Max-margin sequential learning methods

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Max-margin sequential learning methods

• William W. Cohen
• CALD

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Announcements

• Upcoming assignments
• Wed 3/3 project proposal due
• personnel 1-2 page
• Spring break next week, no class
• Will get feedback on project proposals by end of
  break
• No write-ups for Distance Metrics for Text week
  are due Wed 3/17
• not the Monday after spring break

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Collins paper

• Notation
• label (y) is a tag t
• observation (x) is word w
• history h is a 4-tuple ltti,ti-1,w1n,igt
• phis(h,t) is a feature of h, t

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Collins papers

• Notation cont
• Phi is summation of phi for all positions i
• alphas is weight to give phis

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Collins paper
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The theory
Claim 1 the algorithm is an instance of this
perceptron variant
Claim 2 the arguments in the mistake-bounded
classification results of FS99 extend
immediately to this ranking task as well.
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(No Transcript)
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FS99 algorithm
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FS99 result
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Collins result
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Results

• Two experiments
• POS tagging, using the Adwaits features
• NP chunking (Start,Continue,Outside tags)
• NER on special ATT dataset (another paper)

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Features for NP chunking
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Results
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More ideas

• The dual version of a perceptron
• w is built up by repeatedly adding examples gt w
  is a weighted sum of the examples x1,...,xn
• inner product ltw,xgt is can be rewritten

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Dual version of perceptron ranking
alpha i,j i,j range over example and
correct/incorrect tag sequence
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NER features for re-ranking MAXENT tagger output
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NER features
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NER results
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Altun et al paper

• Starting point dual version of Collins
  perceptron algorithm
• final hypothesis is weighted sum of inner
  products with a subset of the examples
• this a lot like an SVM except that the
  perceptron algorithm is used to set the weights
  rather than quadratic optimization

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SVM optimization

• Notation
• yi is the correct tag for xi
• y is an incorrect tag
• F(xi,yi) are features
• Optimization problem
• find weights w on the examples that maximize
  minimal margin, limiting w1, or
• minimize w2 such that every margin gt 1

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SVMs for ranking
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SVMs for ranking
Proposition (14) and (15) are equivalent
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SVMs for ranking
A binary classification problem with xi yi the
positive example and xi y negative examples,
except that thetai varies for each example. Why?
because were ranking.
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SVMs for ranking

• Altun et al work give the remaining details
• Like for perceptron learning, negative data is
  found by running Viterbi given the learned
  weights and looking for errors
• Each mistake is a possible new support vector
• Need to iterate over the data repeatedly
• Could be exponential time before convergence if
  the support vectors are dense...

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Altun et al results

• NER on 300 sentences from CoNLL2002 shared task
• Spanish
• Four entity types, nine labels (beginning-T,
  intermediate-T, other)
• POS tagging on 300 sentences from Penn TreeBank
• 5-CV, window of size 3, simple features

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Altun et al results
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Altun et al results