This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 openbook and opennotes. 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 uniformcost 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 uniformcost search for the same problem. [True/False] Answer: True . For A* search, f ( n ) = g ( n ) + h ( n ) . For uniformcost 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 uniformcost search). We assigned partial credit on this question. ii. [2 points] A* search with an inadmissible heuristic never expands more nodes than a uniformcost 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...
View Full
Document
 Winter '09
 KOLLER,NG
 Artificial Intelligence

Click to edit the document details