Lab Assignment 1

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Lab Assignment 1. Environments Search Bayes Nets. Problem 1: Peg Solitaire. Is Peg Solitaire: Partially observable? Stochastic? Continuous? Adversarial?. Play online at: http:// www.novelgames.com/flashgames/game.php?id=61 http ://www.gamedesign.jp/flash/peg/peg.html.

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### Lab Assignment 1

Environments

Search

Bayes Nets

Problem 1: Peg Solitaire

Is Peg Solitaire:

Partially observable?

Stochastic?

Continuous?

Play online at:

http://www.novelgames.com/flashgames/game.php?id=61

http://www.gamedesign.jp/flash/peg/peg.html

Partially observable?

Stochastic?

Continuous?

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 Traversal

start

Is Maze Traversal:

Partially observable?

Stochastic?

Continuous?

goal

Maze Traversal: get from the start position to the goal position.

Problem 4: Search Tree

start

Counting the start node and goal node, how many nodes are expanded if we go

• Left-to-right
• Depth-first:
• Right-to-left
• Depth-first:

goal

Problem 5: Search Network

start

Counting the start node and goal node, how many nodes are expanded if we go

• Left-to-right
• Depth-first:
• Right-to-left
• Depth-first:

goal

Problem 6: A* Search
• Is the heuristic function admissible?
• Which node will be expanded first: A2 or B1?
• Which node will be expanded second: B1, C1, A2, A3, or B2?
• Which node will be expanded third: D1, C2, B3, or A4?

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.

Problem 7: Bayes Rule

Assume the following are true regarding binary random variables A and B:

P(A) = 0.5

P(B | A) = 0.2

P(B | A) = 0.8

What is P(A | B)?

Problem 8: Simple Bayes Net

P(A) = 0.5

iP(Xi | A) = 0.2

iP(Xi| A) = 0.6

1. What is

P(A | X1 X2 X3)?

2. What is

P(X3 | X1)?

A

X1

X2

X3

Problem 9: Conditional Independence

BC?

BC | D?

BC | A?

BC | A, D?

A

C

B

D

Problem 10: Conditional Independence 2

CE | A?

BD | C, E?

AC | E?

AC | B?

C

A

D

B

E

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?

C

A

D

B

E