Nov 6, 2006
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- Probabilistic learning paradigms
	- use probability to reason about multiple hypotheses

- Where do probabilities come from?
	- frequentist view
	- Bayesian view

- How to use probabilities
	- begin with a prior
	- look at data, and update
	- prior into a posterior

- Finding which hypothesis is most likely
	- calculate P(H|D) = P(D|H) * P(H) / P(D)
		- for each H
	- find out which has highest posterior

- Back to PlayTennis handout
	- Hypotheses are
		- PlayTennis = Yes
		- PlayTennis = No
	
- What if we have an example that doesn't appear in the given dataset?
	- how do we compute P(D|H) and P(D)

- "Naive" Bayes assumption
	- independent probabilities for each attribute of D

- More complex assumptions
	- can be encoded by Bayesian networks

- Bayesian network
	- directed acyclic graph of random variables

- What does a Bayesian network mean?
	- a way to decompose joint probabilities

- Bayesian networks of two variables
	- only two possibilities
		- independent case
		- dependent case

- Bayesian networks of three variables
	- many more possibilities
		- fully independent
		- fully dependent
		- in-between cases

- Examples of networks that mean the same thing
	- but which look different