1. Statistical learning, cross- constraints, and the acquisition of speech categories: a computational approach. Joseph Toscano & Bob McMurray Psychology Department University of Iowa

2. Acknowledgements Acknowledgements: –Dick Aslin –The MACLab

3. Learning phonetic categories Infants are initially able to discriminate many different phonetic contrasts. They must learn which ones are relevant to their native language. This is accomplished within the first year of life, and infants quickly adopt the categories present in their language (Werker & Tees, 1984).

4. Learning phonetic categories What is needed for statistical learning? A signal and a mechanism –Availability of statistics (signal) –Sensitivity to statistics (mechanism) continuous sensitivity to VOT ability to track frequencies and build clusters

5. Statistics in the signal What statistical information is available? Lisker & Abramson, 1964 did a cross-language analysis of speech –Measured voice-onset time (VOT) from several speakers in different languages

6. Statistics in the signal The statistics are available in the signal Tamil Cantonese English

7. Sensitivity to statistics Are infants sensitive to statistics in speech? –Maye et al., 2002 asked this –Two groups of infants Infants are sensitive to within-category detail (McMurray & Aslin, 2005)

8. Learning phonetic categories Infants can obtain phoneme categories from exposure to tokens in the speech signal VOT frequency 0ms50ms +voice-voice

9. Statistical Learning Model Statistical learning in a computational model What do we need the model to do: –Show learnability. Are statistics sufficient? –Developmental timecourse. –Implications for speech in general. –Can model explain more than category learning?

10. Statistical Learning Model Clusters of VOTs are Gaussian distributions Tamil Cantonese English

11. Statistical Learning Model Gaussians defined by three parameters: Each phoneme category can be represented by these three parameters  VOT  Φ μ – the center of the distribution σ – the spread of the distribution Φ – the height of the distribution, reflected by the probability of a particular value

12. Statistical Learning Model Modeling approach: mixture of Gaussians /b//p/

13. Statistical Learning Model Gaussian distributions represent the probability of occurrence of a particular feature (e.g. VOT) Start with a large number of Gaussians to reflect many different values for the feature. /b//p/

14. Statistical Learning Model Learning occurs via gradient descent –Take a single data point as input –Adjust the location and width of the distribution by a certain amount, defined by a learning rule   Move the center of the dist closer to the data point Make the dist wider to accommodate the data point

15. Statistical Learning Model Learning rule: { Probability of a particular point Proportion of space under that Gaussian Equation of a Gaussian = x

16. Can the model learn? Can the model learn speech categories?

17. Can the model learn? The model in action Fails to learn correct number of categories –Too many distributions under each curve –Is this a problem? Maybe. Solution: Introduce competition Competition through winner-take-all strategy –Only the closest matching Gaussian is adjusted

18. Does learning need to be constrained? Can the model learn speech categories?Yes. Does learning need to be constrained?

19. Unconstrained feature space –Starting VOTs distributed from -1000 to +1000 ms –Model fails to learn –Similar to a situation in which the model has too few starting distributions

20. Does learning need to be constrained? Constrained feature space –Starting VOTs distributed from -100 to +100 ms –Within the range of actual voice onset times used in language.

21. Are constraints linguistic? Can the model learn speech categories?Yes. Does learning need to be constrained?Yes. Do constraints need to be linguistic?

22. Are constraints linguistic? Cross-linguistic constraints –Combined data from languages used in Lisker & Abramson, 1964, and several other languages

23. Are constraints linguistic? VOTs from: –English –Thai –Spanish –Cantonese –Korean –Navajo –Dutch –Hungarian –Tamil –Eastern Armenian –Hindi –Marathi –French

24. Test the model with two different sets of starting states: Cross-linguistic: based on distribution of VOTs across languages Random normally distributed: centered around 0ms, range ~ - 100ms to +100ms VOT

25. Test the model with two different sets of starting states: Cross-linguistic: based on distribution of VOTs across languages Random normally distributed: centered around 0ms, range ~ - 100ms to +100ms

26. Are linguistic constraints helpful? Can the model learn speech categories?Yes. Does learning need to be constrained?Yes. Do constraints need to be linguistic?No. Do cross-language constraints help?

27. Are linguistic constraints helpful? This is the part of the talk that I don’t have any slides for yet.

28. What do infants do? Can the model learn speech categories?Yes. Does learning need to be constrained?Yes. Do constraints need to be linguistic?No. Do cross-language constraints help? Sometimes. What do infants do?

29. As infants get older, their ability to discriminate different VOT contrasts decreases. –Initially able to discriminate many contrasts –Eventually discriminate only those of their native language

30. What do infants do? Each model’s discrimination over time –Random normal: decreases –Cross-linguistic: slight increase

31. What do infants do? Cross-linguistic starting states lead to faster category acquisition Why wouldn’t infants take advantage of this? –Too great a risk of over-generalization –Better to take more time to do the job right than to do it too quickly