61.182 Informaatiotekn. ek II, spring 1997
Exercise problems
(Ch. 4, Ripley)
9. Here is a part of the "medical diagnosis" graph of Ripley, p. 270, and all the related probabilities. Using just the Bayes rule, what would be the probability of a) heart disease, b) breathlessness for a person, who does not smoke, but who has a family history of heart disease.
Figure 1: The DAG for an artificial medical diagnosis system.
| Pr{A}=0.5 | Pr{B} = 0.2 | Pr{C}=0.3 | |
| Pr{D | F,F}=0.05 | Pr{D | F,T}=0.3 | Pr{D | T,F }=0.2 | Pr{D | T,T} = 0.5 |
| Pr{E | F}=0.3 | Pr{E | T} = 0.5 | ||
| Pr{F | F} = 0.1 | Pr{F | T}=0.4 | ||
| Pr{G | F,F}=0.01 | Pr{G | F,T}=0.5 | Pr{G | D=T}=1 |
(Ch. 9, Ripley)
10. Jones and Sibson introduced a Projection Pursuit index based on moments:
where
are the skewness and the kurtosis of the projection 
. Here x
is the multidimensional zero-mean data vector, a is the projection direction,
and 
is expectation.
You wish to find the direction a that will maximize this index. Device a suitable algorithm.