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Lab Assignment 1

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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  1. Lab Assignment 1 Environments Search Bayes Nets

  2. 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

  3. 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.

  4. 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.

  5. 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

  6. 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

  7. 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.

  8. 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)?

  9. 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

  10. Problem 9: Conditional Independence BC? BC | D? BC | A? BC | A, D? A C B D

  11. Problem 10: Conditional Independence 2 CE | A? BD | C, E? AC | E? AC | B? C A D B E

  12. 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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