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

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Lab assignment 1

Lab Assignment 1

Environments

Search

Bayes Nets


Problem 1 peg solitaire

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


Problem 2 loaded coin

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 traversal

Problem 3: Maze Traversal

start

Is Maze Traversal:

Partially observable?

Stochastic?

Continuous?

Adversarial?

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

Problem 4: Search Tree

start

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

  • Left-to-right

    • Breadth-first:

    • Depth-first:

  • Right-to-left

    • Breadth-first:

    • Depth-first:

goal


Problem 5 search network

Problem 5: Search Network

start

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

  • Left-to-right

    • Breadth-first:

    • Depth-first:

  • Right-to-left

    • Breadth-first:

    • Depth-first:

goal


Problem 6 a search

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

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

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

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

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

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


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