1
From Data To Understanding
•
In machine learning, maintain critical perspective
Making predictions is only part of the story
Also try to get some understanding
of the domain
•
Example
True statement: palm size negatively correlates with
life expectancy
o
The larger your palm size, the shorter your life (on average)
Why?
o
Women have smaller palms than men on average
o
Women live 5 years longer than men on average
Sometimes you need better model of your domain!
Bayesian Networks
•
Bayesian Network
Graphical representation of joint probability distribution
o
Node: random variable
o
Arc (X, Y): variable X has direct influence on variable Y
•
Call X a “parent” of Y
o
Each node X has conditional probability: P(X  parents(X))
o
Graph has no cycles (loops by following arcs)
•
Called “Directed Acyclic Graph” (DAG)
Palm size
Gender
Life
Expectancy
•
Conditional independence encoded in network
Each node (variable) is conditionally independent of its
nondescendants, given it parents
In network above Palm Size and Life Expectancy are
conditionally independent, given Gender
o
Formally: P(PS, LE  G) = P(PS  G) P(LE  G)
•
Network structure provides insight about domain
Network Shows Conditional Independence
Palm size
Gender
Life
Expectancy
•
Each node has conditional probability table (CPT)
For node X: P(X  Parents(X))
Conditional independence modularizes joint probability:
Conditional Probability Tables
P(G = M) = 0.49
P(G = F) = 0.51
P(PS = L  G = M)
= 0.45
P(PS = M  G = M)
= 0.35
P(PS = S  G = M)
= 0.20
P(PS = L  G = F)
= 0.10
P(PS = M  G = F)
= 0.30
P(PS = S  G = F)
= 0.60
P(LE = < 70
 G = M) = 0.20
P(LE = 7080  G = M) = 0.50
P(LE = > 80
 G = M) = 0.30
P(LE = < 70
 G = F) = 0.10
P(LE = 7080  G = F) = 0.35
P(LE = > 80
 G = F) = 0.55
n
i
i
i
n
X
X
P
X
X
X
P
1
2
1
))
(
Parents

(
)
,...,
,
(
Palm size
Gender
Life
Expectancy
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
•
Each node has conditional probability table (CPT)
Reduces number of parameters needed in model
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Machine Learning, Utility, Probability theory, Bayesian network

Click to edit the document details