1. Max-margin sequential learning methods
William W. Cohen
CALD

2. Announcements Upcoming assignments: Wed 3/3: project proposal due:
personnel 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

3. Collins’ paper Notation: label (y) is a “tag” t
observation (x) is word w
history h is a 4-tuple <ti,ti-1,w[1:n],i>
phis(h,t) is a feature of h, t

4. Collins’ papers Notation con’t:
Phi is summation of phi for all positions i
alphas is weight to give phis

5. Collins’ paper

6. The theory
Claim 1: the algorithm is an instance of this perceptron variant:
Claim 2: the arguments in the mistake-bounded classification results of F&S99 extend immediately to this ranking task as well.

8. F&S99 algorithm

9. F&S99 result

10. Collins’ result

11. Results Two experiments POS tagging, using the Adwait’s features
NP chunking (Start,Continue,Outside tags)
NER on special AT&T dataset (another paper)

12. Features for NP chunking

13. Results

14. More ideas The dual version of a perceptron:
w is built up by repeatedly adding examples => w is a weighted sum of the examples x1,...,xn
inner product <w,x> is can be rewritten:

15. Dual version of perceptron ranking
alpha i,j = i,j range over example and correct/incorrect tag sequence

16. NER features for re-ranking MAXENT tagger output

17. NER features

18. NER results

19. 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

20. 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 ||w||=1, or
minimize ||w||2 such that every margin >= 1

21. SVMs for ranking

22. SVMs for ranking
Proposition: (14) and (15) are equivalent:

23. 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 we’re ranking.

24. 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...

25. 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

26. Altun et al results

27. Altun et al results