bayesian networks for data mining david heckerman microsoft research (data mining and knowledge...
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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 QuestionWhat 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
)(
)()|()|(
Dp
hphDpDhp
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 #3Mention 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.