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Unformatted text preview: CS221 Midterm Solutions 1 CS 221, Autumn 2007 Practice Midterm Solutions STANFORD UNIVERSITY CS 221 Practice Midterm, Fall 2007 Question Points 1 Short Answers /32 2 Motion Planning /12 3 Search Space Formulation /16 4 A* /12 5 Supervised Learning /20 6 Reinforcement Learning /14 7 Constraint Satisfaction /14 Total /120 Name of Student: Exam policy: This exam is open-book and open-notes. Any printed material is allowed. However, the use of mobile devices is not per- mitted. This includes laptops, cellular phones and pagers. Time: 3 hours. The Stanford University Honor Code: I attest that I have not given or received aid in this examination, and that I have done my share and taken an active part in seeing to it that others as well as myself uphold the spirit and letter of the Honor Code. Signed: CS221 Midterm Solutions 2 1. Short answers [32 points] The following questions require a true/false accompanied by one sentence of explanation, or a very short answer. To discourage random guessing, one point will be deducted for a wrong answer on multiple choice (such as yes/no or true/false) questions! Also, no credit will be given for answers without a correct explanation. (a) [4 points] For this question only, assume that there are no ties in the priority queue for A* search or uniform-cost search (i.e., all f and g values are unique). i. [2 points] A* search with an admissible heuristic never expands more nodes than a uniform-cost search for the same problem. [True/False] Answer: True . For A* search, f ( n ) = g ( n ) + h ( n ) . For uniform-cost search, we know that f ( n ) = g ( n ) , which means it is in fact a special case of A* in which f ( n ) = g ( n ) + h ( n ) for h ( n ) = 0 for all n . In the case where h ( n ) is admissible, we know that h ( n ) h ( n ) for all n where h ( n ) is the true cost of the path from n to the goal. Thus, we know that h ( n ) h ( n ) h ( n ) , which means that an A* algorithm using h ( n ) will always expand the same number of or fewer nodes the one using h ( n ) (as in the case of uniform-cost search). We assigned partial credit on this question. ii. [2 points] A* search with an inadmissible heuristic never expands more nodes than a uniform-cost search for the same problem. [True/False] Answer: False . Consider a tree graph with two branches: one directly to a goal node A with g=1, but h=10000 the other branch has a long chain of nodes, each with g=2, but h=0. Then, UCS will directly go down the first branch and find the goal. A* will keep going down the second branch for a long time before expanding the first branch. We assigned partial credit on this question. (b) [3 points] Linear regression as studied in class optimizes i ( y ( i ) j j x ( i ) j ) 2 over a training set. The maximum likelihood estimate for will be unchanged if we optimize i ( y ( i ) j j x ( i ) j ) 4 instead. [True/False] Answer: False . This is a different objective function so theres no reason to believe CS221 Midterm Solutions...
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