations.

Semi-Supervised Results• Use of additional unlabeled data improves on

supervised learning when amount of labeled data is very small and amount of unlabeled data is large.

• Can degrade performance when there is sufficient labeled data to learn a decent model and when unsupervised learning tends to create labels that are incompatible with the desired ones.– There are negative results for semi-supervised POS

tagging since unsupervised learning tends to learn semantic labels (e.g. eating verbs, animate nouns) that are better at predicting the data than purely syntactic labels (e.g. verb, noun).

Conclusions• POS Tagging is the lowest level of syntactic

analysis.• It is an instance of sequence labeling, a collective

classification task that also has applications in information extraction, phrase chunking, semantic role labeling, and bioinformatics.

• HMMs are a standard generative probabilistic model for sequence labeling that allows for efficiently computing the globally most probable sequence of labels and supports supervised, unsupervised and semi-supervised learning.

1 computational lexicology, morphology and syntax course 5 diana trandab ă ț academic year:...

Documents

adverbs nouns

verbs adverbs

count nouns

open class of words

open class words

word classes words

words short common words

mass nouns count