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CPSC 503Computational Linguistics

Lecture 7Giuseppe Carenini

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Knowledge-Formalisms Map

Logical formalisms (First-Order Logics)

Rule systems (and prob. versions)(e.g., (Prob.) Context-Free

Grammars)

State Machines (and prob. versions)

(Finite State Automata,Finite State Transducers, Markov Models)

Morphology

Syntax

PragmaticsDiscourse and

Dialogue

Semantics

AI planners

Markov Models

Markov Chains -> n-grams

Hidden Markov Models (HMM)

MaxEntropy Markov Models (MEMM)

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Today 30/9

• Hidden Markov Models: – definition– the three key problems (only one in

detail)• Part-of-speech tagging

– What it is– Why we need it– How to do it

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HMMs (and MEMM) introThey are probabilistic sequence-classifier /

sequence-lablers: assign a class/label to each unit in a sequence

Used extensively in NLP• Part of Speech Tagging e.g Brainpower_NN ,_,

not_RB physical_JJ plant_NN ,_, is_VBZ now_RB a_DT firm_NN 's_POS chief_JJ asset_NN ._.

• Partial parsing

[NP The HD box] that [NP you] [VP ordered] [PP from] [NP Shaw] [VP never arrived].

• Named entity recognition

[John Smith PERSON] left [IBM Corp. ORG] last summer.

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Hidden Markov Model(State Emission)

.7.3

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SjiaA ij ,},{

Hidden Markov Model

Formal Specification as five-tuple

Set of States

Output Alphabet

Initial State Probabilities

State Transition Probabilities

Symbol EmissionProbabilities

BAKS ,,,,

Sii },{

},...,{ 1 NssS },...,1{},...,{ 1 MkkK M

KoSiobB tti ,)},({

11

N

j

ija

1)(1

M

t

ti ob

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Three fundamental questions for HMMs

Decoding: Finding the probability of an observation sequence

• brute force or Forward/Backward-Algorithms

Manning/Schütze, 2000: 325

)|(compute ),,,( model aGiven OPBA

Finding the most likely state sequence

• Viterbi-Algorithm

Training: find model parameters which best explain the observations

),|(maxarg OXPX

)|(maxarg

trainingOP

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Computing the probability of an observation sequence O= o1 ...

oT

)|( OP XX

XPXOPXOP )|(),|()|,(

)(),|(1

t

t

T

t

oX

bXOP

1

)|(1

11

tX

tXa

XXP

T

t

X = all sequences of T states

e.g., P(b,i | sample HMM )

X

T

t

t

t

T

t tX

tXa

Xo

XbOP

1)()|(

1

11 1

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Decoding Example

Manning/Schütze, 2000: 327

4statesof#,2);,( NTibP

s1, s1 = 0 ?

s1, s4 = 1 * .5 * .6 * .7s2, s4 = 0?……….

s1, s2 = 1 * .1 * .6 * .3

……….

……….

……….

tXX ...1

Complexity

X

T

t

t

t

T

t tX

tXa

Xo

XbOP

1)()|(

1

11 1

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The forward procedure

1. Initialization

Niobi ii 1),()( 11

2. Induction

NjNiobaij tj

N

i

ijtt

1,1),()()(1

1

3. Total

N

i

T iOP1

)()|( Complexity

)|,....()( 21 iXoooPi ttt

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Three fundamental questions for HMMs

Decoding: Finding the probability of an observation sequence

• brute force or Forward or Backward Algorithm

)|(compute ),,,( model aGiven OPBA

Finding the most likely state sequence

• Viterbi-AlgorithmTraining: find model parameters

which best explain the observations

),|(maxarg OXPX

)|(maxarg

trainingOP

If interested in details of Backward algorithm and the next two questions, read (Sections 6.4 –

6.5)

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Today 30/9• Hidden Markov Models:

– definition– the three key problems (only one in

detail)• Part-of-speech tagging

– What it is, Why we need it…– Word classes (Tags)

• Distribution• Tagsets

– How to do it• Rule-based• Stochastic

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Parts of Speech Tagging: What

• Brainpower_NN ,_, not_RB physical_JJ plant_NN ,_, is_VBZ now_RB a_DT firm_NN 's_POS chief_JJ asset_NN ._.

Tag meanings• NNP (Proper N sing), RB (Adv), JJ (Adj), NN (N

sing. or mass), VBZ (V 3sg pres), DT (Determiner), POS (Possessive ending), . (sentence-final punct)

Output

• Brainpower, not physical plant, is now a firm's chief asset.

Input

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Parts of Speech Tagging: Why?

• As a basis for (Partial) Parsing • Information Retrieval• Word-sense disambiguation• Speech synthesis

• Part-of-speech (word class, morph. class, syntactic category) gives a significant amount of info about the word and its neighborsUseful in the following NLP

tasks:

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Parts of Speech

• Eight basic categories– Noun, verb, pronoun, preposition,

adjective, adverb, article, conjunction• These categories are based on:

– morphological properties (affixes they take)

– distributional properties (what other words can occur nearby)

– e.g, green It is so… , both…, The… is• Not semantics!

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Parts of Speech• Two kinds of category

– Closed class (generally are function words)

•Prepositions, articles, conjunctions, pronouns, determiners, aux, numerals

– Open class•Nouns (proper/common; mass/count), verbs, adjectives, adverbs

Very short, frequent and important

Objects, actions, events, properties

• If you run across an unknown word….??

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PoS Distribution• Parts of speech follow a usual

behavior in Language

Words

1 PoS2 PoS

(unfortunately very frequent)>2 PoS

…but luckily different tags associated with a word are not equally likely

~35k~4k

~4k

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Sets of Parts of Speech:Tagsets• Most commonly used:

– 45-tag Penn Treebank, – 61-tag C5, – 146-tag C7

• The choice of tagset is based on the application (do you care about distinguishing between “to” as a prep and “to” as a infinitive marker?)

• Accurate tagging can be done with even large tagsets

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PoS Tagging

Dictionarywordi -> set of tags

from Tagset

• Brainpower_NN ,_, not_RB physical_JJ plant_NN ,_, is_VBZ now_RB a_DT firm_NN 's_POS chief_JJ asset_NN ._. ……….

• Brainpower, not physical plant, is now a firm's chief asset. …………

Input text

Output

Tagger

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Tagger Types• Rule-based ‘95

• Stochastic– HMM tagger ~ >= ’92– Transformation-based tagger (Brill) ~

>= ’95– MEMM (Maximum Entropy Markov Models) ~ >= ’97 (if interested sec. 6.6-6.8)

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Rule-Based (ENGTWOL ‘95)1. A lexicon transducer returns for each

word all possible morphological parses 2. A set of ~3,000 constraints is applied to

rule out inappropriate PoSStep 1: sample I/O

“Pavlov had show that salivation….”Pavlov N SG PROPERhad HAVE V PAST SVO

HAVE PCP2 SVOshown SHOW PCP2 SVOO

……that ADV

PRON DEM SG CS……..…….

Sample ConstraintExample: Adverbial “that” ruleGiven input: “that”If

(+1 A/ADV/QUANT)(+2 SENT-LIM)(NOT -1 SVOC/A)

Then eliminate non-ADV tagsElse eliminate ADV

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HMM Stochastic Tagging•Tags corresponds to an HMM states

•Words correspond to the HMM alphabet symbols Tagging: given a sequence of words (observations), find the most likely sequence of tags (states)But this is…..!We need: State transition and symbol emission probabilities

1) From hand-tagged corpus2) No tagged corpus: parameter estimation (forward/backward aka Baum-Welch)

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Evaluating Taggers

•Accuracy: percent correct (most current taggers 96-7%) *test on unseen data!*

•Human Celing: agreement rate of humans on classification (96-7%)

•Unigram baseline: assign each token to the class it occurred in most frequently in the training set (race -> NN). (91%)

•What is causing the errors? Build a confusion matrix…

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Confusion matrix

• Look at a confusion matrix

• Precision ?• Recall ?

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Error Analysis (textbook)

• Look at a confusion matrix

• See what errors are causing problems– Noun (NN) vs ProperNoun (NNP) vs Adj (JJ)– Preterite (VBD) vs Participle (VBN) vs Adjective

(JJ)

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Knowledge-Formalisms Map(next three lectures)

Logical formalisms (First-Order Logics)

Rule systems (and prob. versions)(e.g., (Prob.) Context-Free

Grammars)

State Machines (and prob. versions)

(Finite State Automata,Finite State Transducers, Markov Models)

Morphology

Syntax

PragmaticsDiscourse

and Dialogue

Semantics

AI planners

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Next Time

• Read Chapter 12 (syntax & Context Free Grammars)