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# Lab Assignment 1 - PowerPoint PPT Presentation

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

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.

start

Is Maze Traversal:

Partially observable?

Stochastic?

Continuous?

goal

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

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

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

• 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.

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)?

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

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

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