2. A Bayesian approach to word segmentation: Theoretical and experimental results Sharon Goldwater Department of Linguistics Stanford University

3. Word segmentation One of the first problems infants must solve when learning language. Infants make use of many different cues.  Phonotactics, allophonic variation, metrical (stress) patterns, effects of coarticulation, and statistical regularities in syllable sequences. Statistics may provide initial bootstrapping.  Used very early (Thiessen & Saffran, 2003).  Language-independent.

4. Modeling statistical segmentation Previous work often focuses on how statistical information (e.g., transitional probabilities) can be used to segment speech. Bayesian approach asks what information should be used by a successful learner.  What statistics should be collected?  What assumptions (by the learner) constrain possible generalizations?

5. Outline 1. Computational model and theoretical results  What are the consequences of using different sorts of information for optimal word segmentation? (joint work with Tom Griffiths and Mark Johnson) 2. Modeling experimental data  Do humans behave optimally? (joint work with Mike Frank, Vikash Mansinghka, Tom Griffiths, and Josh Tenenbaum)

6. Statistical segmentation Work on statistical segmentation often discusses transitional probabilities (Saffran et al. 1996; Aslin et al. 1998, Johnson & Jusczyk, 2001).  P(syl i | syl i-1 ) is often lower at word boundaries. What do TPs have to say about words?  A word is a unit whose beginning predicts its end, but it does not predict other words.  A word is a unit whose beginning predicts its end, and it also predicts future words. Or…

7. Interpretation of TPs Most previous work assumes words are statistically independent.  Experimental work: Saffran et al. (1996), many others.  Computational work: Brent (1999). What about words predicting other words? tupiro golabu bidaku padoti golabubidakugolabutupiropadotibidakupadotitupi…

8. Questions If a learner assumes that words are independent units, what is learned (from more realistic input)?  Unigram model: Generate each word independently. What if the learner assumes that words are units that help predict other units?  Bigram model: Generate each word conditioned on the previous word. Approach: use a Bayesian ideal observer model to examine the consequences of each assumption.

9. Bayesian learning The Bayesian learner seeks to identify an explanatory linguistic hypothesis that  accounts for the observed data.  conforms to prior expectations. Focus is on the goal of computation, not the procedure (algorithm) used to achieve the goal.

10. Bayesian segmentation In the domain of segmentation, we have:  Data: unsegmented corpus (transcriptions).  Hypotheses: sequences of word tokens. Optimal solution is the segmentation with highest prior probability. = 1 if concatenating words forms corpus, = 0 otherwise. Encodes unigram or bigram assumption (also others).

11. Brent (1999) Describes a Bayesian unigram model for segmentation.  Prior favors solutions with fewer words, shorter words. Problems with Brent’s system:  Learning algorithm is approximate (non-optimal).  Difficult to extend to incorporate bigram info.

12. A new unigram model (Dirichlet process) Assume word w i is generated as follows: 1. Is w i a novel lexical item? Fewer word types = Higher probability

13. A new unigram model (Dirichlet process) Assume word w i is generated as follows: 2. If novel, generate phonemic form x 1 …x m : If not, choose lexical identity of w i from previously occurring words: Shorter words = Higher probability Power law = Higher probability

14. Unigram model: simulations Same corpus as Brent (Bernstein-Ratner, 1987) :  9790 utterances of phonemically transcribed child- directed speech (19-23 months).  Average utterance length: 3.4 words.  Average word length: 2.9 phonemes. Example input: yuwanttusiD6bUk lUkD*z6b7wIThIzh&t &nd6dOgi yuwanttulUk&tDIs...

15. Example results

16. Comparison to previous results Proposed boundaries are more accurate than Brent’s, but fewer proposals are made. Result: word tokens are less accurate. Boundary Precision Boundary Recall Brent.80.85 GGJ.92.62 Token F-score Brent.68 GGJ.54 Precision: #correct / #found = [= hits / (hits + false alarms)] Recall: #found / #true = [= hits / (hits + misses)] F-score: an average of precision and recall.

17. What happened? Model assumes (falsely) that words have the same probability regardless of context. Positing amalgams allows the model to capture word-to-word dependencies. P( D&t ) =.024 P( D&t | WAts ) =.46 P( D&t | tu ) =.0019

18. What about other unigram models? Brent’s learning algorithm is insufficient to identify the optimal segmentation.  Our solution has higher probability under his model than his own solution does.  On randomly permuted corpus, our system achieves 96% accuracy; Brent gets 81%. Formal analysis shows undersegmentation is the optimal solution for any (reasonable) unigram model.

19. Bigram model (hierachical Dirichlet process) Assume word w i is generated as follows: 1. Is ( w i-1,w i ) a novel bigram? 2. If novel, generate w i using unigram model (almost). If not, choose lexical identity of w i from words previously occurring after w i-1.

20. Example results

21. Quantitative evaluation Compared to unigram model, more boundaries are proposed, with no loss in accuracy: Accuracy is higher than previous models: Boundary Precision Boundary Recall GGJ (unigram).92.62 GGJ (bigram).92.84 Token F-scoreType F-score Brent (unigram).68.52 GGJ (bigram).77.63

22. Summary Two different assumptions about what defines a word are consistent with behavioral evidence. Different assumptions lead to different results.  Beginning of word predicts end of word: Optimal solution undersegments, finding common multi-word units.  Word also predicts next word: Segmentation is more accurate, adult-like.

23. Remaining questions Is unigram segmentation sufficient to start bootstrapping other cues (e.g., stress)? How prevalent are multi-word chunks in infant vocabulary? Are humans able to segment based on bigram statistics? Is there any evidence that human performance is consistent with Bayesian predictions?

24. Testing model predictions Goal: compare our model (and others) to human performance in a Saffran-style experiment. Problem: all models have near-perfect accuracy on experimental stimuli. Solution: compare changes in model performance relative to humans as task difficulty is varied. tupiro golabu bidaku padoti golabubidakugolabutupiropadotibidakupadotitupiro…

25. Experimental method Examine segmentation performance under different utterance length conditions. Example lexicon: lagi dazu tigupi bavulu kabitudu kipavazi Conditions: # wds/utt# uttstot # wds 11200 26001200 43001200 62001200 81501200 121001200 24501200

26. Procedure Training: adult subjects listened to synthesized utterances in one length condition.  No pauses between syllables within utterances.  500 ms pauses between utterances. Testing: 2AFC between words and part-word distractors. lagi dazu tigupi bavulu kabitudu kipavazi lagitigupibavulukabitudulagikipavazi dazukipavazibavululagitigupikabitudu kipavazitigupidazukabitudulagitigupi … Lexicon:

27. Human performance

28. Model comparison Evaluated six different models. Each model trained and tested on same stimuli as humans. To simulate 2AFC, produce a score s(w) for each word in choice pair and use Luce choice rule: Compute best linear fit of each model to human data, then calculate correlation.

29. Models used Three local statistic models, all similar to transitional probabilities (TP)  Segment at minima of P(syl i | syl i-1 ).  s(w) = minimum TP in w. Swingley (2005)  Builds lexicon using local statistic and frequency thresholds.  s(w) = max threshold at which w appears in lexicon. PARSER (Perruchet and Vinter, 1998)  Incorporates principles of lexical competition and memory decay.  s(w) = P(w) as defined by model. GGJ (our Bayesian model)  s(w) = P(w) as defined by model.

30. Results: linear fit

31. Results: words vs. part-words

32. Summary Statistical segmentation is more difficult when utterances contain more words. Gradual decay in performance is predicted by Bayesian model, but not by others tested. Bayes predicts difficulty is primarily due to effects of competition.  In longer utterances, correct words are less probable because more other possibilities exist.  Local statistic approaches don’t model competition.

33. Continuing work Experiments with other task modifications will further test our model’s predictions. Vary the length of exposure to training stimulus:  Bayes: longer exposure => better performance.  TPs: no effect of exposure. Vary the number of lexical items:  Bayes: larger lexicon => worse performance.  TPs: larger lexicon => better performance.

34. Conclusions Computer simulations and experimental work suggest that Unigram assumption causes ideal learners to undersegment fluent speech. Human word segmentation may approximate Bayesian ideal learning.

36. Bayesian segmentation whatsthat thedoggie wheresthedoggie... whatsthat thedoggie wheresthedoggie wh at sth at thedo ggie wh eres thedo ggie whats that the doggie wheres the doggie w h a t s t h a t t h e d o g g i e w h e r e s t h e d o g g i e Input data:Some hypotheses:

37. Search algorithm Model defines a distribution over hypotheses. We use Gibbs sampling to find a good hypothesis. Iterative procedure produces samples from the posterior distribution of hypotheses. A batch algorithm (but online algorithms are possible, e.g., particle filtering). P(h|d) h

38. Gibbs sampler 1. Consider two hypotheses differing by a single word boundary: 2. Calculate probabilities of words that differ, given current analysis of all other words.  Model is exchangeable: probability of a set of outcomes does not depend on ordering. 3. Sample one of the two hypotheses according to the ratio of probabilities. whats.that the.doggie wheres.the.doggie whats.that the.dog.gie wheres.the.doggie

39. Models used Transitional probabilities (TP)  Segment at minima of P(syl i | syl i-1 ).  s(w) = minimum TP in w. (Equivalently, use product). Smoothed transitional probabilities  Avoid 0 counts by using add-λ smoothing. Mutual information (MI)  Segment where MI between syllables is lowest.  s(w) = minimum MI in w. (Equivalently, use sum).

40. Models used Swingley (2005)  Builds a lexicon, including syllable sequences above some threshold for both MI and n-gram frequency.  s(w) = max threshold at which w appears in lexicon. PARSER (Perruchet and Vinter, 1998)  Lexicon-based model incorporating principles of lexical competition and memory decay.  s(w) = P(w) as defined by model. GGJ (our Bayesian model)  s(w) = P(w) as defined by model.

41. Results: linear fit

42. Continuing work Comparisons to human data and other models: Which words/categories are most robust?  Compare to Frequent Frames predictions (Mintz, 2003).  Compare to corpus data from children’s production. Modeling cue combination: Integrate morphology into syntactic model. Model experimental work on cue combination in category learning.