1 Parts of Speech Sudeshna Sarkar 7 Aug 2008. 2 Why Do We Care about Parts of Speech? Pronunciation...

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Parts of Speech

Sudeshna Sarkar

7 Aug 2008

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Why Do We Care about Parts of Speech?

•PronunciationHand me the lead pipe.

•Predicting what words can be expected nextPersonal pronoun (e.g., I, she) ____________

•Stemming-s means singular for verbs, plural for nouns

•As the basis for syntactic parsing and then meaning extractionI will lead the group into the lead smelter.

•Machine translation• (E) content +N (F) contenu +N• (E) content +Adj (F) content +Adj or satisfait +Adj

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What is a Part of Speech?

Is this a semantic distinction? For example, maybe Noun is the class of words for people, places and things. Maybe Adjective is the class of words for properties of nouns.

Consider: green book

book is a Noun

green is an Adjective

Now consider: book worm

This green is very soothing.

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How Many Parts of Speech Are There?

A first cut at the easy distinctions:

Open classes:

•nouns, verbs, adjectives, adverbs

Closed classes: function words

•conjunctions: and, or, but

•pronounts: I, she, him

•prepositions: with, on

•determiners: the, a, an

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Part of speech tagging

8 (ish) traditional parts of speechNoun, verb, adjective, preposition, adverb, article, interjection, pronoun, conjunction, etc

This idea has been around for over 2000 years (Dionysius Thrax of Alexandria, c. 100 B.C.)

Called: parts-of-speech, lexical category, word classes, morphological classes, lexical tags, POS

We’ll use POS most frequently

I’ll assume that you all know what these are

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POS examples

N noun chair, bandwidth, pacing

V verb study, debate, munch

ADJ adj purple, tall, ridiculous

ADV adverb unfortunately, slowly,

P preposition of, by, to

PRO pronoun I, me, mine

DET determiner the, a, that, those

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Tagsets

Brown corpus tagset (87 tags):

http://www.scs.leeds.ac.uk/amalgam/tagsets/brown.html

Penn Treebank tagset (45 tags):

http://www.cs.colorado.edu/~martin/SLP/Figures/ (8.6)

C7 tagset (146 tags)

http://www.comp.lancs.ac.uk/ucrel/claws7tags.html

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POS Tagging: Definition

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

thekoalaputthekeysonthetable

WORDSTAGS

NVPDET

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POS Tagging example

WORD tag

the DETkoala Nput Vthe DETkeys Non Pthe DETtable N

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POS tagging: Choosing a tagset

There are so many parts of speech, potential distinctions we can draw

To do POS tagging, need to choose a standard set of tags to work with

Could pick very coarse tagetsN, V, Adj, Adv.

More commonly used set is finer grained, the “UPenn TreeBank tagset”, 45 tags

PRP$, WRB, WP$, VBG

Even more fine-grained tagsets exist

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Penn TreeBank POS Tag set

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Using the UPenn tagset

The/DT grand/JJ jury/NN commmented/VBD on/IN a/DT number/NN of/IN other/JJ topics/NNS ./.

Prepositions and subordinating conjunctions marked IN (“although/IN I/PRP..”)

Except the preposition/complementizer “to” is just marked “to”.

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POS Tagging

Words often have more than one POS: backThe back door = JJ

On my back = NN

Win the voters back = RB

Promised to back the bill = VB

The POS tagging problem is to determine the POS tag for a particular instance of a word.

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How hard is POS tagging? Measuring ambiguity

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Algorithms for POS Tagging

•Ambiguity – In the Brown corpus, 11.5% of the word types are ambiguous (using 87 tags):

Worse, 40% of the tokens are ambiguous.

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Algorithms for POS Tagging

Why can’t we just look them up in a dictionary?

•Words that aren’t in the dictionary

http://story.news.yahoo.com/news?tmpl=story&cid=578&ncid=578&e=1&u=/nm/20030922/ts_nm/iraq_usa_dc

•One idea: P(ti | wi) = the probability that a random hapax legomenon in the corpus has tag ti.

Nouns are more likely than verbs, which are more likely than pronouns.

•Another idea: use morphology.

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Algorithms for POS Tagging - Knowledge

•Dictionary

•Morphological rules, e.g.,•_____-tion•_____-ly•capitalization

•N-gram frequencies•to _____•DET _____ N•But what about rare words, e.g, smelt (two verb forms, melt and past tense of smell, and one noun form, a small fish)

•Combining these• V _____-ing I was gracking vs. Gracking is fun.

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POS Tagging - Approaches

ApproachesRule-based tagging

(ENGTWOL)Stochastic (=Probabilistic) tagging

HMM (Hidden Markov Model) taggingTransformation-based tagging

Brill tagger

• Do we return one best answer or several answers and let later steps decide?

• How does the requisite knowledge get entered?

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3 methods for POS tagging

1. Rule-based taggingExample: Karlsson (1995) EngCG tagger based on the Constraint Grammar architecture and ENGTWOL lexicon

– Basic Idea:

Assign all possible tags to words (morphological analyzer used)

Remove wrong tags according to set of constraint rules (typically more than 1000 hand-written constraint rules, but may be machine-learned)

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2. Transformation-based taggingExample: Brill (1995) tagger - combination of rule-based and stochastic (probabilistic) tagging methodologies– Basic Idea:

Start with a tagged corpus + dictionary (with most frequent tags) Set the most probable tag for each word as a start value Change tags according to rules of type “if word-1 is a determiner

and word is a verb then change the tag to noun” in a specific order (like rule-based taggers)

machine learning is used—the rules are automatically induced from a previously tagged training corpus (like stochastic approach)

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3. Stochastic (=Probabilistic) taggingExample: HMM (Hidden Markov Model) tagging - a training corpus used to compute the probability (frequency) of a given word having a given POS tag in a given context

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Hidden Markov Model (HMM) Tagging

Using an HMM to do POS tagging

HMM is a special case of Bayesian inference

It is also related to the “noisy channel” model in ASR (Automatic Speech Recognition)

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Goal: maximize P(word|tag) x P(tag|previous n tags)

P(word|tag) word/lexical likelihoodprobability that given this tag, we have this word NOT probability that this word has this tagmodeled through language model (word-tag matrix)

P(tag|previous n tags)tag sequence likelihoodprobability that this tag follows these previous tagsmodeled through language model (tag-tag matrix)

Hidden Markov Model (HMM) Taggers

Lexical information Syntagmatic information

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POS tagging as a sequence classification task

We are given a sentence (an “observation” or “sequence of observations”)

Secretariat is expected to race tomorrow

sequence of n words w1…wn.

What is the best sequence of tags which corresponds to this sequence of observations?

Probabilistic/Bayesian view:Consider all possible sequences of tags

Out of this universe of sequences, choose the tag sequence which is most probable given the observation sequence of n words w1…wn.

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Getting to HMM

Let T = t1,t2,…,tn

Let W = w1,w2,…,wn

Goal: Out of all sequences of tags t1…tn, get the the most probable sequence of POS tags T underlying the observed sequence of words w1,w2,…,wn

Hat ^ means “our estimate of the best = the most probable tag sequence”

Argmaxx f(x) means “the x such that f(x) is maximized”

it maximazes our estimate of the best tag sequence

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Getting to HMM

This equation is guaranteed to give us the best tag sequence

But how do we make it operational? How do we compute this value?Intuition of Bayesian classification:

Use Bayes rule to transform it into a set of other probabilities that are easier to computeThomas Bayes: British mathematician (1702-1761)

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Bayes Rule

Breaks down any conditional probability P(x|y) into three other probabilities

P(x|y): The conditional probability of an event x assuming that y has occurred

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Bayes Rule

We can drop the denominator: it does not change for each tag sequence; we are looking for the best tag sequence for the same observation, for the same fixed set of words

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Bayes Rule

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Likelihood and prior

n

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Likelihood and prior Further Simplifications

n

1. the probability of a word appearing depends only on its own POS tag, i.e, independent of other words around it

2. BIGRAM assumption: the probability of a tag appearing depends only on the previous tag

3. The most probable tag sequence estimated by the bigram tagger

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n

1. the probability of a word appearing depends only on its own POS tag, i.e, independent of other words around it

thekoalaputthekeysonthetable

WORDSTAGS

NVPDET

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2. BIGRAM assumption: the probability of a tag appearing depends only on the previous tag

Bigrams are groups of two written letters, two syllables, or two words; they are a special case of N-gram.

Bigrams are used as the basis for simple statistical analysis of text

The bigram assumption is related to the first-order Markov assumption

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3. The most probable tag sequence estimated by the bigram tagger

n

biagram assumption

---------------------------------------------------------------------------------------------------------------

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Two kinds of probabilities (1)

Tag transition probabilities p(ti|ti-1)

Determiners likely to precede adjs and nouns– That/DT flight/NN– The/DT yellow/JJ hat/NN

– So we expect P(NN|DT) and P(JJ|DT) to be high– But P(DT|JJ) to be:?

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Tag transition probabilities p(ti|ti-1)

Compute P(NN|DT) by counting in a labeled corpus:

# of times DT is followed by NN

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Word likelihood probabilities p(wi|ti)P(is|VBZ) = probability of VBZ (3sg Pres verb) being “is”

Compute P(is|VBZ) by counting in a labeled corpus:

If we were expecting a third person singular verb, how likely is it that

this verb would be is?

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An Example: the verb “race”

Secretariat/NNP is/VBZ expected/VBN to/TO race/VB tomorrow/NRPeople/NNS continue/VB to/TO inquire/VB the/DT reason/NN for/IN the/DT race/NN for/IN outer/JJ space/NNHow do we pick the right tag?

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Disambiguating “race”

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Hidden Markov Models

What we’ve described with these two kinds of probabilities is a Hidden Markov Model (HMM)

Let’s just spend a bit of time tying this into the model

In order to define HMM, we will first introduce the Markov Chain, or observable Markov Model.

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Definitions

A weighted finite-state automaton adds probabilities to the arcs

The sum of the probabilities leaving any arc must sum to one

A Markov chain is a special case of a WFST in which the input sequence uniquely determines which states the automaton will go throughMarkov chains can’t represent inherently ambiguous problems

Useful for assigning probabilities to unambiguous sequences

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Markov chain = “First-order observed Markov Model”

a set of states

Q = q1, q2…qN; the state at time t is qt

a set of transition probabilities:

a set of probabilities A = a01a02…an1…ann.

Each aij represents the probability of transitioning from state i to state jThe set of these is the transition probability matrix A

Distinguished start and end states

Special initial probability vector

i the probability that the MM will start in state i, each i expresses the probability p(qi|START)

aij P(qt j | qt 1 i) 1i, j N

aij 1; 1i Nj1

N

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Markov Chain for weather: Example 1

three types of weather: sunny, rainy, foggy

we want to find the following conditional probabilities:

P(qn|qn-1, qn-2, …, q1)

- I.e., the probability of the unknown weather on day n, depending on the (known) weather of the preceding days

- We could infer this probability from the relative frequency (the statistics) of past observations of weather sequences

Problem: the larger n is, the more observations we must collect.

Suppose that n=6, then we have to collect statistics for 3(6-1) =

243 past histories

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Therefore, we make a simplifying assumption, called the (first-order) Markov assumption

for a sequence of observations q1, … qn,

current state only depends on previous state

the joint probability of certain past and current observations

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Markov chain = “First-order observable Markov Model”

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Given that today the weather is sunny, what's the probability that tomorrow is sunny and the day after is rainy?

Using the Markov assumption and the probabilities in table 1, this translates into:

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The weather figure: specific example

Markov Chain for weather: Example 2

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Markov chain for weather

What is the probability of 4 consecutive rainy days?

Sequence is rainy-rainy-rainy-rainy

I.e., state sequence is 3-3-3-3

P(3,3,3,3) = 1a11a11a11a11 = 0.2 x (0.6)3 = 0.0432

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Hidden Markov Model

For Markov chains, the output symbols are the same as the states.

See sunny weather: we’re in state sunny

But in part-of-speech tagging (and other things)The output symbols are words

But the hidden states are part-of-speech tags

So we need an extension!

A Hidden Markov Model is an extension of a Markov chain in which the output symbols are not the same as the states.

This means we don’t know which state we are in.

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Markov chain for weather

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Markov chain for words

Observed events: words

Hidden events: tags

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States Q = q1, q2…qN; Observations O = o1, o2…oN;

Each observation is a symbol from a vocabulary V = {v1,v2,…vV}

Transition probabilities (prior)

Transition probability matrix A = {aij}

Observation likelihoods (likelihood)

Output probability matrix B={bi(ot)}a set of observation likelihoods, each expressing the probability of an observation ot being generated from a state i, emission probabilities

Special initial probability vector

i the probability that the HMM will start in state i, each i expresses the probability

p(qi|START)

Hidden Markov Models

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Assumptions

Markov assumption: the probability of a particular state depends only on the previous state

Output-independence assumption: the probability of an output observation depends only on the state that produced that observation

P(qi | q1...qi 1) P(qi | qi 1)

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HMM for Ice Cream

You are a climatologist in the year 2799

Studying global warming

You can’t find any records of the weather in Boston, MA for summer of 2007

But you find Jason Eisner’s diary

Which lists how many ice-creams Jason ate every date that summer

Our job: figure out how hot it was

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Noam task

GivenIce Cream Observation Sequence: 1,2,3,2,2,2,3…

(cp. with output symbols)

Produce:Weather Sequence: C,C,H,C,C,C,H …

(cp. with hidden states, causing states)

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HMM for ice cream

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Different types of HMM structure

Bakis = left-to-right Ergodic = fully-connected

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HMM Taggers

Two kinds of probabilitiesA transition probabilities (PRIOR)

B observation likelihoods (LIKELIHOOD)

HMM Taggers choose the tag sequence which maximizes the product of word likelihood and tag sequence probability

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Weighted FSM corresponding to hidden states of HMM, showing A probs

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B observation likelihoods for POS HMM

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The A matrix for the POS HMM

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The B matrix for the POS HMM

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HMM Taggers

The probabilities are trained on hand-labeled training corpora (training set)

Combine different N-gram levels

Evaluated by comparing their output from a test set to human labels for that test set (Gold Standard)

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The Viterbi Algorithm

best tag sequence for "John likes to fish in the sea"?efficiently computes the most likely state sequence given a particular output sequencebased on dynamic programming

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A smaller example

b

What is the best sequence of states for the input string “bbba”?

Computing all possible paths and finding the one with the max probability is exponential

a

0.6

q rstart end

0.5

0.7

a

0.4 0.80.2

b

1 1

0.3 0.5

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A smaller example (con’t)

For each state, store the most likely sequence that could lead to it (and its probability)

Path probability matrix: An array of states versus time (tags versus words)

That stores the prob. of being at each state at each time in terms of the prob. for being in each state at the preceding time.

Best sequence Input sequence / time

ε --> b b --> b bb --> b bbb --> a

leading

to q

coming

from qε --> q 0.6

(1.0x0.6)

q --> q 0.108

(0.6x0.3x0.6)

qq --> q 0.01944 (0.108x0.3x0.6)

qrq --> q 0.018144

(0.1008x0.3x0.4)

coming

from rr --> q 0

(0x0.5x0.6)

qr --> q 0.1008

(0.336x0.5x 0.6)

qrr --> q 0.02688 (0.1344x0.5x0.4)

leading

to r

coming

from qε --> r 0

(0x0.8)

q --> r 0.336

(0.6x0.7x0.8)

qq --> r 0.0648 (0.108x0.7x0.8)

qrq --> r 0.014112

(0.1008x0.7x0.2)

coming

from rr --> r 0 (0x0.5x0.8)

qr --> r 0.1344 (0.336x0.5x0.8)

qrr --> r 0.01344

(0.1344x0.5x0.2)

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Viterbi intuition: we are looking for the best ‘path’

promised to back the bill

VBD

VBN

TO

VB

JJ

NN

RB

DT

NNP

VB

NN


VBD

VBN

TO

VB

JJ

NN

RB

DT

NNP

VB

NN

S1 S2 S4S3 S5


VBD

VBN

TO

VB

JJ

NN

RB

DT

NNP

VB

NN

Slide from Dekang Lin

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The Viterbi Algorithm

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Intuition

The value in each cell is computed by taking the MAX over all paths that lead to this cell. An extension of a path from state i at time t-1 is computed by multiplying:

Previous path probability from previous cell viterbi[t-1,i]

Transition probability aij from previous state I to current state j

Observation likelihood bj(ot) that current state j matches observation symbol t

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Viterbi example

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Smoothing of probabilities

Data sparseness is a problem when estimating probabilities based on corpus data.The “add one” smoothing technique –

BN

wCwP n

n

1,1

,1

C- absolute frequencyN: no of training instancesB: no of different types

Linear interpolation methods can compensate for data sparseness with higher order models. A common method is interpolating trigrams, bigrams and unigrams:

iii

iiiiiiii ttPttPtPttP

1,10

)|()|()(| 2,133122111,1

The lambda values are automatically determined using a variant of the Expectation Maximization algorithm.

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in bigram POS tagging, we condition a tag only on the preceding tag

why not...use more context (ex. use trigram model)

– more precise: “is clearly marked” --> verb, past participle “he clearly marked” --> verb, past tense

– combine trigram, bigram, unigram models

condition on words too

but with an n-gram approach, this is too costly (too many parameters to model)

Possible improvements

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Further issues with Markov Model tagging

Unknown words are a problem since we don’t have the required probabilities. Possible solutions:

Assign the word probabilities based on corpus-wide distribution of POSUse morphological cues (capitalization, suffix) to assign a more calculated guess.

Using higher order Markov models:Using a trigram model captures more contextHowever, data sparseness is much more of a problem.

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TnT

Efficient statistical POS tagger developed by Thorsten Brants, ANLP-2000

Underlying model:

Trigram modelling –The probability of a POS only depends on its two preceding POS

The probability of a word appearing at a particular position given that its POS occurs at that position is independent of everything else.

T

iTTiiiii

ttttPtwPtttP

T 1121 )|()|(),|(maxarg

1

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Training

Maximum likelihood estimates:

)(

),()|(:

),(

),,(),|(:

)(

),()|( : Bigrams

: Unigrams

3

3333

32

321213

^

3

3223

33

tc

twctwPLexical

ttc

tttctttPTrigrams

tc

ttcttP

N

)c(t)(tP

^

^

Smoothing : context-independent variant of linear interpolation.

),|()|()(),|( 213

^

323

^

23

^

1213 tttPttPtPtttP

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Smoothing algorithm

Set λi=0

For each trigram t1 t2 t3 with f(t1,t2,t3 )>0

Depending on the max of the following three values:– Case (f(t1,t2,t3 )-1)/ f(t1,t2) : incr λ3 by f(t1,t2,t3 )

– Case (f(t2,t3 )-1)/ f(t2) : incr λ2 by f(t1,t2,t3 )

– Case (f(t3 )-1)/ N-1 : incr λ1 by f(t1,t2,t3 )

Normalize λi

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Evaluation of POS taggers

compared with gold-standard of human performance

metric: accuracy = % of tags that are identical to gold standard

most taggers ~96-97% accuracy

must compare accuracy to:ceiling (best possible results)

– how do human annotators score compared to each other? (96-97%)– so systems are not bad at all!

baseline (worst possible results)– what if we take the most-likely tag (unigram model) regardless of previous

tags ? (90-91%) – so anything less is really bad

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More on tagger accuracy

is 95% good?that’s 5 mistakes every 100 words

if on average, a sentence is 20 words, that’s 1 mistake per sentence

when comparing tagger accuracy, beware of:size of training corpus

– the bigger, the better the results

difference between training & testing corpora (genre, domain…)– the closer, the better the results

size of tag set – Prediction versus classification

unknown words– the more unknown words (not in dictionary), the worst the results

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Error Analysis

Look at a confusion matrix (contingency table)

E.g. 4.4% of the total errors caused by mistagging VBD as VBNSee what errors are causing problems

Noun (NN) vs ProperNoun (NNP) vs Adj (JJ)Adverb (RB) vs Particle (RP) vs Prep (IN)Preterite (VBD) vs Participle (VBN) vs Adjective (JJ)

ERROR ANALYSIS IS ESSENTIAL!!!

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Tag indeterminacy

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Major difficulties in POS taggingUnknown words (proper names)

because we do not know the set of tags it can take

and knowing this takes you a long way (cf. baseline POS tagger)

possible solutions:– assign all possible tags with probabilities distribution identical to lexicon as a whole– use morphological cues to infer possible tags

ex. word ending in -ed are likely to be past tense verbs or past participles

Frequently confused tag pairspreposition vs particle

<running> <up> a hill (prep) / <running up> a bill (particle)

verb, past tense vs. past participle vs. adjective

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Unknown Words

Most-frequent-tag approach.

What about words that don’t appear in the training set?

Suffix analysis:

The probability distribution for a particular suffix is generated from all words in the training set that share the same suffix.

Suffix estimation – Calculate the probability of a tag t given the last i letters of an n letter word.

Smoothing: successive abstraction through sequences of increasingly more general contexts (i.e., omit more and more characters of the suffix)

Use a morphological analyzer to get the restriction on the possible tags.

86

Unknown words

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Alternative graphical models for part of speech tagging

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Different Models for POS tagging

HMM

Maximum Entropy Markov Models

Conditional Random Fields

89

Hidden Markov Model (HMM) : Generative Modeling

Source Model PY

Noisy Channel PXY

y x

i

ii yyPP )|()( 1y i

ii yxPP )|()|( yx

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Disadvantage of HMMs (1)

No Rich Feature InformationRich information are required

– When xk is complex– When data of xk is sparse

Example: POS TaggingHow to evaluate Pwk|tk for unknown words wk ?Useful features

– Suffix, e.g., -ed, -tion, -ing, etc.– Capitalization

Generative ModelParameter estimation: maximize the joint likelihood of training examples

T

P),(

2 ),(logyx

yYxX

92

Generative Models

Hidden Markov models (HMMs) and stochastic grammarsAssign a joint probability to paired observation and label sequences

The parameters typically trained to maximize the joint likelihood of train examples

93

Generative Models (cont’d)

Difficulties and disadvantagesNeed to enumerate all possible observation sequences

Not practical to represent multiple interacting features or long-range dependencies of the observations

Very strict independence assumptions on the observations

94

Better ApproachDiscriminative model which models P(y|x) directly

Maximize the conditional likelihood of training examples

T

P),(

2 )|(logyx

xXyY

95

Maximum Entropy modeling

N-gram model : probabilities depend on the previous few tokens.

We may identify a more heterogeneous set of features which contribute in some way to the choice of the current word. (whether it is the first word in a story, whether the next word is to, whether one of the last 5 words is a preposition, etc)

Maxent combines these features in a probabilistic model.

The given features provide a constraint on the model.

We would like to have a probability distribution which, outside of these constraints, is as uniform as possible – has the maximum entropy among all models that satisfy these constraints.

96

Maximum Entropy Markov Model

Discriminative Sub ModelsUnify two parameters in generative model into one conditional model

– Two parameters in generative model,

– parameter in source model and parameter in noisy

channel

– Unified conditional model

Employ maximum entropy principle

)|( 1kk yyP

)|( kk yxP ),|( 1kkk yxyP

i

iii xyyPP ),|()|( 1xy


97

General Maximum Entropy Principle

Model

Model distribution PY|X with a set of features fffl defined on X and Y

IdeaCollect information of features from training data

Principle

– Model what is known

– Assume nothing else

Flattest distribution

Distribution with the maximum Entropy

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Example

(Berger et al., 1996) exampleModel translation of word “in” from English to French

– Need to model P(wordFrench)– Constraints

1: Possible translations: dans, en, à, au course de, pendant 2: “dans” or “en” used in 30% of the time 3: “dans” or “à” in 50% of the time

99

Features

Features0-1 indicator functions

– 1 if x y satisfies a predefined condition

– 0 if not

Example: POS Tagging

otherwise

NN is and tion- with ends if

,0

,1),(1

yxyxf

otherwise ,0

NNP is andtion Captializa with starts if ,1),(2

yxyxf

100

Constraints

Empirical InformationStatistics from training data T

Tyx

ii yxfT

fP),(

),(||

1)(ˆ

Constraints)()(ˆ

ii fPfP

Tyx YDy

ii yxfxXyYPT

fP),( )(

),()|(||

1)(

Expected Value From the distribution PY|X we want to model

101

Maximum Entropy: Objective

Entropy

x y

Tyx

xXyYPxXyYPxP

xXyYPxXyYPT

I

)|(log)|()(ˆ

)|(log)|(||

1

2

),(2

)()(ˆ s.t.

max)|(

fPfP

IXYP

Maximization Problem

102

Dual Problem

Dual Problem Conditional model

Maximum likelihood of conditional data)),(exp()|(

1

l

iii yxfxXyYP

Solution Improved iterative scaling (IIS) (Berger et al. 1996) Generalized iterative scaling (GIS) (McCallum et al.

2000)

Tyx

xXyYPl ),(

2,,

)|(logmax1

103


Use Maximum Entropy Approach to Model1st order

),|( 11 kkkkkk yYxXyYP

Features Basic features (like parameters in HMM)

Bigram (1st order) or trigram (2nd order) in source model

State-output pair feature Xkxk Yk yk Advantage: incorporate other advanced

features on xk yk

104

HMM vs MEMM (1st order)

kY1kY

kX

)|( 1kk YYP

)|( kk YXP

HMMMaximum Entropy

Markov Model (MEMM)

kY1kY

kX

),|( 1kkk YXYP

105

Performance in POS Tagging

POS TaggingData set: WSJFeatures:

– HMM features, spelling features (like –ed, -tion, -s, -ing, etc.)

Results (Lafferty et al. 2001)1st order HMM

– 94.31% accuracy, 54.01% OOV accuracy

1st order MEMM– 95.19% accuracy, 73.01% OOV accuracy

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ME applications

Part of Speech (POS) Tagging (Ratnaparkhi, 1996)P(POS tag | context)

Information sources– Word window (4)– Word features (prefix, suffix, capitalization)– Previous POS tags

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ME applications

Abbreviation expansion (Pakhomov, 2002)Information sources

– Word window (4)– Document title

Word Sense Disambiguation (WSD) (Chao & Dyer, 2002)Information sources

– Word window (4)– Structurally related words (4)

Sentence Boundary Detection (Reynar & Ratnaparkhi, 1997)Information sources

– Token features (prefix, suffix, capitalization, abbreviation)– Word window (2)

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Solution

Global OptimizationOptimize parameters in a global model simultaneously, not in sub models separately

AlternativesConditional random fields

Application of perceptron algorithm

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Why ME?

AdvantagesCombine multiple knowledge sources

– Local Word prefix, suffix, capitalization (POS - (Ratnaparkhi, 1996)) Word POS, POS class, suffix (WSD - (Chao & Dyer, 2002)) Token prefix, suffix, capitalization, abbreviation (Sentence Boundary -

(Reynar & Ratnaparkhi, 1997))– Global

N-grams (Rosenfeld, 1997) Word window Document title (Pakhomov, 2002) Structurally related words (Chao & Dyer, 2002) Sentence length, conventional lexicon (Och & Ney, 2002)

Combine dependent knowledge sources

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Why ME?

AdvantagesAdd additional knowledge sources

Implicit smoothing

DisadvantagesComputational

– Expected value at each iteration

– Normalizing constant

Overfitting– Feature selection

Cutoffs Basic Feature Selection (Berger et al., 1996)

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Conditional Models

Conditional probability P(label sequence y | observation sequence x) rather than joint probability P(y, x)

Specify the probability of possible label sequences given an observation sequence

Allow arbitrary, non-independent features on the observation sequence X

The probability of a transition between labels may depend on past and future observations

Relax strong independence assumptions in generative models

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Discriminative ModelsMaximum Entropy Markov Models (MEMMs)

Exponential modelGiven training set X with label sequence Y:

Train a model θ that maximizes P(Y|X, θ)For a new data sequence x, the predicted label y maximizes P(y|x, θ)Notice the per-state normalization

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MEMMs (cont’d)

MEMMs have all the advantages of Conditional Models

Per-state normalization: all the mass that arrives at a state must be distributed among the possible successor states (“conservation of score mass”)

Subject to Label Bias Problem

Bias toward states with fewer outgoing transitions

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Solve the Label Bias Problem

Change the state-transition structure of the model

Not always practical to change the set of states

Start with a fully-connected model and let the training procedure figure out a good structure

Prelude the use of prior, which is very valuable (e.g. in information extraction)

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Random Field

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Conditional Random Fields (CRFs)

CRFs have all the advantages of MEMMs without label bias problem

MEMM uses per-state exponential model for the conditional probabilities of next states given the current state

CRF has a single exponential model for the joint probability of the entire sequence of labels given the observation sequence

Undirected acyclic graph

Allow some transitions “vote” more strongly than others depending on the corresponding observations

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Definition of CRFs

X is a random variable over data sequences to be labeled

Y is a random variable over corresponding label sequences

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Example of CRFs

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Graphical comparison among HMMs, MEMMs and CRFs

HMM MEMM CRF

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Conditional Distribution

1 2 1 2( , , , ; , , , ); andn n k k

x is a data sequencey is a label sequence v is a vertex from vertex set V = set of label random variablese is an edge from edge set E over Vfk and gk are given and fixed. gk is a Boolean vertex feature; fk is a

Boolean edge featurek is the number of features

are parameters to be estimated

y|e is the set of components of y defined by edge ey|v is the set of components of y defined by vertex v

If the graph G = (V, E) of Y is a tree, the conditional distribution over the label sequence Y = y, given X = x, by fundamental theorem of random fields is:

(y | x) exp ( , y | , x) ( , y | , x)

k k e k k v

e E,k v V ,k

p f e g v

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Conditional Distribution (cont’d)

• CRFs use the observation-dependent normalization Z(x) for the conditional distributions:

Z(x) is a normalization over the data sequence x

(y | x) exp ( , y | , x) ( , y |1

(x), x)

k k e k k v

e E,k v V ,k

p f e g vZ

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Parameter Estimation for CRFs

The paper provided iterative scaling algorithms

It turns out to be very inefficient

Prof. Dietterich’s group applied Gradient Descendent Algorithm, which is quite efficient

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Training of CRFs (From Prof. Dietterich)

log ( | )( , y | , x) ( , y | , x) log (x)

k k e k k ve E,k v V ,k

p y xf e g v Z

log ( | ) ( , y | , x) ( , y | , x) log (x)k k e k k ve E,k v V ,k

p y x f e g v Z

• First, we take the log of the equation

• Then, take the derivative of the above equation

• For training, the first 2 items are easy to get. • For example, for each k, fk is a sequence of Boolean numbers, such

as 00101110100111. is just the total number of 1’s in the sequence.( , y | , x)k k ef e

• The hardest thing is how to calculate Z(x)

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Training of CRFs (From Prof. Dietterich) (cont’d)

• Maximal cliques

y1 y2 y3 y4c1 c2 c3

c1 c2 c3

1 2 3 4

1 2 3 4

1 1 2 2 2 3 3 3 4y ,y ,y ,y

1 1 2 2 2 3 3 3 4y y y y

(x) (y ,y ,x) (y ,y ,x) (y ,y ,x)

(y ,y ,x) (y ,y ,x) (y ,y ,x)

Z c c c

c c c

3 4 3 4 3 3 4: exp( (y ,x) (y ,y ,x)) (y ,y ,x)c c

1 1 2 1 2 1 1 2: exp( (y ,x) (y ,x) (y ,y ,x)) (y ,y ,x)c c

2 3 2 3 2 2 3: exp( (y ,x) (y ,y ,x)) (y ,y ,x)c c

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POS tagging Experiments

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POS tagging Experiments (cont’d)

• Compared HMMs, MEMMs, and CRFs on Penn treebank POS tagging• Each word in a given input sentence must be labeled with one of 45 syntactic tags• Add a small set of orthographic features: whether a spelling begins with a number

or upper case letter, whether it contains a hyphen, and if it contains one of the following suffixes: -ing, -ogy, -ed, -s, -ly, -ion, -tion, -ity, -ies

• oov = out-of-vocabulary (not observed in the training set)

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Summary

Discriminative models are prone to the label bias problem

CRFs provide the benefits of discriminative models

CRFs solve the label bias problem well, and demonstrate good performance

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