Questions and Answers of Artificial Intelligence Modern

1 In Figure 24(b), we encountered an augmented finite state machine for the control of a single leg of a hexapod robot. In this exercise, the aim is to design an AFSM that, when combined with six
1 Consider a mobile robot moving on a horizontal surface. Suppose that the robot can execute two kinds of motions:• Rolling forward a specified distance.• Rotating in place through a specified
1 This exercise explores the relationship between workspace and configuration space using the examples shown in Figure 32.a. Consider the robot configurations shown in Figure 32(a) through (c),
1 Implement an algorithm for calculating the Voronoi diagram of an arbitrary 2D environment described by an n×n Boolean array. Illustrate your algorithm by plotting the Voronoi diagram for 10
1 Consider the robot arm shown in Figure 14. Assume that the robot’s base element is 60cm long and that its upper arm and forearm are each 40cm long. As argued in section 4.1, the inverse
4 Suppose that you are working with the robot in Exercise 3 and you are given the problem of finding a path from the starting configuration of figure 31 to the ending configuration.Consider a
1 Implement Monte Carlo localization for a simulated robot with range sensors. A grid map and range data are available from the code repository at aima.cs.berkeley.edu.You should demonstrate
1 Monte Carlo localization is biased for any finite sample size—i.e., the expected value of the location computed by the algorithm differs from the true expected value—because of the way particle
Edges in an image can correspond to a variety of events in a scene. Consider figure 4 and assume that it is a picture of a real three-dimensional scene. Identify ten different brightness edges in the
1 We forgot to mention that the text in Exercise 1 is entitled “Washing Clothes.” Reread Reread the text and answer the questions in Exercise 14. Did you do better this time? Bransford and
1 Calculate the most probable path through the HMM in Figure 16 for the output sequence [C1,C2,C3,C4,C4,C6,C7]. Also give its probability.
1 (Adapted from Knight (1999).) Our translation model assumes that, after the phrase translation model selects phrases and the distortion model permutes them, the language model can unscramble the
1 The D values for the sentence in Figure 13 sum to 0. Will that be true of every translation pair? Prove it or give a counterexample.
1 Consider the following sentence (from The New York Times, July 28, 2008):Banks struggling to recover from multibillion-dollar loans on real estate are curtailing loans to American businesses,
1 Augment the E grammar so that it handles article–noun agreement. That is, make sure that “agents” and “an agent” are NPs, but “agent” and “an agents” are not.
1 An augmented context-free grammar can represent languages that a regular context-free grammar cannot. Show an augmented context-free grammar for the language anbncn.The allowable values for
1 Consider the following PCFG:The sentence “I can fish” has two parse trees with this grammar. Show the two trees, their prior probabilities, and their conditional probabilities, given the
1 Using DCG notation, write a grammar for a language that is just like E , except that it enforces agreement between the subject and verb of a sentence and thus does not generate ungrammatical
1 In this exercise you will transform E into Chomsky Normal Form (CNF). There are five steps: (a) Add a new start symbol, (b) Eliminate ǫ rules, (c) Eliminate multiple words on right-hand sides, (d)
1 Consider the sentence “Someone walked slowly to the supermarket” and a lexicon consisting of the following words:For each of the preceding three grammars, write down three sentences of English
1 Consider the following PCFG for simple verb phrases: 0.1: VP Verb 0.2: VP Copula Adjective -> 0.5: VP Verb the Noun 0.2: VP VP Adverb 0.5 Verb is 0.5 Verb shoots -> 0.8: Copula is 0.2 Copula
1 Extend the standard game-playing environment from the chapter, “Adversarial Search” to incorporate a reward signal. Put two reinforcement learning agents into the environment(they may, of
1 Devise suitable features for reinforcement learning in stochastic grid worlds (generalizations of the 4×3 world) that contain multiple obstacles and multiple terminal states with rewards of +1 or
1 Implement an exploring reinforcement learning agent that uses direct utility estimtion. Make two versions—one with a tabular representation and one using the function approximator in Equation
1 Write out the parameter update equations for TD learning with (x,y) =00+01x02y+03(x-xg)2 + (y - yg)2.
1 A proper policy for is MDP is one that is guaranteed to reach a terminal state. Show that it is possible for a passive ADP agent to learn a transition model for which its policy is improper even if
1 Consider the problem of trying to evaluate the quality of an IR system that returns a ranked list of answers (like most Web search engines). The appropriate measure of quality depends on the
1 Try to ascertain which of the search engines from the previous exercise are using case folding, stemming, synonyms, and spelling correction.
1 Create a test set of ten queries, and pose them to three major Web search engines. Evaluate each one for precision at 1, 3, and 10 documents. Can you explain the differences between engines?
1 (Adapted from Jurafsky and Martin (2000).) In this exercise you will develop a classifier for authorship: given a text, the classifier predicts which of two candidate authors wrote the text. Obtain
1 Write a program to do segmentation of words without spaces. Given a string, such as the URL “thelongestlistofthelongeststuffatthelongestdomainnameatlonglast.com,” return a list of component
Consider the application of EM to learn the parameters for the network in Figure 13(a), given the true parameters in Equation (7). a. Explain why the EM algorithm would not work if there were just
Consider a single Boolean random variable Y (the “classification”). Let the prior probability P(Y =true) be π. Let’s try to find π, given a training set D=(y1, . . . , yN) with N independent
1 This exercise investigates properties of the Beta distribution defined in Equation (6). a. By integrating over the range [0, 1], show that the normalization constant for the dis- tribution beta[a,
1 Consider the noisy-OR model for fever described in Section 3 of the chapter “Probabilistic Reasoning”. Explain how to apply maximum-likelihood learning to fit the parameters of such a model to
1 Consider N data points (x , y ), where the y s are generated from the x s according to the linear Gaussian model in Equation (5). Find the values of θ , θ , and σ that maximize the conditional
1 Explain how to apply the boosting method of the chapter “Learning from Examples” to naive Bayes learning. Test the performance of the resulting algorithm on the restaurant learning problem.
1 Suppose that Ann’s utilities for cherry and lime candies are CA and ℓA, whereas Bob’s utilities are cB and ℓB. (But once Ann has unwrapped a piece of candy, Bob won’t buy it.) Presumably,
1 The data used for Figure 1 can be viewed as being generated by h5. For each of the other four hypotheses, generate a data set of length 100 and plot the corresponding graphs for P(hi | d1, . . . ,
1 Using the data from the family tree in Figure 11, or a subset thereof, apply the FOIL algorithm to learn a definition for the Ancestor predicate.
1 Fill in the missing values for the clauses C1 or C2 (or both) in the following sets of clauses, given that C is the resolvent of C1 and C2:If there is more than one possible solution, provide one
1 For each of the following determinations, write down the logical representation and explain why the determination is true (if it is):a. Design and denomination determine the mass of a coin.b. For a
1 Show, by translating into conjunctive normal form and applying resolution, that the conclusion drawn in section 4 concerning Brazilians is sound.
1 Consider the problem of separating N data points into positive and negative examples using a linear separator. Clearly, this can always be done for N =2 points on a line of dimension d=1,
1 The neural network whose learning performance is measured in Figure 25 has four hidden nodes. This number was chosen somewhat arbitrarily. Use a cross-validation method to find the best number of
1 Suppose you had a neural network with linear activation functions. That is, for each unit the output is some constant c times the weighted sum of the inputs.a. Assume that the network has one
1 Section 6.4 noted that the output of the logistic function could be interpreted as a probability p assigned by the model to the proposition that f (x)=1; the probability that f(x)=0 is therefore 1
1 Recall that there are 2 distinct Boolean functions of n inputs. How many of these are representable by a threshold perceptron?
1 Consider an ensemble learning algorithm that uses simple majority voting among K learned hypotheses. Suppose that each hypothesis has error and that the errors made by each hypothesis are
1 Construct a support vector machine that computes the XOR function. Use values of +1 and –1 (instead of 1 and 0) for both inputs and outputs, so that an example looks like([−1, 1], 1) or
1 Figure 31 showed how a circle at the origin can be linearly separated by mapping from the features (21, 22) to the two dimensions (2, 3). But what if the circle is not located at the origin? What
1 This exercise concerns the expressiveness of decision lists (Section 5).a. Show that decision lists can represent any Boolean function, if the size of the tests is not limited.b. Show that if the
1 Suppose you are running a learning experiment on a new algorithm for Boolean classification. You have a data set consisting of 100 positive and 100 negative examples. You plan to use leave-one-out
1 In Section 3.6, we noted that attributes with many different possible values can cause problems with the gain measure. Such attributes tend to split the examples into numerous small classes or even
1 This exercise considers χ2 pruning of decision trees (Section 3.5).a. Create a data set with two input attributes, such that the information gain at the root of the tree for both attributes is
1 A decision graph is a generalization of a decision tree that allows nodes (i.e., attributes used for splits) to have multiple parents, rather than just a single parent. The resulting graph must
1 In the recursive construction of decision trees, it sometimes happens that a mixed set of positive and negative examples remains at a leaf node, even after all the attributes have been used.
1 Repeat Exercise 1 for the case of learning to play tennis (or some other sport with which you are familiar). Is this supervised learning or reinforcement learning?
1 Consider the problem faced by an infant learning to speak and understand a language. Explain how this process fits into the general learning model. Describe the percepts and actions of the infant,
1 Teams in the National Hockey League historically received 2 points for winning a game and 0 for losing. If the game is tied, an overtime period is played; if nobody wins in overtime, the game is a
1 Imagine an auction mechanism that is just like an ascending-bid auction, except that at the end, the winning bidder, the one who bid bmax, pays only bmax/2 rather than bmax.Assuming all agents are
1 A Dutch auction is similar in an English auction, but rather than starting the bidding at a low price and increasing, in a Dutch auction the seller starts at a high price and gradually lowers the
1 The following payoff matrix, from Blinder (1983) by way of Bernstein (1996), shows a game between politicians and the Federal Reserve.Politicians can expand or contract fiscal policy, while the Fed
1 Consider a version of the two-state POMDP in section 4.2 in which the sensor is 90% reliable in state 0 but provides no information in state 1 (that is, it reports 0 or 1 with equal probability).
1 Let the initial belief state b0 for the 4 × 3 POMDP in section 4 be the uniform dis- tribution over the nonterminal states, i.e., (1, 1 1 1 1 1 1 1 0, 0). Calculate the exact belief state b after
1 Consider the 101 × 3 world shown in Figure 14(b). In the start state the agent has a choice of two deterministic actions, Up or Down, but in the other states the agent has one deterministic
1 Consider the 3 × 3 world shown in Figure 14(a). The transition model is the same as in the 4×3 Figure 1: 80% of the time the agent goes in the direction it selects; the rest of the time it moves
1 This exercise considers two-player MDPs that correspond to zero-sum, turn-taking games. Let the players be A and B, and let R(s) be the reward for player A in state s. (The reward for B is always
1 Equation (7) states that the Bellman operator is a contraction. a. Show that, for any functions f and g, max f(a) - max g(a)| max|f(a) - g(a)|. a a a b. Write out an expression for (BU - BU)(s)
1 Select a specific member of the set of policies that are optimal for R(s) > 0 as shown in Figure 2(b), and calculate the fraction of time the agent spends in each state, in the limit, if the policy
1 For the 4× 3 world shown in Figure 1, calculate which squares can be reached from (1,1) by the action sequence [Up,Up,Right ,Right ,Right ] and with what probabilities.
1 Recall the definition of value of information in Section 6. a. Prove that the value of information is nonnegative and order independent. b. Explain why it is that some people would prefer not to
1 This exercise completes the analysis of the airport-siting problem in Figure 6.a. Provide reasonable variable domains, probabilities, and utilities for the network, assuming that there are three
1 Consider a student who has the choice to buy or not buy a textbook for a course. We’ll model this as a decision problem with one Boolean decision node, B, indicating whether the agent chooses to
1 For either of the airport-siting diagrams from Exercises 16 and 13, to which conditional probability table entry is the utility most sensitive, given the available evidence?
1 Repeat Exercise 16, using the action-utility representation shown in Figure 7.
1 Tickets to a lottery cost $1. There are two possible prizes: a $10 payoff with probability 1/50, and a $1,000,000 payoff with probability 1/2,000,000. What is the expected monetary value of a
1 Consider the Allais paradox: an agent who prefers over (taking the sure thing), and C over (taking the higher EMV) is not acting rationally, according to utility theory. Do you think this indicates
1 Write a computer program to automate the process in Exercise 9. Try your program out on several people of different net worth and political outlook. Comment on the consistency of your results, both
1 Chris considers four used cars before buying the one with maximum expected utility. Pat considers ten cars and does the same. All other things being equal, which one is more likely to have the
1 Consider applying the variable elimination algorithm to the umbrella DBN unrolled for three slices, where the query is P(R3|u1, u2, u3). Show that the space complexity of the algorithm—the size
1 This exercise analyzes in more detail the persistent-failure model for the battery sensor in Figure 15(a). a. Figure 15(b) stops at t=32. Describe qualitatively what should happen as if the sensor
1 Suppose that a particular student shows up with red eyes and sleeps in class every day. Given the model described in Exercise 13, explain why the probability that the student had enough sleep the
1 For the DBN specified in Exercise 13 and for the evidence values e1 = not red eyes, not sleeping in class e2 = red eyes, not sleeping in class e3 = red eyes, sleeping in class perform the following
1 Let us examine the behavior of the variance update in Equation (20). oo, and calculate a. Plot the value of off as a function of t, given various values for and . b. Show that the update has a
1 Complete the missing step in the derivation of Equation (19), the first update step for the one-dimensional Kalman filter.
1 Often, we wish to monitor a continuous-state system whose behavior switches unpredictably among a set of k distinct “modes.” For example, an aircraft trying to evade a missile can execute a
1 Consider the vacuum world of Figure 7 (noisy sensing). Suppose that the robot receives an observation sequence such that, with perfect sensing, there is exactly one possible location it could be
1 Equation (12) describes the filtering process for the matrix formulation of HMMs. Give a similar equation for the calculation of likelihoods, which was described generically in Equation (7).
1 In ection 2.3, we outlined a flawed procedure for finding the most likely state sequence, given an observation sequence. The procedure involves finding the most likely state at each time step,
1 This exercise develops a space-efficient variant of the forward–backward algorithm described in Figure 4. We wish to compute P(X e1t) for k = 1,..., t. This will be done with a
1 Show that any second-order Markov process can be rewritten as a first-order Markov process with an augmented set of state variables. Can this always be done parsimoniously, i.e., without increasing
1 Three soccer teams A, B, and C, play each other once. Each match is between two teams, and can be won, drawn, or lost. Each team has a fixed, unknown degree of quality—an integer ranging from 0
1 The Metropolis–Hastings algorithm is a member of the family; as such, it is designed to generate samples x (eventually) according to target probabilities (x). (Typically we are interested in
1 Consider the query P(Rain | Sprinkler = true,WetGrass = true) in Figure 12(a) and how Gibbs sampling can answer it.a. How many states does the Markov chain have?b. Calculate the transition matrix Q
1 Consider the problem of generating a random sample from a specified distribution on a single variable. Assume you have a random number generator that returns a random number uniformly distributed
1 Consider the variable elimination algorithm in Figure 11. a. Section 4 applies variable elimination to the query P(Burglary John Calls = true, MaryCalls = true). Perform the calculations indicated
1 Consider the Bayes net shown in Figure 23.a. Which of the following are asserted by the network structure?(i) P(B, I,M) = P(B)P(I)P(M).(ii) P(J |G) = P(J |G, I).(iii) P(M |G,B, I) = P(M |G,B, I,
1 Consider the network shown in Figure 22(ii), and assume that the two telescopes work identically. N ∈ {1, 2, 3} and M1,M2 ∈{0, 1, 2, 3, 4}, with the symbolic CPTs as de scribed in Exercise 12.
1 The probit distribution defined in section 3 describes the probability distribution for a Boolean child, given a single continuous parent.a. How might the definition be extended to cover multiple

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