1. Albert Gatt Corpora and Statistical Methods

2. POS Tagging Assign each word in continuous text a tag indicating its part of speech. Essentially a classification problem. Current state of the art: taggers typically have 96-97% accuracy figure evaluated on a per-word basis in a corpus with sentences of average length 20 words, 96% accuracy can mean one tagging error per sentence

3. Sources of difficulty in POS tagging Mostly due to ambiguity when words have more than one possible tag. need context to make a good guess about POS context alone won’t suffice A simple approach which assigns only the most common tag to each word performs with 90% accuracy!

4. The information sources 1. Syntagmatic information: the tags of other words in the context of w Not sufficient on its own. E.g. Greene/Rubin 1977 describe a context-only tagger with only 77% accuracy 2. Lexical information (“dictionary”): most common tag(s) for a given word e.g. in English, many nouns can be used as verbs (flour the pan, wax the car…) however, their most likely tag remains NN distribution of a word’s usages across different POSs is uneven: usually, one highly likely, other much less

5. Tagging in other languages (than English) In English, high reliance on context is a good idea, because of fixed word order Free word order languages make this assumption harder Compensation: these languages typically have rich morphology Good source of clues for a tagger

6. Evaluation and error analysis Training a statistical POS tagger requires splitting corpus into training and test data. Often, we need a development set as well, to tune parameters. Using (n-fold) cross-validation is a good idea to save data. randomly divide data into train + test train and evaluate on test repeat n times and take an average NB: cross-validation requires the whole corpus to be blind. To examine the training data, best to have fixed training & test sets, perform cross-validation on training data, and final evaluation on test set.

7. Evaluation Typically carried out against a gold standard based on accuracy (% correct). Ideal to compare accuracy of our tagger with: baseline (lower-bound): standard is to choose the unigram most likely tag ceiling (upper bound): e.g. see how well humans do at the same task humans apparently agree on 96-7% tags means it is highly suspect for a tagger to get 100% accuracy

8. Part 1 HMM taggers

9. Using Markov models Basic idea: sequences of tags are a Markov Chain: Limited horizon assumption: sufficient to look at previous tag for information about current tag Time invariance: The probability of a sequence remains the same over time

10. Implications/limitations Limited horizon ignores long-distance dependences e.g. can’t deal with WH-constructions Chomsky (1957): this was one of the reasons cited against probabilistic approaches Time invariance: e.g. P(finite verb|pronoun) is constant but we may be more likely to find a finite verb following a pronoun at the start of a sentence than in the middle!

11. Notation We let t i range over tags Let w i range over words Subscripts denote position in a sequence Use superscripts to denote word types: w j = an instance of word type j in the lexicon t j = tag t assigned to word w j Limited horizon property becomes:

12. Basic strategy Training set of manually tagged text extract probabilities of tag sequences: e.g. using Brown Corpus, P(NN|JJ) = 0.45, but P(VBP|JJ) = 0.0005 Next step: estimate the word/tag probabilities: These are basically symbol emission probabilities

13. Training the tagger: basic algorithm 1. Estimate probability of all possible sequences of 2 tags in the tagset from training data 2. For each tag t j and for each word w l estimate P(w l | t j ). 3. Apply smoothing.

14. Finding the best tag sequence Given: a sentence of n words Find: t 1,n = the best n tags Application of Bayes’ rule denominator can be eliminated as it’s the same for all tag sequences.

15. Finding the best tag sequence The expression needs to be reduced to parameters that can be estimated from the training corpus need to make some simplifying assumptions 1. words are independent of eachother 2. a word’s identity depends only on its tag

16. The independence assumption Probability of a sequence of words given a sequence of tags is computed as a function of each word independently

17. The identity assumption Probability of a word given a tag sequence = probability a word given its own tag

18. Applying these assumptions

19. Tagging with the Markov Model Can use the Viterbi Algorithm to find the best sequence of tags given a sequence of words (sentence) Reminder: probability of being in state (tag) j at word i on the best path most probable state (tag) at word i given that we’re in state j at word i+1

20. The algorithm: initialisation Assume that P(PERIOD) = 1 at end of sentence Set all other tag probs to 0

21. Algorithm: induction step for i = 1 to n step 1: for all tags t j do: Probability of tag t j at i+1 on best path through i Most probable tag leading to tj at i+1

22. Algorithm: backtrace State at n+1 for j = n to 1 do: retrieve the most probable tags for every point in sequence Calculate probability for the sequence of tags selected

23. Some observations The model is a Hidden Markov Model we only observe words when we tag In actuality, during training we have a visible Markov Model because the training corpus provides words + tags

24. “True” HMM taggers Applied to cases where we do not have a large training corpus We maintain the usual MM assumptions Initialisation: use dictionary: set emission probability for a word/tag to 0 if it’s not in dictionary Training: apply to data, use forward-backward algorithm Tagging: exactly as before

25. Part 2 Transformation-based error-driven learning

26. Transformation-based learning Approach proposed by Brill (1995) uses quantitative information at training stage outcome of training is a set of rules tagging is then symbolic, using the rules Components: a set of transformation rules learning algorithm

27. Transformations General form: t1  t2 “replace t1 with t2 if certain conditions are satisfied” Examples: Morphological: Change the tag from NN to NNS if the word has the suffix "s" dogs_NN  dogs_NNS Syntactic: Change the tag from NN to VB if the word occurs after "to" go_NN to_TO  go_VB Lexical: Change the tag to JJ if deleting the prefix "un" results in a word. uncool_XXX  uncool_JJ uncle_NN -/-> uncle_JJ

28. Learning Unannotated text Initial state annotator e.g. assign each word its most frequent tag in a dictionary truth: a manually annotated version of corpus against which to compare Learner: learns rules by comparing initial state to Truth rules

29. Learning algorithm Simple iterative process: apply a rule to the corpus compare to the Truth if error rate is reduced, keep the results A priori specifications: how initial state annotator works the space of possible transformations Brill (1995) used a set of initial templates the function to compare the result of applying the rules to the truth

30. Non-lexicalised rule templates Take only tags into account, not the shape of words Change tag a to tag b when: 1. The preceding (following) word is tagged z. 2. The word two before (after) is tagged z. 3. One of the three preceding (following) words is tagged z. 4. The preceding (following) word is tagged z and the word two before (after) is tagged w. 5. …

31. Lexicalised rule templates Take into account specific words in the context Change tag a to tag b when: 1. The preceding (following) word is w. 2. The word two before (after) is w. 3. The current word is w, the preceding (following) word is w 2 and the preceding (following) tag is t. 4. …

32. Morphological rule templates Usful for completely unknown words. Sensitive to the word’s “shape”. Change the tag of an unknown word (from X) to Y if: 1. Deleting the prefix (suffix) x, |x| ≤ 4, results in a word 2. The first (last) (1,2,3,4) characters of the word are x. 3. Adding the character string x as a prefix (suffix) results in a word (|x| ≤ 4). 4. Word w ever appears immediately to the left (right) of the word. 5. Character z appears in the word. 6. …

33. Order-dependence of rules Rules are triggered by environments satisfying their conditions E.g. “A  B if preceding tag is A” Suppose our sequence is “AAAA” Two possible forms of rule application: immediate effect: applications of the same transformation can influence eachother result: ABAB delayed effect: results in ABBB the rule is triggered multiple times from the same initial input Brill (1995) opts for this solution

34. More on Transformation-based tagging Can be used for unsupervised learning like HMM-based tagging, the only info available is the allowable tags for each word takes advantage of the fact that most words have only one tag E.g. word can = NN in context AT ___ BEZ because most other words in this context are NN therefore, learning algorithm would learn the rule “change tag to NN in context AT ___ BEZ” Unsupervised method achieves 95.6% accuracy!!

35. Part 3 Maximum Entropy models and POS Tagging

36. Limitations of HMMs An HMM tagger relies on: P(tag|previous tag) P(word|tag) these are combined by multiplication TBL includes many other useful features which are hard to model in HMM: prefixes, suffixes capitalisation … Can we combine both, i.e. have HMM-style tagging with multiple features?

37. The rationale In order to tag a word, we consider its context or “history” h. We want to estimate a probability distribution p(h,t) from sparse data. h is encoded in terms of features (e.g. morphological features, surrounding tag features etc) There are some constraints on these features that we discover from training data. We want our model to make the fewest possible assumptions beyond these constraints.

38. Motivating example Suppose we wanted to tag the word w. Assume we have a set T of 45 different tags: T ={NN, JJ, NNS, NNP, VVS, VB, …} The probabilistic tagging model that makes fewest assumptions assigns a uniform distribution over the tags:

39. Motivating example Suppose we find that the possible tags for w are NN, JJ, NNS, VB. We therefore impose our first constraint on the model: (and the prob. of every other tag is 0) The simplest model satisfying this constraint:

40. Motivating example We suddenly discover that w is tagged as NN or NNS 8 out of 10 times. Model now has two constraints: Again, we require our model to make no further assumptions. Simplest distribution leaves probabilities for all tags except NN/NNS equal: P(NN) = 4/10 P(NNS) = 4/10 P(JJ) = 1/10 P(VB) = 1/10

41. Motivating example We suddenly discover that verbs (VB) occur 1 in every 20 words. Model now has three constraints: Simplest distribution is now: P(NN) = 4/10 P(NNS) = 4/10 P(JJ) = 3/20 P(VB) = 1/20

42. What we’ve been doing Maximum entropy builds a distribution by continuously adding features. Each feature picks out a subset of the training observations. For each feature, we add a constraint on our total distribution. Our task is then to find the best distribution given the constraints.

43. Features for POS Tagging Each tagging decision for a word occurs in a specific context or “history” h. For tagging, we consider as context: the word itself morphological properties of the word other words surrounding the word previous tags For each relevant aspect of the context h i, we can define a feature f j that allows us to learn how well that aspect is associated with a tag t i. Probability of a tag given a context is a weighted function of the features.

44. Features for POS Tagging In a maximum entropy model, this information is captured by a binary or indicator feature each feature f i has a weight α i reflecting its importance NB: each α i is uniquely associated with a feature

45. Features for POS Tagging in Ratnaparkhi (1996) Had three sets of features, for non-rare, rare and all words:

46. Features for POS Tagging Given the large number of possible features, which ones will be part of the model? We do not want redundant features We do not want unreliable and rarely occurring features (avoid overfitting) Ratnaparkhi (1996) used only those features which occur 10 times or more in the training data

47. The form of the model Features f j and their parameters are used to compute the probability p(h i, t i ): where j ranges over features & Z is a normalisation constant Transform into a linear equation:

48. Conditional probabilities The conditional probabilities can be computed based on the joint probabilities Probability of a sequence of tags given a sequence of words: NB: unlike an HMM, we have one probability here. we directly estimate p(t|h) model combines all features in h i into a single estimate no limit in principle on what features we can take into account

49. The use of constraints Every feature we have imposes a constraint or expectation on the probability model. We want: Where: the model p’s expectation of f j the empirical expectation of f j

50. Why maximum entropy? Recall that entropy is a measure of uncertainty in a distribution. Without any knowledge, simplest distribution is uniform uniform distributions have the highest entropy As we add constraints, the MaxEnt principle dictates that we find the simplest model p* satisfying the constraints: where P is the set of possible distributions with p* is unique and has the form given earlier Basically, an application of Occam’s razor: make no further assumptions than necessary.

51. Part 4 Training a MaxEnt model

52. Training 1: computing empirical expectation Recall that: Suppose we are interested in the feature: In a corpus of 10k words + tags, where the word moving occurs as VBG 20 times:

53. Training 2: computing model expectation Recall that: Requires sum over all possible histories and tags! Approximate by computing model expectation of the feature on training data only:

54. Learning the optimal parameters Our goal is to learn the best parameter α j for each feature f j, such that: i.e.: One method is Generalised Iterative Scaling

55. Generalised Iterative Scaling: assumptions for all (h,t), features sum to a constant value: If this is not the case, we set C to: and add a filler feature f l, such that:

56. Generalised Iterative Scaling: assumptions (II) for all (h,t), there is at least one feature f which is active, i.e.:

57. Generalised Iterative Scaling Input: Features f 1,..., f n and empirical distribution Output: Optimal parameter values α 1,..., α n 1. Initialise α i = 0 for all i Є {1, 2,..., n} 2. For each i do: a. set b. set 3. If model has not converged, repeat from (2)

58. Part 5 Finding tag sequences with MaxEnt models

59. Tagging sequences We want to tag a sequence w 1,...,w n This can be decomposed into: The history h i consists of the words w 1,...,w i-1 and previous tags t 1,..., t i−1

60. Finding the best tag sequence: beam search (Ratnaparki, 1996) To find the best sequence of n tags given N features. s ij = the j th highest probability tag sequence up to word i. 1. Generate all tags for w 1 a. find the top N tags b. set s 1j for 1 ≤ j ≤ N 2. for i = 2 to n do: a. for j = 1 to N do: i. Generate tags for w i given s (i-1)j ii. Append each tag to s (i-1)j to create new sequence b. Find the N highest probability sequences generated by loop 2a. 3. Return s n1

61. Worked example Suppose our data consists of the sequence: a, b, c Assume the correct tags are A, B, C Assume that N = 1 (i.e. we only ever consider the top most likely tag)

62. Worked Example abc s 11 s 21 s 31 Step 1: generate all possible tags for a: A, B, C Step 2: find the most likely tag for a: A

63. Worked Example abc s 11 s 21 s 31 A Step 2: generate all possible tags for b: A, B, C merge with s 11 : A-A, A-B, A-C Find the most likely sequence: A-B

64. Worked Example abc s 11 s 21 s 31 AA-B Step 3: generate all possible tags for w3: A, B, C merge with s 21 : A-B-A, A-B-B, A-B-C Find the most likely: A-B-C

65. Worked Example abc s 11 s 21 s 31 AA-BA-B-C Return s 31 (=A-B-C)

66. Part 6 Markov Models vs. MaxEnt

67. HMM vs MaxEnt Standard HMMs cannot compute conditional probability directly. E.g. for tagging: we want p(t 1,n |w 1,n ) we obtain it via Bayes’ rule, combining p(w 1,n |t 1,n ) with the prior p(t 1,n ) HMMs are generative models which optimise p(w 1,n |t 1,n ) By contrast, a MaxEnt Markov Model (MEMM) is a discriminative model which optimises p(t 1,n |w 1,n ) directly.

68. Graphically (after Jurafsky & Martin 2009) HMM has separate models for P(w|t) and for P(t) MEMM has a single model to estimate P(t|w)

69. More formally… With an HMM: With a MEMM:

70. Adapting Viterbi We can easily adapt the Viterbi algorithm to find the best state sequence in a MEMM. Recall that with HMMs: Adaptation for MEMMs:

71. Summary MaxEnt is a powerful classification model with some advantages over HMM: direct computation of conditional probabilities from the training data can handle multiple features First introduced by Ratnaparkhi (1996) for POS Tagging. Used for many other applications since then.