04-practice-final-solutions-sp06 - NAME SID Login Sec 1 CS...

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NAME: SID#: Login: Sec: 1 CS 188 Introduction to Spring 2006 Artifcial Intelligence Practice Final Sol’ns 1. (20 points.) True/False Each problem is worth 2 points. Incorrect answers are worth 0 points. Skipped questions are worth 1 point. (a) True/False : All MDPs can be solved using expectimax search. False. MDPs with self loops lead to inFnite expectimax trees. Unlike search problems, this issue cannot be addressed with a graph-search variant. (b) True/False : There is some single Bayes’ net structure over three variables which can represent any prob- ability distribution over those variables. True. A fully connected Bayes’ net can represent any joint distribution. (c) True/False : Any rational agent’s preferences over outcomes can be summarized by a single real valued utility function over those outcomes. True. Any set of preferences which conform to the six constraints on rational preferences (orderability, transitivity, continuity, substitutability, monotonicity, decomposability) can be summarized by a single, real-valued function. (d) True/False : Temporal di±erence learning of optimal utility values (U) requires knowledge of the transition probability tables (T). Mostly True. Temporal di±erence learning is a model-less learning technique that requires only example state sequences to learn the utilities for a Fxed policy. However, to derive the best policy from those utilities, which would be required to Fnd the optimal utility values, we would need to compute π ( s ) = arg max a ± s ± T ( s,a,s ± ) U ( s ± ) which of course includes a transition probability. The solution reads “mostly” true because the optimal utility values could be found without the transition probabilities if the agent were also supplied with the optimal policy. In practice, we could also estimate the transition probabilities from the training data (using maximum-likelihood estimates, for example), so they need not necessarily be known in advance. NOTE: This solution was updated since the review session. (e) True/False : Pruning nodes from a decision tree may have no e±ect on the resulting classiFer. True. Trivially, a decision tree may have branches that are unreachable. ²urthermore, splits in the decision tree may also reFne P ( class ), but have no e±ect in practice because of rounding. Imagine a leaf has 10 true, 3 false, and splits to 5/2 and 5/1 – you’ll still guess true on each branch, but the split is reFning the conditional probabilities. NOTE: This solution was updated since the review session.
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2 2. (20 points.) Search Consider the following search problem formulation: States : 16 integer coordinates, ( x,y ) [1 , 4] × [1 , 4] Initial state : (1 , 1) Successor function : The successor function generates 2 states with diFerent y -coordinates Goal test : (4 , 4) is the only goal state Step cost : The cost of going from one state to another is the Euclidean distance between the points We can specify a state space by drawing a graph with directed edges from each state to its successors: 1 2 3 4 1 2 3 4 x y Uninformed Search Consider the performance of D±S, B±S, and UCS on the state space above. Order
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04-practice-final-solutions-sp06 - NAME SID Login Sec 1 CS...

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