1. 1 Parts of Speech Sudeshna Sarkar 7 Aug 2008

2. 2 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

3. 3 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.

4. 4 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

5. 5 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

6. 6 POS examples Nnounchair, bandwidth, pacing Vverbstudy, debate, munch ADJadjpurple, tall, ridiculous ADVadverbunfortunately, slowly, Pprepositionof, by, to PROpronounI, me, mine DETdeterminerthe, a, that, those

7. 7 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)http://www.cs.colorado.edu/~martin/SLP/Figures/ C7 tagset (146 tags) http://www.comp.lancs.ac.uk/ucrel/claws7tags.html

8. 8 POS Tagging: Definition The process of assigning a part-of-speech or lexical class marker to each word in a corpus: the koala put the keys on the table WORDS TAGS N V P DET

9. 9 POS Tagging example WORDtag theDET koalaN put V the DET keysN onP theDET tableN

10. 10 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

11. 11 Penn TreeBank POS Tag set

12. 12 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”.

13. 13 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.

14. 14 How hard is POS tagging? Measuring ambiguity

15. 15 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.

16. 16 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(t i | w i ) = the probability that a random hapax legomenon in the corpus has tag t i. Nouns are more likely than verbs, which are more likely than pronouns. Another idea: use morphology.

17. 17 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.

18. 18 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?

19. 19 3 methods for POS tagging 1. Rule-based tagging Example: 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)

20. 20 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)

21. 21 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

22. 22 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)

23. 23 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) Hidden Markov Model (HMM) Taggers Lexical information Syntagmatic information

24. 24 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.

25. 25 Getting to HMM Let T = t 1,t 2,…,t n Let W = w 1,w 2,…,w n Goal: Out of all sequences of tags t 1 …t n, get the the most probable sequence of POS tags T underlying the observed sequence of words w 1,w 2,…,w n Hat ^ means “our estimate of the best = the most probable tag sequence” Argmax x f(x) means “the x such that f(x) is maximized” it maximazes our estimate of the best tag sequence

26. 26 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)

27. 27 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

28. 28 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

29. 29 Bayes Rule

30. 30 Likelihood and prior n

31. 31 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

32. 32 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 the koala put the keys on the table WORDS TAGS N V P DET

33. 33 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

34. 34 Likelihood and prior Further Simplifications 3. The most probable tag sequence estimated by the bigram tagger n biagram assumption ---------------------------------------------------------------------------------------------------------------

35. 35 Two kinds of probabilities (1) Tag transition probabilities p(t i |t i-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:?

36. 36 Two kinds of probabilities (1) Tag transition probabilities p(t i |t i-1 ) Compute P(NN|DT) by counting in a labeled corpus: # of times DT is followed by NN

37. 37 Two kinds of probabilities (2) Word likelihood probabilities p(w i |t i ) 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?

38. 38 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/DT race/NN for/IN outer/JJ space/NN How do we pick the right tag?

39. 39 Disambiguating “race”

40. 40 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

41. 41 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.

42. 42 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

43. 43 Markov chain = “First-order observed Markov Model” a set of states Q = q 1, q 2 …q N; the state at time t is q t a set of transition probabilities: a set of probabilities A = a 01 a 02 …a n1 …a nn. Each a ij 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   i the probability that the MM will start in state i, each  i expresses the probability p(q i |START)

44. 44 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

45. 45 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

46. 46 Markov chain = “First-order observable Markov Model”

47. 47 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:

48. 48 The weather figure: specific example Markov Chain for weather: Example 2

49. 49 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) =  1 a 11 a 11 a 11 a 11 = 0.2 x (0.6) 3 = 0.0432

50. 50 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.

51. 51 Markov chain for weather

52. 52 Markov chain for words Observed events: words Hidden events: tags

53. 53 States Q = q 1, q 2 …q N; Observations O = o 1, o 2 …o N; Each observation is a symbol from a vocabulary V = {v 1,v 2,…v V } Transition probabilities (prior) Transition probability matrix A = {a ij } Observation likelihoods (likelihood) Output probability matrix B={b i (o t )} a set of observation likelihoods, each expressing the probability of an observation o t 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(q i |START) Hidden Markov Models

54. 54 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

55. 55 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

56. 56 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)

57. 57 HMM for ice cream

58. 58 Different types of HMM structure Bakis = left-to-right Ergodic = fully-connected

59. 59 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

60. 60 Weighted FSM corresponding to hidden states of HMM, showing A probs

61. 61 B observation likelihoods for POS HMM

62. 62 The A matrix for the POS HMM

63. 63 The B matrix for the POS HMM

64. 64 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)

65. 65 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

66. 66 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 r start end 0.5 0.7 a 0.4 0.8 0.2 b 11 0.3 0.5

67. 67 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 sequenceInput sequence / time ε --> bb --> bbb --> bbbb --> a leading to q coming from q ε --> 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 r r --> 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 q ε --> 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 r r --> r 0 (0x0.5x0.8) qr --> r 0.1344 (0.336x0.5x0.8) qrr --> r 0.01344 (0.1344x0.5x0.2)

68. 68 Viterbi intuition: we are looking for the best ‘path’ S1S1 S2S2 S4S4 S3S3 S5S5 Slide from Dekang Lin

69. 69 The Viterbi Algorithm

70. 70 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 a ij from previous state I to current state j Observation likelihood b j (o t ) that current state j matches observation symbol t

71. 71 Viterbi example

72. 72 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.

73. 73 Viterbi for POS tagging Let: n = nb of words in sentence to tag (nb of input tokens) T = nb of tags in the tag set (nb of states) vit = path probability matrix (viterbi) vit[i,j] = probability of being at state (tag) j at word i state = matrix to recover the nodes of the best path (best tag sequence) state[i+1,j] = the state (tag) of the incoming arc that led to this most probable state j at word i+1 // Initialization vit[1,PERIOD]:=1.0 // pretend that there is a period before // our sentence (start tag = PERIOD) vit[1,t]:=0.0 for t ≠ PERIOD

74. 74 Viterbi for POS tagging (con’t) // Induction (build the path probability matrix) for i:=1 to n step 1 do // for all words in the sentence for all tags t j do // for all possible tags // store the max prob of the path vit[i+1,t j ] := max 1≤k≤T (vit[i,t k ] x P(w i+1 |t j ) x P(t j | t k )) // store the actual state path[i+1,t j ] := argmax 1≤k≤T ( vit[i,t k ] x P(w i+1 |t j ) x P(t j | t k )) end //Termination and path-readout bestState n+1 := argmax 1≤j≤T vit[n+1,j] for j:=n to 1 step -1 do // for all the words in the sentence bestState j := path[i+1, bestState j+1 ] end P(bestState 1,…, bestState n ) := max 1≤j≤T vit[n+1,j] emission probability state transition probability probability of best path leading to state t k at word i

75. 75 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

76. 76 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.

77. 77 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.

78. 78 Training Maximum likelihood estimates: Smoothing : context-independent variant of linear interpolation.

79. 79 Smoothing algorithm Set λ i =0 For each trigram t 1 t 2 t 3 with f(t 1,t 2,t 3 )>0 Depending on the max of the following three values: –Case (f(t 1,t 2,t 3 )-1)/ f(t 1,t 2 ) : incr λ 3 by f(t 1,t 2,t 3 ) –Case (f(t 2,t 3 )-1)/ f(t 2 ) : incr λ 2 by f(t 1,t 2,t 3 ) –Case (f(t 3 )-1)/ N-1 : incr λ 1 by f(t 1,t 2,t 3 ) Normalize λ i

80. 80 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

81. 81 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

82. 82 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!!!

83. 83 Tag indeterminacy

84. 84 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 a hill (prep) / a bill (particle) verb, past tense vs. past participle vs. adjective

85. 85 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. 86 Unknown words

87. 87 Alternative graphical models for part of speech tagging

88. 88 Different Models for POS tagging HMM Maximum Entropy Markov Models Conditional Random Fields

89. 89 Hidden Markov Model (HMM) : Generative Modeling Source Model P  Y  Noisy Channel P  X  Y  y x

90. 90 Dependency (1st order)

91. 91 Disadvantage of HMMs (1) No Rich Feature Information Rich information are required –When x k is complex –When data of x k is sparse Example: POS Tagging How to evaluate P  w k |t k  for unknown words w k ? Useful features –Suffix, e.g., -ed, -tion, -ing, etc. –Capitalization Generative Model Parameter estimation: maximize the joint likelihood of training examples

92. 92 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

93. 93 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

94. 94 Better Approach Discriminative model which models P(y|x) directly Maximize the conditional likelihood of training examples

95. 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. 96 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

97. 97 General Maximum Entropy Principle Model Model distribution P  Y  |X  with a set of features  f   f     f l  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

98. 98 Example ( Berger et al., 1996) example Model translation of word “in” from English to French –Need to model P(word French ) –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. 99 Features 0-1 indicator functions –1 if  x  y  satisfies a predefined condition –0 if not Example: POS Tagging

100. 100 Constraints Empirical Information Statistics from training data T Constraints Expected Value From the distribution P  Y  |X  we want to model

101. 101 Maximum Entropy: Objective Entropy Maximization Problem

102. 102 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)

103. 103 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  X k  x k  Y k  y k  Advantage: incorporate other advanced features on  x k  y k 

104. 104 HMM vs MEMM (1st order) HMM Maximum Entropy Markov Model (MEMM)

105. 105 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

106. 106 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

107. 107 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)

108. 108 Solution Global Optimization Optimize parameters in a global model simultaneously, not in sub models separately Alternatives Conditional random fields Application of perceptron algorithm

109. 109 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

110. 110 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)

111. 111 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

112. 112 Discriminative Models Maximum Entropy Markov Models (MEMMs) Exponential model Given 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

113. 113 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

114. 114 Label Bias Problem 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) Since P(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 Therefore P(2 | 1) = 1, so P(2 | 1 and x) = 1 for all x However, we expect P(1 and 2 | ri) to be greater than P(1 and 2 | ro). Per-state normalization does not allow the required expectation Consider this MEMM:

115. 115 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)

116. 116 Random Field

117. 117 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

118. 118 Definition of CRFs X is a random variable over data sequences to be labeled Y is a random variable over corresponding label sequences

119. 119 Example of CRFs

120. 120 Graphical comparison among HMMs, MEMMs and CRFs HMM MEMM CRF

121. 121 Conditional Distribution 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 f k and g k are given and fixed. g k is a Boolean vertex feature; f k 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 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:

122. 122 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

123. 123 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

124. 124 Training of CRFs (From Prof. Dietterich) 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, f k 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 calculate Z(x)

125. 125 Training of CRFs (From Prof. Dietterich) (cont’d) Maximal cliques y1y1 y2y2 y3y3 y4y4 c1c1 c2c2 c3c3 c1c1 c2c2 c3c3

126. 126 POS tagging Experiments

127. 127 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)

128. 128 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