Transcript statLecture9bx

Corpora and Statistical Methods
Lecture 9
Albert Gatt
Part 2
POS Tagging overview; HMM taggers, TBL tagging
The task
 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
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!
The information sources
Syntagmatic information: the tags of other words in the context of w
1.

Not sufficient on its own. E.g. Greene/Rubin 1977 describe a context-only tagger
with only 77% accuracy
Lexical information (“dictionary”): most common tag(s) for a given word
2.



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
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
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.
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
HMM taggers
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
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!
Notation
 We let ti range over tags
 Let wi range over words
 Subscripts denote position in a sequence
 Use superscripts to denote word types:
 wj = an instance of word type j in the lexicon
 tj = tag t assigned to word wj
 Limited horizon property becomes:
P(ti 1 | t1,.., i )  P(ti 1 | ti )
Basic strategy
 Training set of manually tagged text
 extract probabilities of tag sequences:
k
j
C
(
t
,
t
)
k
j
P(t | t ) 
C (t j )
 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
l
j
C
(
w
,
t
)
l
j
P( w | t ) 
C (t j )
symbol emission
probabilities
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 tj and for each word wl estimate P(wl| tj).
3.
Apply smoothing.
Finding the best tag sequence
 Given: a sentence of n words
 Find: t1,n = the best n tags
arg max P(t1,n | w1,n )  arg max
t i ,n
P( w1,n | t1,n ) P(t1,n )
P( w1,n )
 arg max P( w1,n | t1,n ) P(t1,n )
t1,n
t1,n
 Application of Bayes’ rule
 denominator can be eliminated as it’s the same for all tag sequences.
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

The independence assumption
P( w1,n
 n

| t1,n ) P(t1,n )  
P( wi | t1,n )  P(t n | t n 1 )  ...  P(t 2 | t1 )
 i 1


• Probability of a sequence of words given a sequence of tags is
computed as a function of each word independently
The identity assumption
P( w1,n
 n

| t1,n ) P(t1,n )  
P( wi | t1,n )  P(t n | t n 1 )  ...  P(t 2 | t1 )
 i 1

 n

 
P( wi | ti )  P(t n | t n 1 )  ...  P(t 2 | t1 )
 i 1



 Probability of a word given a tag sequence = probability a
word given its own tag
Applying these assumptions
arg max P(t1,n | w1,n )  arg max
t i ,n
P( w1,n | t1,n ) P(t1,n )
P( w1,n )
 arg max P( w1,n | t1,n ) P(t1,n )
t1,n
t1,n
n
 arg max
t1,n
 P(w | t )P(t | t
i
i 1
i
i
i 1 )
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
i
 ( j)
 i 1
most probable state (tag) at
word i given that we’re in state j at word i+1
The algorithm: initialisation
 i ( PERIOD )  1.0
 i (t )
 0 for all other t
 Assume that P(PERIOD) = 1 at end of sentence
 Set all other tag probs to 0
Algorithm: induction step
for i = 1 to n step 1:
for all tags tj do:
 i 1 (t )  max[ i (t )  P(t | t )  P(wi 1 | t )]
j
k
j
k
j
1k T
Probability of tag tj at i+1 on best path through i
 i 1 (t j )  arg max [ i (t k )  P(t j | t k )  P( wi 1 | t j )]
i  k T
Most probable tag leading to tj at i+1
Algorithm: backtrace
X n 1  arg max  n 1 (t j )
State at n+1
1 j T
for j = n to 1 do:
X
j

j 1 ( X j 1 )
retrieve the most probable tags for every point in
sequence
P( X 1... X n )  max  n1 (t j )
1 j T
Calculate probability for the sequence of tags
selected
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
“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