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Understanding Human Learning Through Manifold Approaches

This research explores how humans learn by employing manifold structures, investigating supervised and semi-supervised learning in behavioral experiments. Using various stimuli, subjects classified data based on majority voting, with results revealing preferences in learning models. Experiments included highlighting connected components and analyzing subjects’ responses to new labeled points. Findings indicate that humans challenge highlighted suggestions, often opting for more complex reasoning. The study deepens insight into human manifold learning behaviors and suggests implications for future learning model applications.

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Understanding Human Learning Through Manifold Approaches

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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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