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Parts of Speech. Sudeshna Sarkar 7 Aug 2008. Why Do We Care about Parts of Speech?. Pronunciation Hand me the lead pipe. Predicting what words can be expected next Personal pronoun (e.g., I , she ) ____________ Stemming -s means singular for verbs, plural for nouns

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parts of speech

Parts of Speech

Sudeshna Sarkar

7 Aug 2008

why do we care about parts of speech
Why Do We Care about Parts of Speech?
  • Pronunciation
  • Hand me the lead pipe.
  • Predicting what words can be expected next
      • Personal pronoun (e.g., I, she) ____________
  • Stemming
      • -s means singular for verbs, plural for nouns
  • As the basis for syntactic parsing and then meaning extraction
      • I 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
what is a part of speech
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.

how many parts of speech are there
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
part of speech tagging
Part of speech tagging
  • 8 (ish) traditional parts of speech
    • Noun, 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
pos examples
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
tagsets
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

pos tagging definition

WORDS

TAGS

the

koala

put

the

keys

on

the

table

N

V

P

DET

POS Tagging: Definition
  • The process of assigning a part-of-speech or lexical class marker to each word in a corpus:
pos tagging example
POS Tagging example

WORD tag

the DET

koala N

put V

the DET

keys N

on P

the DET

table N

pos tagging choosing a tagset
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 tagets
    • N, 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
using the upenn tagset
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”.
pos tagging
POS Tagging
  • Words often have more than one POS: back
    • The 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.
algorithms for pos tagging
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.
algorithms for pos tagging16
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.
algorithms for pos tagging knowledge
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.
pos tagging approaches
POS Tagging - Approaches
  • Approaches
    • Rule-based tagging
      • (ENGTWOL)
    • Stochastic (=Probabilistic) tagging
      • HMM (Hidden Markov Model) tagging
    • Transformation-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?
3 methods for pos tagging
3 methods for POS tagging

1. Rule-based tagging

  • Example: Karlsson (1995) EngCGtagger 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)
3 methods for pos tagging20
3 methods for POS tagging

2. Transformation-based tagging

  • Example: 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)
3 methods for pos tagging21
3 methods for POS tagging

3. Stochastic (=Probabilistic) tagging

  • Example: 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
hidden markov model hmm tagging
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)
slide23

Hidden Markov Model (HMM) Taggers

  • Goal: maximize P(word|tag) x P(tag|previous n tags)
  • P(word|tag)
    • word/lexical likelihood
    • probability that given this tag, we have this word
    • NOT probability that this word has this tag
    • modeled through language model (word-tag matrix)
  • P(tag|previous n tags)
    • tag sequence likelihood
    • probability that this tag follows these previous tags
    • modeled through language model (tag-tag matrix)

Lexical information

Syntagmatic information

pos tagging as a sequence classification task
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.
getting to hmm
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”
  • Argmaxxf(x) means “the x such that f(x) is maximized”

it maximazes our estimate of the best tag sequence

getting to hmm26
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 compute
    • Thomas Bayes: British mathematician (1702-1761)
bayes rule
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

bayes rule28
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

likelihood and prior further simplifications
Likelihood and prior Further Simplifications

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

n

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

likelihood and prior further simplifications32

WORDS

TAGS

the

koala

put

the

keys

on

the

table

N

V

P

DET

Likelihood and prior Further Simplifications

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

n

likelihood and prior further simplifications33
Likelihood and prior Further Simplifications

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

likelihood and prior further simplifications34
Likelihood and prior Further Simplifications

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

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

n

biagram assumption

two kinds of probabilities 1
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:?
two kinds of probabilities 136
Two kinds of probabilities (1)
  • Tag transition probabilities p(ti|ti-1)
    • Compute P(NN|DT) by counting in a labeled corpus:

# of times DT is followed by NN

two kinds of probabilities 2
Two kinds of probabilities (2)
  • 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?

an example the verb race
An Example: the verb “race”
  • Secretariat/NNP is/VBZ expected/VBN to/TO race/VB tomorrow/NR
  • People/NNS continue/VB to/TO inquire/VB the/DT reason/NN for/IN the/DTrace/NN for/IN outer/JJ space/NN
  • How do we pick the right tag?
disambiguating race40
Disambiguating “race”
  • P(NN|TO) = .00047
  • P(VB|TO) = .83

The tag transition probabilities P(NN|TO) and P(VB|TO) answer the question: ‘How likely are we to expect verb/noun given the previous tag TO?’

  • P(race|NN) = .00057
  • P(race|VB) = .00012

Lexical likelihoods from the Brown corpus for ‘race’ given a POS tag NN or VB.

  • P(NR|VB) = .0027
  • P(NR|NN) = .0012

tag sequence probability for the likelihood of an adverb occurring given the previous tag verb or noun

  • P(VB|TO)P(NR|VB)P(race|VB) = .00000027
  • P(NN|TO)P(NR|NN)P(race|NN)=.00000000032

Multiply the lexical likelihoods with the tag sequence probabiliies: the verb wins

hidden markov models
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.
definitions
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 through
  • Markov chains can’t represent inherently ambiguous problems
    • Useful for assigning probabilities to unambiguous sequences
markov chain first order observed markov model
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 j
    • The set of these is the transition probability matrix A
  • Distinguished start and end states

Special initial probability vector 

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

markov chain first order observed markov model44
Markov chain = “First-order observed Markov Model”

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

markov chain first order observed markov model45
Markov chain = “First-order observed Markov Model”
  • 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
markov chain first order observed markov model47
Markov chain = “First-order observed Markov Model”
  • 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:
the weather figure specific example
The weather figure: specific example
  • Markov Chain for weather: Example 2
markov chain for weather
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
hidden markov model
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.
markov chain for words
Markov chain for words

Observed events: words

Hidden events: tags

hidden markov models53
Hidden Markov Models
  • 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 

ithe probability that the HMM will start in state i, each iexpresses the probability

p(qi|START)

assumptions
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
hmm for ice cream
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
noam task
Noam task
  • Given
    • Ice 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)

different types of hmm structure
Different types of HMM structure

Ergodic =

fully-connected

Bakis = left-to-right

hmm taggers
HMM Taggers
  • Two kinds of probabilities
    • A transition probabilities (PRIOR)
    • B observation likelihoods (LIKELIHOOD)
  • HMM Taggers choose the tag sequence which maximizes the product of word likelihood and tag sequence probability
hmm taggers64
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)
the viterbi algorithm
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 sequence
  • based on dynamic programming
a smaller example

b

a

0.2

0.8

0.4

0.6

0.7

end

start

r

q

1

1

0.5

0.3

0.5

A smaller example

a

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 smaller example con t
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.
intuition
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
smoothing of probabilities
Smoothing of probabilities
  • Data sparseness is a problem when estimating probabilities based on corpus data.
  • The “add one” smoothing technique –

C- absolute frequency

N: no of training instances

B: 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:
  • The lambda values are automatically determined using a variant of the Expectation Maximization algorithm.
possible improvements
Possible improvements
  • 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)
further issues with markov model tagging
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 POS
    • Use morphological cues (capitalization, suffix) to assign a more calculated guess.
  • Using higher order Markov models:
    • Using a trigram model captures more context
    • However, data sparseness is much more of a problem.
slide75
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.
training
Training
  • Maximum likelihood estimates:

Smoothing : context-independent variant of linear interpolation.

smoothing algorithm
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
evaluation of pos taggers
Evaluation of POS taggers
  • compared with gold-standard ofhuman 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
more on tagger accuracy
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
error analysis
Error Analysis
  • Look at a confusion matrix (contingency table)
  • E.g. 4.4% of the total errors caused by mistagging VBD as VBN
  • See 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!!!
major difficulties in pos tagging
Major difficulties in POS tagging
  • Unknown 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 pairs
    • preposition vs particle

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

    • verb, past tense vs. past participle vs. adjective
unknown words
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.
different models for pos tagging
Different Models for POS tagging
  • HMM
  • Maximum Entropy Markov Models
  • Conditional Random Fields
hidden markov model hmm generative modeling
Hidden Markov Model (HMM) : Generative Modeling

Source Model P(Y)

Noisy Channel P(X|Y)

y

x

disadvantage of hmms 1
Disadvantage of HMMs (1)
  • No Rich Feature Information
    • Rich information are required
      • When xk is complex
      • When data of xk is sparse
  • Example: POS Tagging
    • How to evaluate P(wk|tk) for unknown words wk ?
    • Useful features
      • Suffix, e.g., -ed, -tion, -ing, etc.
      • Capitalization
  • Generative Model
    • Parameter estimation: maximize the joint likelihood of training examples
generative models
Generative Models
  • Hidden Markov models (HMMs) and stochastic grammars
    • Assign a joint probability to paired observation and label sequences
    • The parameters typically trained to maximize the joint likelihood of train examples
generative models cont d
Generative Models (cont’d)
  • Difficulties and disadvantages
    • Need 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
slide92
Better Approach
    • Discriminative model which models P(y|x) directly
    • Maximize the conditional likelihood of training examples
maximum entropy modeling
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.
maximum entropy markov model
Maximum Entropy Markov Model
  • Discriminative Sub Models
    • Unify 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
  • Maximum Entropy Markov Model
general maximum entropy principle
General Maximum Entropy Principle
  • Model
    • Model distribution P(Y|X) with a set of features {f1, f2, , fl} defined on X and Y
  • Idea
    • Collect information of features from training data
    • Principle
      • Model what is known
      • Assume nothing else

 Flattest distribution

 Distribution with the maximum Entropy

example
Example
  • (Berger et al., 1996) example
    • Model 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
features
Features
  • Features
    • 0-1 indicator functions
      • 1 if (x, y)satisfies a predefined condition
      • 0 if not
  • Example: POS Tagging
constraints
Constraints
  • Empirical Information
    • Statistics from training data T
  • Expected Value
    • From the distribution P(Y|X) we want to model
  • Constraints
maximum entropy objective
Maximum Entropy: Objective
  • Entropy
  • Maximization Problem
dual problem
Dual Problem
  • Dual Problem
    • Conditional model
    • Maximum likelihood of conditional data
  • Solution
    • Improved iterative scaling (IIS) (Berger et al. 1996)
    • Generalized iterative scaling (GIS) (McCallum et al. 2000)
maximum entropy markov model101
Maximum Entropy Markov Model
  • Use Maximum Entropy Approach to Model
    • 1st order
  • Features
    • Basic features (like parameters in HMM)
      • Bigram (1st order) or trigram (2nd order) in source model
      • State-output pair feature (Xk = xk,Yk=yk)
    • Advantage: incorporate other advanced features on (xk,yk)
hmm vs memm 1st order
HMM vs MEMM (1st order)

Maximum Entropy Markov Model (MEMM)

HMM

performance in pos tagging
Performance in POS Tagging
  • POS Tagging
    • Data set: WSJ
    • Features:
      • 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
me applications
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
me applications105
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)
solution
Solution
  • Global Optimization
    • Optimize parameters in a global model simultaneously, not in sub models separately
  • Alternatives
    • Conditional random fields
    • Application of perceptron algorithm
why me
Why ME?
  • Advantages
    • Combine 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
why me108
Why ME?
  • Advantages
    • Add additional knowledge sources
    • Implicit smoothing
  • Disadvantages
    • Computational
      • Expected value at each iteration
      • Normalizing constant
    • Overfitting
      • Feature selection
        • Cutoffs
        • Basic Feature Selection (Berger et al., 1996)
conditional models
Conditional Models
  • Conditional probabilityP(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 onpastandfutureobservations
    • Relax strong independence assumptions in generative models
discriminative models maximum entropy markov models memms
Discriminative ModelsMaximum Entropy Markov Models (MEMMs)
  • Exponential model
  • Given training set X with label sequence Y:
    • Train a model θthat 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
memms cont d
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
label bias problem
Label Bias Problem
  • Consider this MEMM:
  • P(1 and 2 | ro) = P(2 | 1 and ro)P(1 | ro) = P(2 | 1 and o)P(1 | r)
  • P(1 and 2 | ri) = P(2 | 1 and ri)P(1 | ri) = P(2 | 1 and i)P(1 | r)
  • SinceP(2 | 1 and x) = 1 for all x, P(1 and 2 | ro) = P(1 and 2 | ri)
  • In the training data, label value 2 is the only label value observed after label value 1
  • ThereforeP(2 | 1) = 1, so P(2 | 1 and x) = 1 for all x
  • However, we expectP(1 and 2 | ri)to be greater thanP(1 and 2 | ro).
  • Per-state normalization does not allow the required expectation
solve the label bias problem
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)
conditional random fields crfs
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
definition of crfs
Definition of CRFs

X is a random variable over data sequences to be labeled

Y is a random variable over corresponding label sequences

conditional distribution

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:

x is a data sequence

y is a label sequence

v is a vertex from vertex set V = set of label random variables

e is an edge from edge set E over V

fk and gk are given and fixed. gk is a Boolean vertex feature; fk is a Boolean edge feature

k is the number of features

are parameters to be estimated

y|e is the set of components of y defined by edge e

y|v is the set of components of y defined by vertex v

Conditional Distribution
conditional distribution cont d
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

parameter estimation for crfs
Parameter Estimation for CRFs
  • The paper provided iterative scaling algorithms
  • It turns out to be very inefficient
  • Prof. Dietterich’s group appliedGradient Descendent Algorithm, which is quite efficient
training of crfs from prof dietterich

First, we take the log of the equation

Training of CRFs (From Prof. Dietterich)
  • Then, take the derivative of the above equation
  • For training, the first 2 items are easy to get.
  • For example, for each lk, fk is a sequence of Boolean numbers, such as 00101110100111.
        • is just the total number of 1’s in the sequence.
  • The hardest thing is how to calculateZ(x)
pos tagging experiments cont d
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)
summary
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