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Humans Learn Using Manifolds, Reluctantly

Humans Learn Using Manifolds, Reluctantly. Bryan Gibson, Xiaojin Zhu, Timothy Rogers, Charles Kalish, and Joseph Harrison University of Wisconsin-Madison. A Familiar Task. Question : which one would humans do? Contribution : an empirical study of human manifold learning behaviors.

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Humans Learn Using Manifolds, Reluctantly

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  1. Humans Learn Using Manifolds, Reluctantly Bryan Gibson, Xiaojin Zhu, Timothy Rogers, Charles Kalish, and Joseph Harrison University of Wisconsin-Madison

  2. A Familiar Task Question: which one would humans do? Contribution: an empirical study of human manifold learning behaviors if we choose supervised learning semi-supervised learning Humans Learn Using Manifolds

  3. Manifolds are Common in Life Humans Learn Using Manifolds

  4. Manifolds are Common in Life y=“Bryan Gibson” y=? Humans Learn Using Manifolds

  5. The Stimuli of Our Behavioral Experiments • Not faces: avoid existing knowledge x2=0.41 x2=0.59 x1=0.39 x1=0.61 x2=0.9 x1=1 1 0 x2=0.1 0 1 x1=0 Humans Learn Using Manifolds

  6. Human Behavioral Experiments labeled • Batch learning (instead of sequential) unlabeled Humans Learn Using Manifolds

  7. Aggregated Results: Majority Vote n subjects classified this stimulus o: majority vote blue +: majority vote red *: equal blue, red Humans Learn Using Manifolds

  8. Aggregated Results: Majority Vote condition: L=2 8 subjects Humans Learn Using Manifolds

  9. Individual Subject Fit • If best fitting model m has accuracy >75% • then subject potentially uses m, • Otherwise subject uses “other” • Percentage of subjects potentially using each model: graph [Belkin et al.’06] 1NN l2 [Nosofsky’86] 1NN l1 vertical horizontal Not manifold Humans Learn Using Manifolds

  10. New Experiment: 4 Labeled Points • Intention: remove “vertical” or “horizontal” • L=4: • These 4 labeled points chosen to maximize differences in model predictions: multi-v multi-h v 1NN l1 h graph 1NN l2 Humans Learn Using Manifolds

  11. The Interface for L=4 Humans Learn Using Manifolds

  12. Results for L=4 • Majority vote: • Individual fit: Not manifold L=2, 8 subjects L=4, 24 subjects Humans Learn Using Manifolds

  13. New Experiment: Give People the Graph! • NN graph • 2 connected components with pure labels =0.07 Humans Learn Using Manifolds

  14. Giving People the Graph via Highlighting • Clicking on any item highlights all its neighbors • Instructions to subjects: highlighting not necessarily mean “same class” Humans Learn Using Manifolds

  15. Results for (L=4, Hi) • Majority vote: • Individual fit: L=2, 8 subjects L=4, 24 subjects (L=4, Hi) 23 sub Manifold! Humans Learn Using Manifolds

  16. This is Awfully Suspicious • Humans simply follow highlighting?! • No. Three pieces of evidence + o + o + o + + o + o + o + o o o Humans Learn Using Manifolds

  17. Evidence 1: Leap-of-Faith Against Highlight • A leap-of-faith (lof) move goes against labeled neighbors, or has no labeled neighbors • If people simply follow highlighting, #lof=0 • In (L=4, Hi), average #lof=17 (20% of their moves) highlighted labeled neighbor leap-of-faith Humans Learn Using Manifolds

  18. Evidence 2: New Experiment (L=2, Hi) • Same highlighting, but 2 labeled points • Majority vote: • Individual fit: Not manifold L=2, 8 subjects L=4, 24 subjects (L=2, Hi) 8 sub (L=4, Hi) 23 sub Humans Learn Using Manifolds

  19. Evidence 3: New Experiment (Isomorphic Graph) • Randomly permute the unlabeled nodes, “bring the edges with them” • If people simply follow highlighting, then everything should be the same: 1 is easy blue, 2 is harder but still blue, … 1 2 4 3 Humans Learn Using Manifolds

  20. Evidence 3: New Experiment (Isomorphic Graph) • (L=4, Iso) isomorphic to (L=4, Hi): • There are really two “pure” connected components! Humans Learn Using Manifolds

  21. Evidence 3: New Experiment (Isomorphic Graph) • The interface for (L=4, Iso) Humans Learn Using Manifolds

  22. Evidence 3: New Experiment (Isomorphic Graph) • Highlighting ignored if it contradicts with similarity L=4, Hi (23 subjects) L=4, Iso (30 subjects) Humans Learn Using Manifolds

  23. Why not Always Manifold Learning? • Possible explanation: Bayesian model selection • data-dependent prior: • likelihood: Humans Learn Using Manifolds

  24. Summary provide graph (highlighting) graph agrees w. similarity weaken linear hypotheses (L=4) Humans Learn Using Manifolds

  25. Thank you Humans Learn Using Manifolds

  26. (L=4, Iso) • Majority Vote (30 subjects): • Individual fit: Humans Learn Using Manifolds

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