Problem 1 – First-Order Predicate Calculus (15 points)
- 1. University of Wisconsin – Madison Computer Sciences Department CS 760 - Machine Learning Fall 2001 Exam 7:15-9:15pm, December 13, 2001 Room 1240 CS & Stats CLOSED BOOK (one sheet of notes and a calculator allowed) Write your answers on these pages and show your work. If you feel that a question is not fully specified, state any assumptions you need to make in order to solve the problem. You may use the backs of these sheets for scratch work. Write your name on this and all other pages of this exam. Make sure your exam contains 6 problems on 10 pages. Name ________________________________________________________________ Student ID ________________________________________________________________ Problem Score Max Score 1 ______ 24 2 ______ 15 3 ______ 16 4 ______ 14 5 ______ 7 6 ______ 24 TOTAL ______ 100
- 2. Name: _______________________________________ Problem 1 – Learning from Labelled Examples (24 points) Imagine that you are given the following set of training examples. Each feature can take on one of three nominal values: a, b, or c. F1 F2 F3 Category a c a + c a c + a a c – b c a – c c b – a) How would a Naive Bayes system classify the following test example? Be sure to show your work. F1 = a F2 = c F3 = b b) Describe how a 3-nearest-neighbor algorithm would classify Part a’s test example. Page 2 of 10
- 3. Name: _______________________________________ c) Show the calculations that ID3 would perform to determine the root node of a decision tree using the above training examples. d) Now consider augmenting the standard ID3 algorithm so that it also considers tests like the value of feature X = the value of feature Y for all pairs of features X and Y where X ≠ Y. Show what this variant of ID3 would choose as a root node for the training set above. Page 3 of 10
- 4. Name: _______________________________________ Problem 2 – Weight Space and Neural Networks (15 points) Assume that you wish to train a perceptron on the simple training set below. F1 Category 1 + 8 + 2 – 4 – a) Draw the weight space for this task, assuming that the perceptron’s threshold is always set at 4. Also assume that the perceptron’s output is 1 (i.e., category = +) when the perceptron’s weighted sum meets or exceeds its threshold; otherwise its output is 0. (Since the threshold is constant, you need not draw its dimension in weight space. Also, do not normalize the values of F1) b) Assuming that we initially set the weight on the link between F1 and the output node to the value 5, state the range of final weight settings that could result from applying backpropagation training. Be sure to explain your answer. (Do not train the threshold in this part; hold it constant at the value of 4. Assume that the step function of Part a is replaced with a very steep sigmoidal activation function, so that the activation function is technically differentiable.) c) Starting from the initial state of Part b and using a learning rate of 0.1, draw the perceptron before and after training with (just) the last example in the training set above. For this part, you do need to train the threshold. Page 4 of 10
- 5. Name: _______________________________________ Problem 3 – Overfitting Avoidance (16 points) For each of the following learning methods, briefly describe and motivate one (1) commonly used technique for overfitting avoidance. a) Nearest-neighbor learning Brief Description (of an overfitting-avoidance technique): Motivation (of why it might reduce overfitting): b) Naïve Bayesian learning Brief Description: Motivation: c) Decision-tree induction Brief Description: Motivation: d) Neural network training Brief Description: Motivation: Page 5 of 10
- 6. Name: _______________________________________ Problem 4 – Reinforcement Learning (14 points) Consider the deterministic reinforcement environment drawn below. The numbers on the arcs indicate the immediate rewards. Let the discount rate equal 0.9. 10 5 star a b t -10 -10 -10 c 5 end 0 a) What is the best route for going from start to end? Why? b) Represent the Q table by placing Q values on the arcs on the environment's state-action graph; initialize all of the Q values to 2 except initialize all of the arcs directly involving node a to have a Q value of -1. For Step 1, do exploitation. Show on the graph below the full Q table after Step 1. Specify the action chosen and display the calculations involved in altering the Q table. star a b t c end Page 6 of 10
- 7. Name: _______________________________________ c) Assume that after Step 1, the RL agent is magically transported back to the state start. Show the resulting Q table after the learner takes its second step from the starting state. Step 2 should be exploration. Be sure to again state the action chosen and display your calculations. star a b t c end d) Explain one (1) major advantage and one (1) major disadvantage of using a Q network instead of a Q table in reinforcement learning. advantage: disadvantage: Page 7 of 10
- 8. Name: _______________________________________ Problem 5 – Inductive Logic Programming (7 points) Assume that we tell FOIL that P(a) and P(b) are positive instances of P(?X) and that P(c) and P(d) are negative instances (where ?X is a variable, while a, b, c, and d are constants). We also give the following background knowledge to FOIL: Q(a) ¬Q(b) Q(c) ¬Q(d) R(a) ¬R(b) R(c) R(d) (where “¬” means “not”). Show the calculations that FOIL would go through in order to choose its first rule for P(?X). Page 8 of 10
- 9. Name: _______________________________________ Problem 6 – Short Discussion Questions (24 points) a) Why might it make sense to learn a "world model" when learning from reinforcements? b) What is the major advantage that FOIL has over ID3? Explain your answer. c) Would you expect ensemble methods to work better for decision-tree induction or for Naïve Bayes classifiers? Why? d) Assume that we want to empirically compare the accuracies of two learning algorithms on a given dataset,what experimental methodology should we use? Page 9 of 10
- 10. Name: _______________________________________ e) Assuming one has linearly separable data,what is the key difference between standard perceptron training and Support Vector Machines? f) Briefly explain one (1) connection between the Minimal Description Length principle and Support Vector Machines. g) What role does the VC Dimension play in machine learning? h) Why does one need both tuning and testing sets in machine learning? Have a good vacation! Page 10 of 10