Week 5 — The Size Principle: Bayesian Word Learning from Three Examples

Week 5 of 8. How do children learn a word from three examples without over- or under-generalizing?
Point at a Dalmatian and say "blicket." Does blicket mean this individual dog, Dalmatians, dogs, or animals? Logically, all four are consistent with the evidence, and children still converge on the right one fast. Tenenbaum's size principle gives a startlingly clean answer: smaller hypotheses assign higher likelihood to the data they cover, so three Dalmatians make "Dalmatian" exponentially more likely than "dog." No extra machinery, no innate constraint — it falls out of Bayes.
Agenda:

1. Recap and intros (10 min)
2. The subset problem, and why positive-only evidence is supposed to be impossible to learn from (20 min)
3. The size principle, worked through on the number game (25 min)
4. Xu & Tenenbaum's word-learning experiments: what happened when they tested it on actual children (25 min)
5. Discussion: is the prior doing all the work? The perennial objection (20 min)
   Reference: Xu & Tenenbaum (2007), "Word Learning as Bayesian Inference."
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