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The concepts of joint probability distribution and conditional independence through the example of weather conditions and the presence or absence of fun. the difference between probability distributions and probabilities, the concept of discrete random variables, and the idea of conditional probability. It also covers the concept of conditional independence and its implications, using the example of weather given the presence or absence of fun. The document also touches upon the topic of estimating parameters from data and the use of Bayesian networks for modeling complex systems.
What you will learn
Typology: Study notes
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Sunny Cloudy Rainy Snowy
Distribution vs. Probability
2
2
2
3
2
3
0
Sunny Cloudy Rainy Snowy
Weather given Fun=Yes
5
Sunny Cloudy Rainy Snowy
“A is conditionally independent of B given C”
More Conditional Independence
If A and B are conditionally independent given C
C can still depend on both A and B
P(C|A) P(C) and P(C|B) P(C)
A and B are not necessarily independent:
P(B|A) P(B) and P(A|B) P(A)
But, Given C,
A and B do not influence each other
Knowledge of C separates A and B
Suppose we do NOT know C,
then A and B MAY influence each other
(think about this one until it’s intuitive
Suppose that Symptoms are Conditionally
Independent given the Disease
are more likely but not necessary
headache?
3 Boolean Random Variables:
C – Patient has a cavity
A – Patient reports a
toothache
B – Dentist’s probe catches
on tooth
C directly influences A and B
A and B are conditionally independent given C
CPT at each node specifies a probability distribution for each context
(configuration of parents)
How many numbers do we need for the full joint?
How many for the Bayesian net?
Joint:
3
Bayes Net:
Distribution(s) at C
P(cavity), P(cavity)
Need one number
Distribution(s) at A
P(ache|cavity), P(ache|cavity)
P(ache| cavity), P(ache| cavity)
Distributions at B, like A
1 + 2 + 2 = 5 (a savings of 2!)
5
or c 2
1