Natural Language Processing Lecture 8—2/5/2015 Susan W. Brown

10/5/2015 Speech and Language Processing - Jurafsky and Martin 2 Today  Part of speech tagging  HMMs  Basic HMM model  Decoding  Viterbi  Review chapters 1-4

10/5/2015 Speech and Language Processing - Jurafsky and Martin 3 POS Tagging as Sequence Classification  We are given a sentence (an “observation” or “sequence of observations”)  Secretariat is expected to race tomorrow  What is the best sequence of tags that corresponds to this sequence of observations?  Probabilistic 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 w 1 …w n.

10/5/2015 Speech and Language Processing - Jurafsky and Martin 4 Getting to HMMs  We want, out of all sequences of n tags t 1 …t n the single tag sequence such that P(t 1 …t n |w 1 …w n ) is highest.  Hat ^ means “our estimate of the best one”  Argmax x f(x) means “the x such that f(x) is maximized”

10/5/2015 Speech and Language Processing - Jurafsky and Martin 5 Getting to HMMs  This equation should give us the best tag sequence  But how to make it operational? How to compute this value?  Intuition of Bayesian inference:  Use Bayes rule to transform this equation into a set of probabilities that are easier to compute (and give the right answer)

Bayesian inference  Update the probability of a hypothesis as you get evidence  Rationale: two components  How well does the evidence match the hypothesis?  How probable is the hypothesis a priori? 10/5/2015 Speech and Language Processing - Jurafsky and Martin 6

10/5/2015 Speech and Language Processing - Jurafsky and Martin 7 Using Bayes Rule

10/5/2015 Speech and Language Processing - Jurafsky and Martin 8 Likelihood and Prior

10/5/2015 Speech and Language Processing - Jurafsky and Martin 9 Two Kinds of Probabilities  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  Compute P(NN|DT) by counting in a labeled corpus:

10/5/2015 Speech and Language Processing - Jurafsky and Martin 10 Two Kinds of Probabilities  Word likelihood probabilities p(w i |t i )  VBZ (3sg Pres Verb) likely to be “is”  Compute P(is|VBZ) by counting in a labeled corpus:

10/5/2015 Speech and Language Processing - Jurafsky and Martin 11 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?

10/5/2015 Speech and Language Processing - Jurafsky and Martin 12 Disambiguating “race”

10/5/2015 Speech and Language Processing - Jurafsky and Martin 13 Disambiguating “race”

10/5/2015 Speech and Language Processing - Jurafsky and Martin 14 Example  P(NN|TO) =  P(VB|TO) =.83  P(race|NN) =  P(race|VB) =  P(NR|VB) =.0027  P(NR|NN) =.0012  P(VB|TO)P(NR|VB)P(race|VB) =  P(NN|TO)P(NR|NN)P(race|NN)=  So we (correctly) choose the verb tag for “race”

Question  If there are 30 or so tags in the Penn set  And the average sentence is around 20 words...  How many tag sequences do we have to enumerate to argmax over in the worst case scenario? 10/5/2015 Speech and Language Processing - Jurafsky and Martin

Hidden Markov Models  Remember FSAs?  HMMs are a special kind that use probabilities with the transitions  Minimum edit distance?  Viterbi and Forward algorithms  Dynamic programming?  Efficient means of finding most likely path 10/5/2015 Speech and Language Processing - Jurafsky and Martin 16

10/5/2015 Speech and Language Processing - Jurafsky and Martin 17 Hidden Markov Models  We can represent our race tagging example as an HMM.  This is a kind of generative model.  There is a hidden underlying generator of observable events  The hidden generator can be modeled as a network of states and transitions  We want to infer the underlying state sequence given the observed event sequence

10/5/2015 Speech and Language Processing - Jurafsky and Martin 18  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  Transition probability matrix A = {a ij }  Observation likelihoods  Vectors of probabilities associated with the states  Special initial probability vector  Hidden Markov Models

10/5/2015 Speech and Language Processing - Jurafsky and Martin 19 HMMs for Ice Cream  You are a climatologist in the year 2799 studying global warming  You can’t find any records of the weather in Baltimore for summer of 2007  But you find Jason Eisner’s diary which lists how many ice-creams Jason ate every day that summer  Your job: figure out how hot it was each day

10/5/2015 Speech and Language Processing - Jurafsky and Martin 20 Eisner Task  Given  Ice Cream Observation Sequence: 1,2,3,2,2,2,3…  Produce:  Hidden Weather Sequence: H,C,H,H,H,C, C…

10/5/2015 Speech and Language Processing - Jurafsky and Martin 21 HMM for Ice Cream

Ice Cream HMM  Let’s just do 131 as the sequence  How many underlying state (hot/cold) sequences are there?  How do you pick the right one? 10/5/2015 Speech and Language Processing - Jurafsky and Martin 22 HHH HHC HCH HCC CCC CCH CHC CHH HHH HHC HCH HCC CCC CCH CHC CHH Argmax P(sequence | 1 3 1)

Ice Cream HMM Let’s just do 1 sequence: CHC 10/5/2015 Speech and Language Processing - Jurafsky and Martin 23 Cold as the initial state P(Cold|Start) Cold as the initial state P(Cold|Start) Observing a 1 on a cold day P(1 | Cold) Observing a 1 on a cold day P(1 | Cold) Hot as the next state P(Hot | Cold) Hot as the next state P(Hot | Cold) Observing a 3 on a hot day P(3 | Hot) Observing a 3 on a hot day P(3 | Hot) Cold as the next state P(Cold|Hot) Cold as the next state P(Cold|Hot) Observing a 1 on a cold day P(1 | Cold) Observing a 1 on a cold day P(1 | Cold)

10/5/2015 Speech and Language Processing - Jurafsky and Martin 24 POS Transition Probabilities

10/5/2015 Speech and Language Processing - Jurafsky and Martin 25 Observation Likelihoods

10/5/2015 Speech and Language Processing - Jurafsky and Martin 26 Decoding  Ok, now we have a complete model that can give us what we need. Recall that we need to get  We could just enumerate all paths given the input and use the model to assign probabilities to each.  Not a good idea.  Luckily dynamic programming (last seen in Ch. 3 with minimum edit distance) helps us here

10/5/2015 Speech and Language Processing - Jurafsky and Martin 27 Intuition  Consider a state sequence (tag sequence) that ends at state j with a particular tag T.  The probability of that tag sequence can be broken into two parts  The probability of the BEST tag sequence up through j-1  Multiplied by the transition probability from the tag at the end of the j-1 sequence to T.  And the observation probability of the word given tag T.

10/5/2015 Speech and Language Processing - Jurafsky and Martin 28 The Viterbi Algorithm

10/5/2015 Speech and Language Processing - Jurafsky and Martin 29 Viterbi Summary  Create an array  With columns corresponding to inputs  Rows corresponding to possible states  Sweep through the array in one pass filling the columns left to right using our transition probs and observations probs  Dynamic programming key is that we need only store the MAX prob path to each cell, (not all paths).

10/5/2015 Speech and Language Processing - Jurafsky and Martin 30 Evaluation  So once you have you POS tagger running how do you evaluate it?  Overall error rate with respect to a gold- standard test set  With respect to a baseline  Error rates on particular tags  Error rates on particular words  Tag confusions...

10/5/2015 Speech and Language Processing - Jurafsky and Martin 31 Error Analysis  Look at a confusion matrix  See what errors are causing problems  Noun (NN) vs ProperNoun (NNP) vs Adj (JJ)  Preterite (VBD) vs Participle (VBN) vs Adjective (JJ)

10/5/2015 Speech and Language Processing - Jurafsky and Martin 32 Evaluation  The result is compared with a manually coded “Gold Standard”  Typically accuracy reaches 96-97%  This may be compared with result for a baseline tagger (one that uses no context).  Important: 100% is impossible even for human annotators.  Issues with manually coded gold standards

10/5/2015 Speech and Language Processing - Jurafsky and Martin 33 Summary  Parts of speech  Tagsets  Part of speech tagging  HMM Tagging  Markov Chains  Hidden Markov Models  Viterbi decoding

10/5/2015 Speech and Language Processing - Jurafsky and Martin 34 Review  Exam readings  Chapters 1 to 6  Chapter 2  Chapter 3  Skip 3.4.1, 3.10, 3.12  Chapter 4  Skip 4.7,  Chapter 5  Skip 5.5.4, 5.6,

10/5/2015 Speech and Language Processing - Jurafsky and Martin 35 3 Formalisms  Regular expressions describe languages (sets of strings)  Turns out that there are 3 formalisms for capturing such languages, each with their own motivation and history  Regular expressions  Compact textual strings  Perfect for specifying patterns in programs or command-lines  Finite state automata  Graphs  Regular grammars  Rules

Regular expressions  Anchor expressions  ^, $, \b  Counters  *, +, ?  Single character expressions ., [ ], [ - ]  Grouping for precedence  ( )  [dog]* vs. (dog)*  No need to memorize shortcuts  \d, \s 10/5/2015 Speech and Language Processing - Jurafsky and Martin 36

FSAs  Components of an FSA  Know how to read one and draw one  Deterministic vs. non-deterministic  How is success/failure different?  Relative power  Recognition vs. generation  How do we implement FSAs for recognition? 10/5/2015 Speech and Language Processing - Jurafsky and Martin 37

10/5/2015 Speech and Language Processing - Jurafsky and Martin 38 More Formally  You can specify an FSA by enumerating the following things.  The set of states: Q  A finite alphabet: Σ  A start state  A set of accept states  A transition function that maps Qx Σ to Q

FSTs  Components of an FST  Inputs and outputs  Relations 10/5/2015 Speech and Language Processing - Jurafsky and Martin 39

Morphology  What is a morpheme?  Stems and affixes  Inflectional vs. derivational  Fuzzy -> fuzziness  Fuzzy -> fuzzier  Application of derivation rules  N -> V with –ize  System, chair  Regular vs. irregular 10/5/2015 Speech and Language Processing - Jurafsky and Martin 40

10/5/2015 Speech and Language Processing - Jurafsky and Martin 41 Derivational Rules

10/5/2015 Speech and Language Processing - Jurafsky and Martin 42 Lexicons  So the big picture is to store a lexicon (list of words you care about) as an FSA. The base lexicon is embedded in larger automata that captures the inflectional and derivational morphology of the language.  So what? Well, the simplest thing you can do with such an FSA is spell checking  If the machine rejects, the word isn’t in the language  Without listing every form of every word

10/5/2015 Speech and Language Processing - Jurafsky and Martin 43 Next Time  Three tasks for HMMs  Decoding  Viterbi algorithm  Assigning probabilities to inputs  Forward algorithm  Finding parameters for a model  EM