As stated in the course syllabus, you are permitted (and encouraged!) to work on this homework assignment in groups of up to three students. If you work in a group, you only need to turn in one shared solution, with everyone's name on the assignment. All students in the group will receive the same grade on the assignment. If you choose to work in a group, you must actually produce group solutions, not have each member work independently on one part of the assignment, then submit the collection of independent solutions.
Russell & Norvig, Exercise 18.5 (page 764). Suppose that an attribute splits the set of examples E into subsets E_k and that each subset has p_k positive examples and n_k negative examples. Show that the attribute has strictly positive information gain unless the ratio p_k / (p_k + n_k) is the same for all k.
The following table gives a data set for deciding whether to play or cancel a ball game, depending on the weather conditions.
Outlook | Temp (F) | Humidity (%) | Windy? | Class |
sunny | 75 | 70 | true | Play |
sunny | 80 | 90 | true | Don't Play |
sunny | 85 | 85 | false | Don't Play |
sunny | 72 | 95 | false | Don't Play |
sunny | 69 | 70 | false | Play |
overcast | 72 | 90 | true | Play |
overcast | 83 | 78 | false | Play |
overcast | 64 | 65 | true | Play |
overcast | 81 | 75 | false | Play |
rain | 71 | 80 | true | Don't Play |
rain | 65 | 70 | true | Don't Play |
rain | 75 | 80 | false | Play |
rain | 68 | 80 | false | Play |
rain | 70 | 96 | false | Play |
(a) Russell & Norvig Exercise 7.7, page 281 (10 pts).
(b) Russell & Norvig Exercise 8.28 (c,f,h,k,l), page 320-321 (10 pts)
(b) (8 points) Convert the KB to conjunctive normal form.
(c) (2 points) We wish to prove that
study(Aidan) -> pass(Aidan, 471-exam)
Express the negation of this goal in conjunctive normal form.
(c) (12 points) Add the negated goal to the KB, and use resolution refutation
to prove that it is true. You may show your proof as a series of sentences
to be added to the KB or as a proof tree. In either case, you must
clearly show which sentences are resolved to produce each new sentence, and
what the unifier is for each resolution step.