Download Bayesian Networks for Data Mining

Bayesian Networks for Data
Mining
David Heckerman
Microsoft Research
(Data Mining and Knowledge Discovery 1, 79-119 (1997))
The Bayesian approach
#1 Question
What is Bayesian probability?
• A person’s degree of belief in certain event.
• Personal (subjective)
• Your degree of belief that the coin will land
heads.
The Classical approach
• Physical property of the world.
• Repeated trials (frequency)
• The probability that a coin will land heads.
#2 Question
What are the advantages and disadvantages of the Bayesian
and classical interpretation of probability?
Bayesian probability:
+ Reflects an expert’s knowledge.
+ Compiles with rules of probability
- Arbitrary
Classical probability:
+ Objective, unbiased.
- Not available in most situations.
Bayes Theorem
Posterior = (likelihood X prior) / evidence
p ( D | h)  p ( h)
p ( h | D) 
p ( D)
Bayesian Networks
• Graphical model that encodes the joint
probability distribution (JPD) for a set of
variables X.
• It is a directed acyclic (not cyclic) graph.
• Each node represents one variable and
contains a set local probability distributions
(LPD) associated with each variable.
Bayesian Networks
•
Nodes
–
–
•
•
Parents
Children
Conditional probability tables
Construction
Inference
The computation of a probability of interest
given a model is known as
probabilistic inference
P(X|e)=P(x,e)/P(e) = cP(X,e)
Example on board.
Learning
• Learning from data
– Refine the structure and LPD of a BN
– Combine prior knowledge with data
• Result: IMPROVED KNOWLEDGE
Question #3
Mention at least 3 advantages of Bayesian
Networks for data analysis. Explain each one.
• Handle incomplete data sets
• Learning about causal relationships
• Combine domain knowledge + data
• Avoid over fitting.