COMP-424A Introduction to Artificial Intelligence, Lecture notes of Artificial Intelligence

Download COMP-424A Introduction to Artificial Intelligence and more Lecture notes Artificial Intelligence in PDF only on Docsity! STUDENT NAME: STUDENT ID: McGill University Faculty of Science School of Computer Science Final exam COMP-424A Introduction to Artificial Intelligence April 19, 2010 9:00-12:00 Examiner: Prof. Doina Precup Associate Examiner: Prof. Prakash Panangaden This examination is closed-book, closed-notes. There are 16 pages, including the title page. Start by writing down your name. Answer the questions directly on the exam booklet. Additional pages are provided if necessary. Do not forget to write your name on the additional pages too. Read the whole exam before starting to work on it. There are 10 questions, all of which require written answers. Values for each question are shown in brackets. Partial credit will be given for incomplete or partially correct answers. Good luck! COMP-424: Artificial Intelligence I Page 2 of 16 1. [10 points] Search algorithms (a) [5 points] Suppose you have an admissible heuristic h. For what numbers a is a ∗ h admissible? If you do not know anything about h, are there any values of a for which using a ∗ h in an A∗ algorithm would be better than using h? Justify your answers COMP-424: Artificial Intelligence I Page 5 of 16 3. [15 points] Logic (a) [10 points] Translate the following sentences in first-order logic. Make sure that you use the predicates that you define consistently among the different statements. i. [2 points] All robots are smart. ii. [2 points] Some robots are smart. iii. [1 point] Robbie is a robot. iv. [2 point] All robots are nice to their owner v. [1 point] Bob is Robbie’s owner vi. [2 points] Some people who own robots are smart. COMP-424: Artificial Intelligence I Page 6 of 16 (b) [3 points] Prove formally that Robbie is nice to Bob (c) [2 point] Given this knowledge base, can you prove that Bob is smart? If you answer is yes, show the proof. If your answer is no, explain why not. COMP-424: Artificial Intelligence I Page 7 of 16 4. [20 points] Neural networks and decision trees Suppose that you have been hired by a large on-line company to build a predictor of whether customers will buy their products, based on customer attributes. They already have 5 predictors that they built and would like you to make use of them in a smart way, in order to get better accuracy than these predictors. (a) [5 points] The first thing that comes to mind is that you want to take a majority vote among the existing predictors. Can you implement this function using a perceptron? If so, show the perceptron. If no, explain why not. (b) [5 points] Suppose that instead of 5 predictors they have some arbitrary number n. Explain what changes you need to make to your previous answer to obtain a majority vote in this case. COMP-424: Artificial Intelligence I Page 10 of 16 6. [5 points] Overfitting Suppose that we have a data set in which there are n binary attributes and the desired output is also binary. The examples that you see come from a random function and are perfect (the training data has the correct label). You have a “learning algorithm” that simply memorizes the training data. When asked for the output for a new instance, the algorithm will look up the instance and if it is in memory, it answers with the recorded label. Otherwise, it will answer randomly. (a) [1 point] What is the training error of this algorithm? (b) [2 points] Suppose the algorithm has seen k distinct training examples. It is tested on a new example drawn randomly from the entire space of possible instances. What is the expected error on this test instance? What happens to the error as k increases? (c) [1 points] Suppose that after seeing k training examples, the algorithm is tested on an instance which has not been part of the training data. What is the testing error as a function of k? (d) [1 point] Explain if the cross-validation algorithm would evaluate the error of this learner correctly or not. COMP-424: Artificial Intelligence I Page 11 of 16 7. [4 points] Probabilities Suppose you have two independent binary random variables A and B, and you know that P (A = 1) = 0.1 and P (B = 1) = 0.5. (a) [3 points] What is the probability that at least one of the variables would be 1? (b) [3 points] What is the probability that exactly one of the variables would be 1? COMP-424: Artificial Intelligence I Page 12 of 16 8. [15 points] Bayes nets Students in the AI class like to relax after their final exams by watching movies. How much they like a movie depends on how happy they are and what kind of movie it is. If they are happy, they like any movie with probability 0.8. If they are not happy, they still like sci-fi movies with probability 0.8, but they like non-sci-fi movies only with probability 0.5. They have a 0.6 chance to be happy on any given night. The movie theatre has a 0.5 chance of showing a sci-fi movie on any night. (a) [5 points] Draw a Bayes net describing the problem statement above. Specify both the graph structure and all the parameters. (b) [3 points] Compute the probability that the students will like the movie they see on any given night. Please show the formula you are using, then substitute the adequate parame- ters and show the resulting number. COMP-424: Artificial Intelligence I Page 15 of 16 (d) [3 points] Suppose that your robot has performed a sequence of actions in which it stayed 3 times in the left room, it moved (successfully) to the right room, it stayed in the right room once, then it moved successfully to the left room. If it has been doing TD-learning with a learning rate of 0.1, what are its estimates for the values of the two rooms at this point? (e) [2 points] Suppose that you start with all values at -1 and use a policy that never explores. Will you be able to find the optimal policy? Justify your answer. COMP-424: Artificial Intelligence I Page 16 of 16 10. [5 points] Problem formulation You got a summer job at a sandwich shop downtown. The shop sells different kinds of sand- wiches, each consisting of a type of bread, a type of meat (or substitute), a type of cheese (if the customer wants some) and a type of vegetable. Each day, you have to go to the grocery store and buy supplies for the day’s sandwiches. Bread has to be discarded at the end of the day. Meat and cheese have to be discarded after a week. Vegetables are discarded after 3 days. You know that customers come in randomly. If a customer cannot have the desired sandwich, she will leave and there is a 0.5 probability that she will never come to the shop again. Of course, customers pay different amounts for different sandwiches, and you have to pay for the groceries. Having taken AI, you want to optimize, in a principled way, the amount of purchases you are making. Describe this problem using any AI technique of your choice. Explain all the components of your model. What algorithms could you use to solve this problem?