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Lab Assignment 1
EnvironmentsSearch
Bayes Nets
Problem 1: Peg SolitaireIs Peg Solitaire:
Partially observable?
Stochastic?
Continuous?
Adversarial?Play online at: http://www.novelgames.com/flashgames/game.php?id=61http://www.gamedesign.jp/flash/peg/peg.html
Problem 2: Loaded Coin
Is Loaded Coin:
Partially observable?
Stochastic?
Continuous?
Adversarial?
The coin above might be fair (0.5 chance of heads, 0.5 chance of tails), or it might be loaded (p chance of heads, 1-p chance of tails, p != 0.5).
The Loaded Coin problem is to determine whether the coin is fair or loaded.
You don’t need to solve Loaded Coin, but answer the questions on the right.
Problem 3: Maze TraversalIs Maze Traversal:
Partially observable?
Stochastic?
Continuous?
Adversarial?
O
X
start
goal
Maze Traversal: get from the start position to the goal position.
Answer the questions about the maze traversal problem on the right.
Problem 4: Search Tree
Counting the start node and goal node, how many nodes are expanded if we go1. Left-to-right
a. Breadth-first:b. Depth-first:
2. Right-to-lefta. Breadth-first:b. Depth-first:
start
goal
Problem 5: Search Network
Counting the start node and goal node, how many nodes are expanded if we go1. Left-to-right
a. Breadth-first:b. Depth-first:
2. Right-to-lefta. Breadth-first:b. Depth-first:
start
goal
Problem 6: A* Search
1 2 3 4 5 6
A 4 4 4 3 2 1
B 3 3 3 3 2 1
C 2 2 2 2 2 1
D 1 1 1 1 1 0
start
goal
The table above shows the state space for a search problem: grid elements A1 through D6.
The values in each cell indicate the value of a heuristic function h(x) for that cell grid.
1. Is the heuristic function admissible?
2. Which node will be expanded first: A2 or B1?
3. Which node will be expanded second: B1, C1, A2, A3, or B2?
4. Which node will be expanded third: D1, C2, B3, or A4?
Problem 7: Bayes Rule
Assume the following are true regarding binary random variables A and B:P(A) = 0.5P(B | A) = 0.2P(B | A) = 0.8
What is P(A | B)?
Problem 8: Simple Bayes Net
P(A) = 0.5i P(Xi | A) = 0.2
i P(Xi | A) = 0.6
1. What is P(A | X1 X2 X3)?
2. What isP(X3 | X1)?
A
X1 X2 X3
Problem 9: Conditional Independence
BC?
BC | D?
BC | A?
BC | A, D?
A
B C
D
Problem 10: Conditional Independence 2
CE | A?
BD | C, E?
AC | E?
AC | B?
A
B D
E
C
Problem 11: Parameter Counting
How many parameters are needed to specify a full joint distribution over 5 binary variables?
For the Bayes Net on the left, assuming all 5 variables are binary, how many parameters are needed?
A
B D
E
C