Cogs 118A: Natural Computation I Angela Yu ajyu@ucsd January 6, 2008
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Cogs 118A: Natural Computation I
Angela Yu
January 6, 2008
http://www.cogsci.ucsd.edu/~ajyu/Teaching/Cogs118A_wi09/cogs118A.html
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Course Overview
Statistical methods
Neural networks
Advanced topics
Applications to cognitive science
midterm
finalproject
assignments
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Three Types of Learning
Supervised learning
The agent also observes a seqence of labels or outputs y1, 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} at that maximizes rewards.
Imagine an agent observes a sequence of of inputs: x1, x2, x3, …
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Supervised LearningClassification: the outputs y1, y2, … are discrete labels
Dog Cat
Regression: the outputs y1, y2, … are continuously valued
x
y
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Applications: Cognitive ScienceObject Categorization Speech Recognition
WET VET
Face Recognition Motor Learning
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Challenges
Motor Learning• Noisy sensory inputs
• Incomplete information
• Changing environment
• Many variables (mostly irrelevant)
• No (one) right answer
• Prior knowledge
• Inductive inference (open-ended)
• Uncertainty, not deterministic
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An Example: Curve-Fitting
x
y
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Polynomial Curve-Fitting
€
y(x;w) = w0 + w1x +w2x 2 +K + wn x n = w j xj
j= 0
n
∑
Linear model
Error function (root-mean-square)
€
E(w) = y(x i,w) − y j( )2
j= 0
n
∑ N
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Linear Fit?
x
y
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Quadratic Fit?
x
y
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5th-Order Polynomial Fit?
x
y
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10th-Order Polynomial Fit?
x
y
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And the Answer is…
x
y
Quadratic
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Training Error vs. Test Error
x
y
y
x
1st-order
5th-order 10th-order
2nd-order
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• 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)
What Did We Learn?