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

Neural networks

Advanced topics

Applications to cognitive science

midterm

finalproject

assignments

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, …

Supervised LearningClassification: the outputs y1, y2, … are discrete labels

Dog Cat

Regression: the outputs y1, y2, … are continuously valued

x

y

Applications: Cognitive ScienceObject Categorization Speech Recognition

WET VET

Face Recognition Motor Learning

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

An Example: Curve-Fitting

x

y

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

Linear Fit?

x

y

Quadratic Fit?

x

y

5th-Order Polynomial Fit?

x

y

10th-Order Polynomial Fit?

x

y

And the Answer is…

x

y

Quadratic

Training Error vs. Test Error

x

y

y

x

1st-order

5th-order 10th-order

2nd-order

• 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?