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Cogs 118A: Natural Computation I Angela Yu ajyu@ucsd January 6, 2008

Cogs 118A: Natural Computation I Angela Yu ajyu@ucsd.edu January 6, 2008. http://www.cogsci.ucsd.edu/~ajyu/Teaching/Cogs118A_wi09/cogs118A.html. Course Overview. Statistical methods. assignments. Neural networks. Advanced topics. midterm. Applications to cognitive science. final project.

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Cogs 118A: Natural Computation I Angela Yu ajyu@ucsd January 6, 2008

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  1. Cogs 118A: Natural Computation IAngela Yuajyu@ucsd.eduJanuary 6, 2008 http://www.cogsci.ucsd.edu/~ajyu/Teaching/Cogs118A_wi09/cogs118A.html

  2. Course Overview Statistical methods assignments Neural networks Advanced topics midterm Applications to cognitive science final project

  3. Supervised learning The agent also observes a seqence of labels or outputsy1, y2, …, and the goal is to learn the mapping f: x  y. Unsupervised learning The agent’s goal is to learn a statistical model for the inputs, p(x), to be used for prediction, compact representation, decisions, … Reinforcement learning The agent can perform actions a1, a2, a3, …, which affect the state of the world, and receives rewards r1, r2, r3, … Its goal is to learn a policy: {x1, x2, …, xt} atthat maximizes rewards. Three Types of Learning Imagine an agent observes a sequence of of inputs: x1, x2, x3, …

  4. Cat Dog y x Supervised Learning Classification: the outputs y1, y2, … are discrete labels Regression: the outputs y1, y2, … are continuously valued

  5. Object Categorization Speech Recognition VET WET Face Recognition Motor Learning Applications: Cognitive Science

  6. Motor Learning Challenges • Noisy sensory inputs • Incomplete information • Changing environment • Many variables (mostly irrelevant) • No (one) right answer • Prior knowledge • Inductive inference (open-ended) • Uncertainty, not deterministic

  7. An Example: Curve-Fitting y x

  8. Error function (root-mean-square) Polynomial Curve-Fitting Linear model

  9. Linear Fit? y x

  10. Quadratic Fit? y x

  11. 5th-Order Polynomial Fit? y x

  12. 10th-Order Polynomial Fit? y x

  13. And the Answer is… Quadratic y x

  14. Training Error vs. Test Error 1st-order 2nd-order y 5th-order 10th-order y x x

  15. What Did We Learn? • Model complexity important • Minimizing training error  overtraining • A better error metric: test error • But test error costs extra data (precious) • Fix 1: regularization (3.1) • Fix 2: Bayesian model comparison (3.3)

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