Topics

• Genetic Algorithms
• Bitstring Fitness
• Crossover
• Mutation
• Selecting Parents for Crossover: Roulette Selection vs Tournament Selection
• Eliteism
• First-Order Logic
• Converting sentences into first order logic
• Removing Quantifiers / Converting to CNF
• Resolution and Unification
• Probability
  • Bayes Rule
  • Conditional Independence
  • Naive Bayes
• Decision Trees
• Using Decision Trees to classify an instance
• Building decision trees from data
• Utility Theory
• Expected Utility of an action
• Maximizing Expected Utility
• Value of Information

Potential Questions

1. First-Order Logic
   1. Write the following sentences in First-Order Logic:
      1. All men are mortal
      2. Socrartes is a man
      3. Any mortal who drinks Hemlock will die
      4. Every man loves a woman
      5. There is a man who loves all women
      6. There is a woman whom every man loves
      7. Every woman loves every man who loves her
      8. If a man is loved, he will drink Hemlock
      using the predicates: Man(x), Mortal(x), Drinks(x,y), Die(X), Loves(x,y), Woman(x,y)
   2. Rewrite all of the above statements in CNF (without quantifiers)
   3. Use resolution by refutation (and unification!) to prove Die(Socrates)
2. Joe Student comes to his professor and tells him that he forgot to bring his project to hand in, and wants to turn it in tomorrow without penalty. The professor knows that 1 time in 100, a student completes her assignment and forgets to bring it. The professor also knows that 50% of the time, a student who hasn't completed the assignment will say that they forgot it. Finally, the professor believes that 90% of the students in the class completed the assignment. What is the probability that the student completed the homework?
3. You are playng a simplified blackjack-style game. Your opponent is assigned a random number between 1 and 10 (each number being equally likely). You are not allowed to see your opponents number. You are then given a random number between 1 and 10 (each number being equally likely). After seeing your number, you are allowed to receive a second random number between 1 and 10. If the sum of your two numbers is less than your opponent's number, you lose $10. If the sum of your two numbers is the same as your opponent's number, you lose nothing. If the sum of your two numbers is greater than your opponent's number, and less than or equal to 10, then you win $10. Finally, if the sum of your two numbers is greater than 10, you lose $10.
   1. If you draw a 3, what is the expected utility if you do not get another number? If you do get another number?
   2. If you draw a 5, what is the expected utility if you do not get another number? If you do get another number?
   3. If you draw a 10, what is the expected utility if you do not get another number? If you do get another number?
   4. What is the maximum expected utility for this game?
   5. You draw a 5. What would you be willing to pay to see your opponent's number before deciding to draw another number?
   6. Before you get your number (but after your opponent gets his number), What would you be willing to pay to see your opponent's number before playing?