Description
1. For three random variables A, B and C, show with a counterexample that the statement “A
is independent of B” does not imply the statement “A is independent of B given C.”
(9/11)
2. Points are sampled uniformly at random from the interval (0,1)2 so that they lie on the
line x+y=1. Determine the expected squared distance between any two sampled points.
(9/11)
3. Describe two learning tasks that might be suitable for machine learning approaches. For
each task, write down the goal, a possible performance measure, what examples you
might get and what a suitable hypothesis space might be. What learning setting
(supervised, unsupervised, etc.) seems most appropriate for each task? What example
representation seems most appropriate? Be original—don’t write about tasks discussed in
class or described in the texts. Preferably select tasks from your research area. Describe
any aspect of the task(s) that may not fit well with the learning settings and
representations we have discussed. (9/11)
4. Explain in your own words: (i) why memorization should not be considered a valid
learning approach, (ii) why tabula rasa learning is impossible, and (iii) why picking a
good example representation is important for learning. Try to use good, intuitive
examples from human learning to motivate your arguments. (9/11)
